[cig-commits] r13654 - in seismo/3D/ADJOINT_TOMO/flexwin/latex: . figures/japan
carltape at geodynamics.org
carltape at geodynamics.org
Thu Dec 11 11:27:21 PST 2008
Author: carltape
Date: 2008-12-11 11:27:20 -0800 (Thu, 11 Dec 2008)
New Revision: 13654
Modified:
seismo/3D/ADJOINT_TOMO/flexwin/latex/appendix.tex
seismo/3D/ADJOINT_TOMO/flexwin/latex/figures/japan/200511211536A_T06_rs.pdf
seismo/3D/ADJOINT_TOMO/flexwin/latex/figures/japan/200511211536A_T24_rs.pdf
seismo/3D/ADJOINT_TOMO/flexwin/latex/figures/japan/KIS_BO_091502B.pdf
seismo/3D/ADJOINT_TOMO/flexwin/latex/figures/japan/SHR_BO_200511211536A.pdf
seismo/3D/ADJOINT_TOMO/flexwin/latex/figures/japan/stats_T06.pdf
seismo/3D/ADJOINT_TOMO/flexwin/latex/figures_paper.tex
seismo/3D/ADJOINT_TOMO/flexwin/latex/flexwin_paper.pdf
seismo/3D/ADJOINT_TOMO/flexwin/latex/results.tex
Log:
Checking in Min's updated figures and edits to flexwin paper.
Modified: seismo/3D/ADJOINT_TOMO/flexwin/latex/appendix.tex
===================================================================
--- seismo/3D/ADJOINT_TOMO/flexwin/latex/appendix.tex 2008-12-11 17:22:51 UTC (rev 13653)
+++ seismo/3D/ADJOINT_TOMO/flexwin/latex/appendix.tex 2008-12-11 19:27:20 UTC (rev 13654)
@@ -1,211 +1,211 @@
-\appendix
-\section{Tuning considerations\label{ap:tuning}}
-FLEXWIN is not a black-box application, and as such cannot be applied blindly
-to any given dataset or tomographic scenario. The data windowing required by
-any given problem will differ depending on the inversion method, the scale of
-the problem (local, regional, global), the quality of the data set and that of
-the model and method used to calculate the synthetic seismograms. The user
-must configure and tune the algorithm for the given problem. In this appendix we
-shall discuss some general considerations the user should bear in mind during
-the tuning process. For more detailed information on tuning, and for further
-examples of tuning parameter sets, we refer the reader to the user manual that
-accompanies the source code.
-
-The order in which the parameters in Table~\ref{tb:params} are discussed in the
-main text of this paper follows the order in which they are used by the
-algorithm, but is not necessarily the best order in which to consider them for
-tuning purposes. We suggest the following as a practical starting sequence
-(the process may need to be repeated and refined several times before
-converging on the optimal set of parameters for a given problem and data-set).
-
-$T_{0,1}$ : In setting the corner periods of the bandpass filter, the
-user is deciding on the frequency content of the information to be used in the
-tomographic problem. Values of these corner periods should reflect the
-information content of the data, the quality of the Earth model and the
-accuracy of the simulation used to generate the synthetic seismogram. The
-frequency content in the data depends on the spectral characteristics of the
-source, on the instrument responses, and on the attenuation
-characteristics of the medium. As $T_{0,1}$ depend on the source and station
-characteristics, which may be heterogeneous in any given data-set, these filter
-periods can be modified dynamically by constructing an appropriate user
-function (e.g. {\em if station is in list of stations with instrument X then
-reset T0 and T1 to new values}).
-
-$r_{P,A}$ : In setting the signal-to-noise ratios for the entire seismogram the
-user is applying a simple quality control on the data. Note that these criteria
-are applied after filtering. No windows will be defined on data that fail this
-quality control.
-
-$w_E(t)$ : The short-term average long-term average ratio $E(t)$ of a constant signal
-converges to a constant value when
-the length of the time-series is greater than the effective averaging length of
-the long-term average. This value would be 1 if $C_S=C_L$ in equations
-(\ref{eq:sta}) and (\ref{eq:lta}). For $C_S$ and $C_L$ given by equation
-(\ref{eq:Cs_Cl}), $E(t)$ of a constant signal converges to a value close to
-0.08, with only a weak dependence on $T_0$. We suggest the user start with a constant
-level for $w_E(t)$ equal to this convergence value. The time dependence of
-$w_E(t)$ should then be adjusted to exclude those portions of the waveform the
-user is not interested in, by raising $w_E(t)$ (e.g. to exclude the fundamental
-mode surface-wave: {\em if t $>$ fundamental mode surface-wave arrival time then set $w_E(t)=1$}).
-We suggest finer adjustments to $w_E(t)$ be made after $r0(t)$,
-$CC_0(t)$, $\Delta T_0(t)$ and $\Delta \ln A_0(t)$ have been configured.
-
-$r_0(t)$, $\mathrm{CC}_0(t)$, $\Delta \tau_{\rm ref}$, $\Delta
-\tau_0(t)$, $\Delta \ln A_{\rm ref}$ and $\Delta \ln A_0(t)$ : These parameters ---
-window signal-to-noise ratio, normalized cross-correlation value between
-observed and synthetic seismograms, cross-correlation time lag, and amplitude
-ratio --- control the degree of well-behavedness of the data within accepted
-windows (\stgd). The user first sets constant values for these four parameters, then
-adds a time dependence if required. Considerations that should be taken into
-account include the quality of the Earth model used to calculate the synthetic
-seismograms, the frequency range, the dispersed nature of certain arrivals (e.g.
-{\em for t corresponding to the group velocities of surface-waves, reduce
-$CC_0(t)$}), and {\em a priori} preferences for picking certain small-amplitude seismic phases
-(e.g. {\em for t close to the expected arrival for $P_{\rm diff}$, reduce $r_0(t)$}).
-$\Delta \tau_{\rm ref}$ and $\Delta \ln A_{\rm ref}$ should be set to zero at first, and only
-reset if the synthetics contain a systematic bias in traveltimes or amplitudes.
-
-
-$c_{0-4}$ : These parameters are active in \stgc\ of the algorithm, the stage in which the suite of all possible data windows is pared down using criteria on the shape of the STA:LTA $E(t)$ waveform alone. Detailed descriptions of the behavior of each parameter are available in Section~\ref{sec:stageC} and will not be repeated here. We suggest the user start by setting these values to those used in our global example (see Table~\ref{tb:example_params}). Subsequent minimal tuning should be performed by running the algorithm on a subset of the data and closely examining the lists of windows rejected at each stage to make sure the user agrees with the choices made by the algorithm.
-
-$w_{\mathrm{CC}}$, $w_{\rm len}$ and $w_{\rm nwin}$ : These parameters control the overlap resolution stage of the algorithm (\stge), and are discussed in detail in Section~\ref{sec:stageE}. Values of $w_{\mathrm{CC}}= w_{\rm len} = w_{\rm nwin} = 1$ should be reasonable for most applications.
-
-The objective of the tuning process summarily described here should be to maximize the selection of windows around desirable features in the seismogram, while minimizing the selection of undesirable features, bearing in mind that the desirability or undesirability of a given feature is subjective, and depends on how the user subsequently intends to use the information contained within he data windows.
-
-\subsection{Examples of user functions\label{ap:user_fn}}
-
-As concrete examples of how the time dependence of the tuning parameters can be exploited, we present here the functional forms of the time dependencies used for the three example tomographic scenarios described in the text (Section~\ref{sec:results}).
-%CHT modified:
-In each example we use predicted arrival times derived from 1D Earth models to help modulate certain parameters. Note, however, that the actual selection of individual windows is based on the details of the waveforms, and not on information from 1D Earth models.
-
-\subsubsection{Global scenario\label{ap:user_global}}
-
-In the following, $h$ indicates earthquake depth, $t_Q$ indicates the approximate start of the Love wave predicted by a group wave speed of 4.2~\kmps, and $t_R$ indicates the approximate end of the Rayleigh wave predicted by a group wave speed of 3.2~\kmps. In order to reduce the number of windows picked beyond R1, and to ensure that those selected beyond R1 are a very good match to the synthetic waveform, we raise the water level on the STA:LTA waveform and impose stricter criteria on the signal-to-noise ratio and the waveform similarity after the approximate end of the surface-wave arrivals. We allow greater flexibility in cross-correlation time lag $\Delta\tau$ for intermediate depth and deep earthquakes. We lower the cross-correlation value criterion for surface-waves in order to retain windows with a slight mismatch in dispersion characteristics.
-
-We therefore use the following time modulations:
-\begin{align}
-w_E(t) & =
- \begin{cases}
- w_E \text{$t \leq t_R$} ,\\
- 2 w_E \text{$t > t_R$},
- \end{cases}
-\\
-r_0(t) & =
- \begin{cases}
- r_0 & \text{$t \leq t_R$}, \\
- 10r_0 & \text{$t > t_R$} ,
- \end{cases}
-\\
-\mathrm{CC}_0(t) & =
- \begin{cases}
- \mathrm{CC}_0 & \text{$t \leq t_R$}, \\
- 0.9 \mathrm{CC}_0 & \text{$t_Q < t \leq t_R$}, \\
- 0.95 & \text{$t > t_R$} ,
- \end{cases}
-\\
-\Delta\tau_0(t) & =
- \begin{cases}
- \begin{cases}
- \tau_0 & \text{$t \leq t_R$}, \\
- \tau_0/3 & \text{$t > t_R$} ,
- \end{cases}
- & \text{$h \leq$ 70~km} \\
- 1.4\tau_0 & \text{70~km $< h <$ 300~km}, \\
- 1.7\tau_0 & \text{$h \geq$ 300~km},
- \end{cases}
- \\
-\Delta \ln A_0(t) & =
- \begin{cases}
- \Delta \ln A_0 & \text{$t \leq t_R$}, \\
- \Delta \ln A_0/3 & \text{$t > t_R$} .
- \end{cases}
-\end{align}
-
-%--------------------------
-
-\subsubsection{Japan scenario\label{ap:user_japan}}
-In the following, $t_P$ and $t_S$ denote the start of the time windows for $P$- and $S$ waves, as predicted by the 1-D IASPEI91 model \citep{KennettEngdahl1991}, and $t_{R1}$ indicates the end of the surface-wave time window. For the \trange{24}{120} data, we consider the waveform between the start of the $P$ wave to the end of the surface-wave. We therefore modulate $w_E(t)$ as follows:
-
-%
-\begin{align}
-w_E(t) & =
- \begin{cases}
- 10 w_E & \text{$t < t_P$}, \\
- w_E & \text{$t_P \le t \leq t_{R1}$}, \\
- 10 w_E & \text{$t > t_{R1}$}.
- \end{cases}
-\end{align}
-
-For the \trange{6}{30} data, the fit between the synthetic and observed surface-waves is expected to be poor, as the 3D model used to calculate the synthetics cannot produce the required complexity. We therefore want to concentrate on body-wave arrivals only, and avoid surface-wave windows altogether by modulating $w_E(t)$ as follows:
-%
-\begin{align}
-w_E(t) & =
- \begin{cases}
- 10 w_E & \text{$t < t_P$}, \\
- w_E & \text{$t_P \le t \leq t_S$}, \\
- 10 w_E & \text{$t > t_S$}.
- \end{cases}
-\end{align}
-
-We use constant values of $r_0(t)=r_0$, $\mathrm{CC}_0(t)=\mathrm{CC}_0$ and $\Delta \ln A_0(t)=\Delta \ln A_0$ for both period ranges. In order to allow greater flexibility in cross-correlation time lag $\Delta\tau$ for intermediate depth and deep earthquakes we use:
-
-\begin{align}
-\Delta\tau_0(t) & =
- \begin{cases}
- 0.08 \text{$t_P$} & \text{$h \leq$ 70~km}, \\
- \max(0.06 \text{$t_P$}, 1.4\tau_0) & \text{70~km $< h <$ 300~km}, \\
- \max(0.06 \text{$t_P$}, 1.7\tau_0) & \text{$h \geq$ 300~km}.
- \end{cases}
-\end{align}
-%--------------------------
-
-\subsubsection{Southern California scenario\label{ap:user_socal}}
-
-In the following, $t_P$ and $t_S$ denote the start of the time windows for the crustal P wave and the crustal S wave, computed from a 1D layered model appropriate to Southern California \citep{Wald95}. The start and end times for the surface-wave time window, $t_{R0}$ and $t_{R1}$, as well as the criteria for the time shifts $\Delta\tau_0(t)$, are derived from formulas in \cite{KomatitschEtal2004}. The source-receiver distance (in km) is denoted by $\Delta$.
-
-%CHT modified
-
-For the \trange{6}{40} and \trange{3}{40} data, we use constant values of $r_0(t)=r_0$, $\mathrm{CC}_0(t)=\mathrm{CC}_0$, $\Delta\tau_0(t)=\Delta\tau_0$, and $\Delta \ln A_0(t)=\Delta \ln A_0$. We exclude any arrivals before the $P$ wave and after the Rayleigh wave. This is achieved by the box-car function for $w_E(t)$:
-%
-\begin{align}
-w_E(t) & =
- \begin{cases}
- 10 w_E & \text{$t < t_P$}, \\
- w_E & \text{$t_P \le t \leq t_{R1}$}, \\
- 10 w_E & \text{$t > t_{R1}$},
- \end{cases}
-\end{align}
-%For the \trange{6}{40} data, we exclude any arrivals before the $P$ wave and reduce the number of windows picked beyond R1 by modulating $w_E(t)$. We use constant values of $r_0(t)=r_0$, $\mathrm{CC}_0(t)=\mathrm{CC}_0$ and $\Delta \ln A_0(t)=\Delta \ln A_0$, but modulate the cross-correlation time lag criterion so that it is less strict at larger epicentral distances and for surface-waves. We therefore use:
-%
-%\begin{align}
-%w_E(t) & =
-% \begin{cases}
-% 10 w_E & \text{$t < t_P$}, \\
-% w_E & \text{$t_P \le t \leq t_{R1}$}, \\
-% 2 w_E & \text{$t > t_{R1}$},
-% \end{cases}
-%\\
-%\Delta\tau_0(t) & =
-% \begin{cases}
-% 3.0 + \Delta/80.0 & \text{$t \le t_{R0}$}, \\
-% 3.0 + \Delta/50.0 & \text{$t > t_{R0}$},
-% \end{cases}
-%\end{align}
-
-For the \trange{2}{40} data, we avoid selecting surface-wave arrivals as the 3D model used to calculate the synthetics cannot produce the required complexity. The water-level criteria then becomes:
-%We remove the distance dependence on $\Delta\tau_0(t)$, as higher frequency body-waves are well behaved in this model, and keep all other criteria the same.
-%The parameter modulation for these data becomes:
-%
-\begin{align}
-w_E(t) & =
- \begin{cases}
- 10 w_E & \text{$t < t_P$}, \\
- w_E & \text{$t_P \le t \leq t_S$}, \\
- 10 w_E & \text{$t > t_S$}.
- \end{cases}
-%\\
-%\Delta\tau_0(t) & = \Delta\tau_0.
-\end{align}
-
-
-%-----------------------
+\appendix
+\section{Tuning considerations\label{ap:tuning}}
+FLEXWIN is not a black-box application, and as such cannot be applied blindly
+to any given dataset or tomographic scenario. The data windowing required by
+any given problem will differ depending on the inversion method, the scale of
+the problem (local, regional, global), the quality of the data set and that of
+the model and method used to calculate the synthetic seismograms. The user
+must configure and tune the algorithm for the given problem. In this appendix we
+shall discuss some general considerations the user should bear in mind during
+the tuning process. For more detailed information on tuning, and for further
+examples of tuning parameter sets, we refer the reader to the user manual that
+accompanies the source code.
+
+The order in which the parameters in Table~\ref{tb:params} are discussed in the
+main text of this paper follows the order in which they are used by the
+algorithm, but is not necessarily the best order in which to consider them for
+tuning purposes. We suggest the following as a practical starting sequence
+(the process may need to be repeated and refined several times before
+converging on the optimal set of parameters for a given problem and data-set).
+
+$T_{0,1}$ : In setting the corner periods of the bandpass filter, the
+user is deciding on the frequency content of the information to be used in the
+tomographic problem. Values of these corner periods should reflect the
+information content of the data, the quality of the Earth model and the
+accuracy of the simulation used to generate the synthetic seismogram. The
+frequency content in the data depends on the spectral characteristics of the
+source, on the instrument responses, and on the attenuation
+characteristics of the medium. As $T_{0,1}$ depend on the source and station
+characteristics, which may be heterogeneous in any given data-set, these filter
+periods can be modified dynamically by constructing an appropriate user
+function (e.g. {\em if station is in list of stations with instrument X then
+reset T0 and T1 to new values}).
+
+$r_{P,A}$ : In setting the signal-to-noise ratios for the entire seismogram the
+user is applying a simple quality control on the data. Note that these criteria
+are applied after filtering. No windows will be defined on data that fail this
+quality control.
+
+$w_E(t)$ : The short-term average long-term average ratio $E(t)$ of a constant signal
+converges to a constant value when
+the length of the time-series is greater than the effective averaging length of
+the long-term average. This value would be 1 if $C_S=C_L$ in equations
+(\ref{eq:sta}) and (\ref{eq:lta}). For $C_S$ and $C_L$ given by equation
+(\ref{eq:Cs_Cl}), $E(t)$ of a constant signal converges to a value close to
+0.08, with only a weak dependence on $T_0$. We suggest the user start with a constant
+level for $w_E(t)$ equal to this convergence value. The time dependence of
+$w_E(t)$ should then be adjusted to exclude those portions of the waveform the
+user is not interested in, by raising $w_E(t)$ (e.g. to exclude the fundamental
+mode surface-wave: {\em if t $>$ fundamental mode surface-wave arrival time then set $w_E(t)=1$}).
+We suggest finer adjustments to $w_E(t)$ be made after $r0(t)$,
+$CC_0(t)$, $\Delta T_0(t)$ and $\Delta \ln A_0(t)$ have been configured.
+
+$r_0(t)$, $\mathrm{CC}_0(t)$, $\Delta \tau_{\rm ref}$, $\Delta
+\tau_0(t)$, $\Delta \ln A_{\rm ref}$ and $\Delta \ln A_0(t)$ : These parameters ---
+window signal-to-noise ratio, normalized cross-correlation value between
+observed and synthetic seismograms, cross-correlation time lag, and amplitude
+ratio --- control the degree of well-behavedness of the data within accepted
+windows (\stgd). The user first sets constant values for these four parameters, then
+adds a time dependence if required. Considerations that should be taken into
+account include the quality of the Earth model used to calculate the synthetic
+seismograms, the frequency range, the dispersed nature of certain arrivals (e.g.
+{\em for t corresponding to the group velocities of surface-waves, reduce
+$CC_0(t)$}), and {\em a priori} preferences for picking certain small-amplitude seismic phases
+(e.g. {\em for t close to the expected arrival for $P_{\rm diff}$, reduce $r_0(t)$}).
+$\Delta \tau_{\rm ref}$ and $\Delta \ln A_{\rm ref}$ should be set to zero at first, and only
+reset if the synthetics contain a systematic bias in traveltimes or amplitudes.
+
+
+$c_{0-4}$ : These parameters are active in \stgc\ of the algorithm, the stage in which the suite of all possible data windows is pared down using criteria on the shape of the STA:LTA $E(t)$ waveform alone. Detailed descriptions of the behavior of each parameter are available in Section~\ref{sec:stageC} and will not be repeated here. We suggest the user start by setting these values to those used in our global example (see Table~\ref{tb:example_params}). Subsequent minimal tuning should be performed by running the algorithm on a subset of the data and closely examining the lists of windows rejected at each stage to make sure the user agrees with the choices made by the algorithm.
+
+$w_{\mathrm{CC}}$, $w_{\rm len}$ and $w_{\rm nwin}$ : These parameters control the overlap resolution stage of the algorithm (\stge), and are discussed in detail in Section~\ref{sec:stageE}. Values of $w_{\mathrm{CC}}= w_{\rm len} = w_{\rm nwin} = 1$ should be reasonable for most applications.
+
+The objective of the tuning process summarily described here should be to maximize the selection of windows around desirable features in the seismogram, while minimizing the selection of undesirable features, bearing in mind that the desirability or undesirability of a given feature is subjective, and depends on how the user subsequently intends to use the information contained within he data windows.
+
+\subsection{Examples of user functions\label{ap:user_fn}}
+
+As concrete examples of how the time dependence of the tuning parameters can be exploited, we present here the functional forms of the time dependencies used for the three example tomographic scenarios described in the text (Section~\ref{sec:results}).
+%CHT modified:
+In each example we use predicted arrival times derived from 1D Earth models to help modulate certain parameters. Note, however, that the actual selection of individual windows is based on the details of the waveforms, and not on information from 1D Earth models.
+
+\subsubsection{Global scenario\label{ap:user_global}}
+
+In the following, $h$ indicates earthquake depth, $t_Q$ indicates the approximate start of the Love wave predicted by a group wave speed of 4.2~\kmps, and $t_R$ indicates the approximate end of the Rayleigh wave predicted by a group wave speed of 3.2~\kmps. In order to reduce the number of windows picked beyond R1, and to ensure that those selected beyond R1 are a very good match to the synthetic waveform, we raise the water level on the STA:LTA waveform and impose stricter criteria on the signal-to-noise ratio and the waveform similarity after the approximate end of the surface-wave arrivals. We allow greater flexibility in cross-correlation time lag $\Delta\tau$ for intermediate depth and deep earthquakes. We lower the cross-correlation value criterion for surface-waves in order to retain windows with a slight mismatch in dispersion characteristics.
+
+We therefore use the following time modulations:
+\begin{align}
+w_E(t) & =
+ \begin{cases}
+ w_E \text{$t \leq t_R$} ,\\
+ 2 w_E \text{$t > t_R$},
+ \end{cases}
+\\
+r_0(t) & =
+ \begin{cases}
+ r_0 & \text{$t \leq t_R$}, \\
+ 10r_0 & \text{$t > t_R$} ,
+ \end{cases}
+\\
+\mathrm{CC}_0(t) & =
+ \begin{cases}
+ \mathrm{CC}_0 & \text{$t \leq t_R$}, \\
+ 0.9 \mathrm{CC}_0 & \text{$t_Q < t \leq t_R$}, \\
+ 0.95 & \text{$t > t_R$} ,
+ \end{cases}
+\\
+\Delta\tau_0(t) & =
+ \begin{cases}
+ \begin{cases}
+ \tau_0 & \text{$t \leq t_R$}, \\
+ \tau_0/3 & \text{$t > t_R$} ,
+ \end{cases}
+ & \text{$h \leq$ 70~km} \\
+ 1.4\tau_0 & \text{70~km $< h <$ 300~km}, \\
+ 1.7\tau_0 & \text{$h \geq$ 300~km},
+ \end{cases}
+ \\
+\Delta \ln A_0(t) & =
+ \begin{cases}
+ \Delta \ln A_0 & \text{$t \leq t_R$}, \\
+ \Delta \ln A_0/3 & \text{$t > t_R$} .
+ \end{cases}
+\end{align}
+
+%--------------------------
+
+\subsubsection{Japan scenario\label{ap:user_japan}}
+In the following, $t_P$ and $t_S$ denote the start of the time windows for $P$- and $S$ waves, as predicted by the 1-D IASPEI91 model \citep{KennettEngdahl1991}, and $t_{R1}$ indicates the end of the surface-wave time window. For the \trange{24}{120} data, we consider the waveform between the start of the $P$ wave to the end of the surface-wave. We therefore modulate $w_E(t)$ as follows:
+
+%
+\begin{align}
+w_E(t) & =
+ \begin{cases}
+ 10 w_E & \text{$t < t_P$}, \\
+ w_E & \text{$t_P \le t \leq t_{R1}$}, \\
+ 10 w_E & \text{$t > t_{R1}$}.
+ \end{cases}
+\end{align}
+
+For the \trange{6}{30} data, the fit between the synthetic and observed surface-waves is expected to be poor, as the 3D model used to calculate the synthetics cannot produce the required complexity. We therefore want to concentrate on body-wave arrivals only, and avoid surface-wave windows altogether by modulating $w_E(t)$ as follows:
+%
+\begin{align}
+w_E(t) & =
+ \begin{cases}
+ 10 w_E & \text{$t < t_P$}, \\
+ w_E & \text{$t_P \le t \leq t_S$}, \\
+ 10 w_E & \text{$t > t_S$}.
+ \end{cases}
+\end{align}
+
+We use constant values of $r_0(t)=r_0$, $\mathrm{CC}_0(t)=\mathrm{CC}_0$ and $\Delta \ln A_0(t)=\Delta \ln A_0$ for both period ranges. In order to allow greater flexibility in cross-correlation time lag $\Delta\tau$ for intermediate depth and deep earthquakes we use:
+
+\begin{align}
+\Delta\tau_0(t) & =
+ \begin{cases}
+ 0.08 \text{$t_P$} & \text{$h \leq$ 70~km}, \\
+ \max(0.05 \text{$t_P$}, 1.4\tau_0) & \text{70~km $< h <$ 300~km}, \\
+ \max(0.05 \text{$t_P$}, 1.7\tau_0) & \text{$h \geq$ 300~km}.
+ \end{cases}
+\end{align}
+%--------------------------
+
+\subsubsection{Southern California scenario\label{ap:user_socal}}
+
+In the following, $t_P$ and $t_S$ denote the start of the time windows for the crustal P wave and the crustal S wave, computed from a 1D layered model appropriate to Southern California \citep{Wald95}. The start and end times for the surface-wave time window, $t_{R0}$ and $t_{R1}$, as well as the criteria for the time shifts $\Delta\tau_0(t)$, are derived from formulas in \cite{KomatitschEtal2004}. The source-receiver distance (in km) is denoted by $\Delta$.
+
+%CHT modified
+
+For the \trange{6}{40} and \trange{3}{40} data, we use constant values of $r_0(t)=r_0$, $\mathrm{CC}_0(t)=\mathrm{CC}_0$, $\Delta\tau_0(t)=\Delta\tau_0$, and $\Delta \ln A_0(t)=\Delta \ln A_0$. We exclude any arrivals before the $P$ wave and after the Rayleigh wave. This is achieved by the box-car function for $w_E(t)$:
+%
+\begin{align}
+w_E(t) & =
+ \begin{cases}
+ 10 w_E & \text{$t < t_P$}, \\
+ w_E & \text{$t_P \le t \leq t_{R1}$}, \\
+ 10 w_E & \text{$t > t_{R1}$},
+ \end{cases}
+\end{align}
+%For the \trange{6}{40} data, we exclude any arrivals before the $P$ wave and reduce the number of windows picked beyond R1 by modulating $w_E(t)$. We use constant values of $r_0(t)=r_0$, $\mathrm{CC}_0(t)=\mathrm{CC}_0$ and $\Delta \ln A_0(t)=\Delta \ln A_0$, but modulate the cross-correlation time lag criterion so that it is less strict at larger epicentral distances and for surface-waves. We therefore use:
+%
+%\begin{align}
+%w_E(t) & =
+% \begin{cases}
+% 10 w_E & \text{$t < t_P$}, \\
+% w_E & \text{$t_P \le t \leq t_{R1}$}, \\
+% 2 w_E & \text{$t > t_{R1}$},
+% \end{cases}
+%\\
+%\Delta\tau_0(t) & =
+% \begin{cases}
+% 3.0 + \Delta/80.0 & \text{$t \le t_{R0}$}, \\
+% 3.0 + \Delta/50.0 & \text{$t > t_{R0}$},
+% \end{cases}
+%\end{align}
+
+For the \trange{2}{40} data, we avoid selecting surface-wave arrivals as the 3D model used to calculate the synthetics cannot produce the required complexity. The water-level criteria then becomes:
+%We remove the distance dependence on $\Delta\tau_0(t)$, as higher frequency body-waves are well behaved in this model, and keep all other criteria the same.
+%The parameter modulation for these data becomes:
+%
+\begin{align}
+w_E(t) & =
+ \begin{cases}
+ 10 w_E & \text{$t < t_P$}, \\
+ w_E & \text{$t_P \le t \leq t_S$}, \\
+ 10 w_E & \text{$t > t_S$}.
+ \end{cases}
+%\\
+%\Delta\tau_0(t) & = \Delta\tau_0.
+\end{align}
+
+
+%-----------------------
Modified: seismo/3D/ADJOINT_TOMO/flexwin/latex/figures/japan/200511211536A_T06_rs.pdf
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Modified: seismo/3D/ADJOINT_TOMO/flexwin/latex/figures/japan/KIS_BO_091502B.pdf
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Modified: seismo/3D/ADJOINT_TOMO/flexwin/latex/figures/japan/SHR_BO_200511211536A.pdf
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Modified: seismo/3D/ADJOINT_TOMO/flexwin/latex/figures/japan/stats_T06.pdf
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Modified: seismo/3D/ADJOINT_TOMO/flexwin/latex/figures_paper.tex
===================================================================
--- seismo/3D/ADJOINT_TOMO/flexwin/latex/figures_paper.tex 2008-12-11 17:22:51 UTC (rev 13653)
+++ seismo/3D/ADJOINT_TOMO/flexwin/latex/figures_paper.tex 2008-12-11 19:27:20 UTC (rev 13654)
@@ -1,445 +1,444 @@
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Table captions
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Tables
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\newpage
-\begin{table}
-\begin{tabular}{lp{0.8\linewidth}}
-\hline
-\multicolumn{2}{l}{Standard tuning parameters:} \\[5pt]
-$T_{0,1}$ & bandpass filter corner periods \\
-$r_{P,A}$ & signal to noise ratios for whole waveform \\
-$r_0(t)$ & signal to noise ratios single windows \\
-$w_E(t)$ & water level on short-term:long-term ratio \\
-$\mathrm{CC}_0(t)$ & acceptance level for normalized cross-correlation\\
-$\Delta\tau_0(t)$ & acceptance level for time lag \\
-$\Delta\ln{A}_0(t)$ & acceptance level for amplitude ratio \\
-$\Delta\tau_{\rm ref}$ & reference time lag \\
-$\Delta\ln{A}_{\rm ref}$ & reference amplitude ratio \\
-\hline
-\multicolumn{2}{l}{Fine tuning parameters:} \\ [5pt]
-$c_0$ & for rejection of internal minima \\
-$c_1$ & for rejection of short windows \\
-$c_2$ & for rejection of un-prominent windows \\
-$c_{3a,b}$ & for rejection of multiple distinct arrivals \\
-$c_{4a,b}$ & for curtailing of windows with emergent starts and/or codas \\
-$w_{\mathrm{CC}}\quad w_{\rm len}\quad w_{\rm nwin}$ & for selection of best non-overlapping window combination \\
-\hline
-\end{tabular}
-\caption{\label{tb:params}
-Overview of standard tuning parameters, and of fine
-tuning parameters. Values are defined in a parameter file, and the
-time dependence of those that depend on time is described by user-defined functions.
-}
-\end{table}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\clearpage
-\begin{table}
-\begin{tabular}{lrrrrrl}
-\hline
-Identifier & Latitude & Longitude & Depth, km & Moment, N m & $M_w$ & Location \\
-\hline
-\multicolumn{7}{c}{Global} \\ \hline
-% CHECK THAT THE MOMENT IS LISTED IN N-M, NOT DYNE-CM
-% CARL HAS FORMULAS TO CONVERT FROM A MOMENT TENSOR TO M0 TO MW
-101895B & 28.06 & 130.18 & 18.5 & 5.68e19 & 7.1 & Ryukyu Islands \\
-200808270646A & -10.49 & 41.44 & 24.0 & 4.68e17 & 5.7 & Comoros Region \\
-050295B & -3.77 & -77.07 & 112.8 & 1.27e19 & 6.7 & Northern Peru \\
-060994A & -13.82 & -67.25 & 647.1 & 2.63e21 & 8.2 & Northern Bolivia \\
-\hline
-\multicolumn{7}{c}{Japan} \\ \hline
-051502B & 24.66 & 121.66 & 22.4 & 1.91e18 & 6.1 & Taiwan \\
-200511211536A & 30.97 & 130.31 & 155.0 & 2.13e18 & 6.2 & Kyuhu, Japan \\
-091502B & 44.77 & 130.04 & 589.4 & 4.24e18 & 6.4 & Northeastern China \\
-\hline
-\multicolumn{7}{c}{Southern California} \\ \hline
-9983429 & 35.01 & -119.14 & 13.5 & 9.19e15 & 4.6 & Wheeler Ridge, California \\
-9818433 & 33.91 & -117.78 & 9.4 & 3.89e15 & 4.3 & Yorba Linda, California \\
-\hline
-\end{tabular}
-\caption{\label{tb:events}
-Example events used in this study. The identifier refers to the CMT catalog for global events and Japan events, and refers to the Southern California Earthquake Data Center catalog for southern California events.
-}
-\end{table}
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\clearpage
-\begin{table}
-\begin{center}
-\begin{tabular}{lcccccc}
-\hline
- & Global & \multicolumn{2}{c}{Japan} & \multicolumn{3}{c}{S. California} \\
-\hline
-$T_{0,1}$ & 50, 150 & 24, 120 & 6, 30 & 6, 30 & 3, 30 & 2, 30 \\
-$r_{P,A}$ & 3.5, 3.0 & 3.5, 3.0 & 3.5, 3.0 & 3.0, 2.5 & 2.5, 3.5 & 2.5, 3.5 \\
-$r_0$ & 2.5 & 1.5 & 3.0 & 3.0 & 4.0 & 4.0 \\
-$w_E$ & 0.08 & 0.10 & 0.12 & 0.18 & 0.11 & 0.07 \\
-$\mathrm{CC}_0$ & 0.85 & 0.70 & 0.70 & 0.71 & 0.80 & 0.85 \\
-$\Delta\tau_0$ & 15 & 12.0 & 3.0 & 8.0 & 4.0 & 3.0 \\
-$\Delta\ln{A}_0$ & 1.0 & 1.0 & 1.0 & 1.5 & 1.0 & 1.0 \\
-$\Delta\tau_{\rm ref}$ & 0.0 & 0.0 & 0.0 & 4.0 & 2.0 & 1.0 \\
-$\Delta\ln{A}_{\rm ref}$& 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\
-\hline
-$c_0$ & 0.7 & 0.7 & 0.7 & 0.7 & 1.3 & 1.0 \\
-$c_1$ & 4.0 & 3.0 & 3.0 & 2.0 & 4.0 & 5.0 \\
-$c_2$ & 0.3 & 0.0 & 1.0 & 0.0 & 0.0 & 0.0 \\
-$c_{3a,b}$ & 1.0, 2.0 & 1.0, 2.0 & 1.0, 2.0 & 3.0, 2.0 & 4.0, 2.5 & 4.0, 2.5 \\
-$c_{4a,b}$ & 3.0, 10.0 & 3.0, 25.0 & 3.0, 12.0 & 2.5, 12.0 & 2.0, 6.0 & 2.0, 6.0 \\
-$w_{\mathrm{CC}}, w_{\rm len}, w_{\rm nwin}$
- & 1, 1, 1 & 1, 1, 1 & 1, 1, 1 & 0.5,1.0,0.7 & 0.70,0.25,0.05 & 1,1,1 \\
-\hline
-\end{tabular}
-\caption{\label{tb:example_params}
-Values of standard and fine-tuning parameters for the three seismological
-scenarios discussed in this study.
-}
-\end{center}
-\end{table}
-
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Figure captions
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Figures
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\clearpage
-\begin{figure}
-\center \includegraphics[width=6in]{figures/050295B.050-150/ABKT_II_LHZ_seis_nowin.pdf}
-\caption{\label{fg:stalta}
-Synthetic seismogram and its corresponding envelope and STA:LTA timeseries.
-The seismogram was calculated using SPECFEM3D and the
-Earth model S20RTS \citep{RitsemaEtal2004} for the CMT catalog event
-050295B, whose details can be found in Table~\ref{tb:events}. The
-station, ABKT, is at an epicentral distance of 14100~km and at an azimuth of 44
-degrees from the event. The top panel shows the vertical component synthetic
-seismogram, filtered between periods of 50 and 150 seconds. The center panel shows its envelope, and the bottom panel
-shows the corresponding STA:LTA waveform. The dashed line overlaid on
-the STA:LTA waveform is the water level $w_E(t)$.
-}
-
-\end{figure}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\clearpage
-\begin{figure}
-\center \includegraphics[width=6in]{figures/fig/window_composite.pdf}
-\caption{\label{fg:win_composite}
-(a)~Window creation process. The thick black line represents the STA:LTA
-waveform $E(t)$, and the thick horizontal dashed line its water level $w_E(t)$.
-Local maxima are indicated by alternating red and blue dots, windows are
-indicated by two-headed horizontal arrows. The time of the local maximum used
-as the window seed $t_M$ is denoted by the position of the dot. Only windows for the fourth local maximum are shown. (b)~Rejection of candidate windows based on the amplitude of the local minima. The two deep
-local minima indicated by the grey arrows form virtual barriers. All candidate
-windows that cross these barriers are rejected.
-(c)~Rejection of candidate
-windows based on the prominence of the seed maximum. The local maxima
-indicated by the grey arrows are too low compared to the local minima
-adjacent to them. All windows that have these local maxima as their seed are
-rejected (black crosses over the window segments below the timeseries).
-(d)~Shortening of long coda windows. The grey bar indicates the maximum coda
-duration $c_{4b} T_0$. Note that after the rejection based on prominence represented in (c) and before shortening of long coda windows represented in (d), the algorithm rejects candidate windows based on the separation of distinct phases, a process that is illustrated in Figure~\ref{fg:separation}.
-}
-\end{figure}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\clearpage
-\begin{figure}
-\center \includegraphics[width=5in]{figures/fig/window_rejection_separation.pdf}
-\caption{\label{fg:separation}
-Rejection of candidate windows based on the separation of distinct phases.
-(a)~Heights of pairs of local maxima above their intervening minimum.
-(b)~The black line represents $f(\Delta T/T_0)$ from
-equation~(\ref{eq:sep}) with $c_{3a}=c_{3b}=1$. Vertical bars represent
-$h/h_M$ for each pair of maxima. Their position along the horizontal axis is
-given by the time separation $\Delta T$ between the maxima of each pair. The
-color of the bar is given by the color of the seed maximum corresponding to $h_M$. Bars whose height
-exceeds the $f(\Delta T/T_0)$ line represent windows to be rejected.
-(c)~The windows that have been rejected by this criterion are indicated by black
-crosses.
-}
-\end{figure}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\clearpage
-\begin{figure}
-\center \includegraphics[width=6in]{figures/fig/window_rejection_global_data.pdf}
-\caption{\label{fg:win_rej_data}
-Window rejection applied to real data.
-Top panel: observed (black) and synthetic (red) seismograms for the 050295B event
-recorded at ABKT (see Figure~\ref{fg:stalta}).
-Subsequent panels: candidate windows at different stages, separated into \stgc\ (shape based rejection) and
-\stgd\ (fit based rejection). Each candidate window is indicated by a black
-segment. The number of windows at each stage is shown to the left of the
-panel.
-}
-\end{figure}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\clearpage
-\begin{figure}
-\center \includegraphics[width=6in]{figures/050295B.050-150/ABKT_II_LHZ_criteria.pdf}
-\caption{\label{fg:criteria}
-Time-dependent fit based criteria
-for the 050295B event recorded at ABKT. The time-dependence of these criteria
-is given by the formulas in Appendix~\ref{ap:user_global}. The lower limit on
-acceptable cross-correlation value, $\mathrm{CC}_0$ (solid line), is
-0.85 for most of the duration of the seismogram; it is lowered to 0.75 during
-the approximate surface-wave window defined by the group velocities 4.2\kmps\
-and 3.2\kmps, and is raised to 0.95 thereafter. The upper limit on time lag,
-$\tau_0$ (dotted line), is 21~s for the whole seismogram. The upper limit on amplitude
-ratio, $\Delta \ln A_0$ (dashed line), is 1.0 for most of the seismogram; it is reduced to
-1/3 of this value after the end of the surface-waves.
-}
-\end{figure}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\clearpage
-\begin{figure}
-\center \includegraphics[width=5in]{figures/fig/window_overlap.pdf}
-\caption{\label{fg:stageE}
-The selection of the best non-overlapping window
-combinations. Each grey box represents a distinct group of windows.
-Non-overlapping subsets of windows are shown on separate lines. Only one
-line from within each group will be chosen, the one corresponding to the
-highest score obtained in equation~(\ref{eq:score}). The resulting optimal set
-of data windows is shown by thick arrows.}
-\end{figure}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\clearpage
-\begin{figure}
-\center \includegraphics[width=6in]{figures/fig/window_results.pdf}
-\caption{\label{fg:res_abkt}
-Window selection results for event 050295B
-from Table~\ref{tb:events} recorded at ABKT ($37.93$\degN,
-$58.11$\degE, $\Delta=127$\deg, vertical
-component).
-(a)~Top: observed and synthetic seismograms (black and red
-traces); bottom: STA:LTA timeseries $E(t)$. Windows chosen by the algorithm
-are shown using light blue shading. The phases contained these windows are:
-(1)~$PP$, (2)~$PS+SP$, (3)~$SS$, (4)~$SSS$, (5)~$S5$, (6)~$S6$, (7)~fundamental
-mode Rayleigh wave.
-(b)~Ray paths corresponding to the body-wave phases present in the data windows in~(a).
-(c)~Window selection results for event 200808270646A from Table~\ref{tb:events} recorded
-at OTAV ($0.24$\degN, $78.45$\degW, $\Delta=119$\deg, vertical component). Phases contained within selected windows:
-(1)~$S_{\rm diff}$ and~$PS+SP$, (2)~$SS$, (3)~fundamental mode Rayleigh wave.
-(d)~Ray paths corresponding to the body-wave phases present in the data windows in~(c).
-}
-\end{figure}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\clearpage
-\begin{figure}
-\center \includegraphics[width=6in]{figures/fig/examples_global.pdf}
-\caption{\label{fg:examples}
-(a)~Window selection results for event 101895B from Table~\ref{tb:events} recorded
-at LBTB ($25.01$\degS, $25.60$\degE, $\Delta=113$\deg, radial component).
-Phases contained within selected windows:
-(1)~$SKS$, (2)~$PS+SP$, (3)~$SS$, (4)~fundamental mode Rayleigh wave (5) unidentified late phase.
-(b)~Body-wave ray paths corresponding to data windows in (a).
-(c)~Window selection results for event 060994A from Table~\ref{tb:events} recorded at WUS ($41.20$\degN, $79.22$\degE, $\Delta=140$\deg, transverse component).
-Phases contained within selected windows: (1)~$S_{\rm diff}$, (2)~$sS_{\rm diff}$, (3)~$SS$, (4)~$sSS$ followed by $SSS$, (5)~$sS5+S6$, (6)~$sS6+S7$ followed by $sS7$, (7)~major arc $sS4$, (8)~major arc $sS6$.
-(d)~Body-wave ray paths corresponding to data windows in~(c).
-}
-\end{figure}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\clearpage
-\begin{figure}
-\center \includegraphics[width=6in]{figures/fig/composites_global.pdf}
-\caption{\label{fg:composites}
-(a)-(c)~Summary plots of windowing results for event 101895B in Table~\ref{tb:events}.
-(a)~Global map showing great-circle paths to stations.
-(b)~Histograms of number of windows as a function of normalised cross-correlation $\mathrm{CC}$, time-lag $\tau$ and amplitude ratio $\Delta \ln A$; these give information about systematic trends in time shift and amplitude scaling.
-(c)~Record sections of selected windows for the vertical, radial and transverse components. The filled portions of the each record in the section indicate where windows have been selected by the algorithm.
-(d)-(f)~Summary plots of windowing results for event 060994A in Table~\ref{tb:events}.
-}
-\end{figure}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% JAPAN
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-
-%\clearpage
-%\begin{figure}
-%%\center
-%\includegraphics[width=5.7in]{figures/japan/ERM_II_051502B}
-%\caption{\label{fg:ERM_II_051502B}
-%Window selection results for event 051502B from Table~\ref{tb:events} recorded at station ERM ($42.01$\degN, $143.16$\degE, $\Delta=24.83$\deg).
-%(a)~Event and station map: event is 051502B indicated by the beach ball with the
-%CMT focal mechanism, station ERM is marked as red triangles and all the other stations
-%which recorded this event are marked by grey triangles.
-%(b)~Results for station ERM for the period range \trange{24}{120}.
-%Vertical (Z), radial (R), and transverse (T) records of data (black, left column) and synthetics (red, left column), as well as the STA:LTA records (right column) used to produce the window picks.
-%(c)~Results for station ERM for the period range \trange{6}{30}.
-%}
-%\end{figure}
-%\clearpage
-
-
-\begin{figure}
-%\center
-\includegraphics[width=5.7in]{figures/japan/KIS_BO_091502B}
-\caption{\label{fg:KIS_BO_091502B}
-Window selection results for event 091502B from Table~\ref{tb:events} recorded at station KIS ($\Delta=11.79$\deg).
-%(a)~Event and station map: event 091502B is indicated by the beach ball with the CMT focal mechanism, station KIS is marked by the red triangle and all the other stations which recorded this event are marked by grey triangles.
-(a)~Map showing all stations with at least one measurement window for the period range \trange{24}{120} for this event.
-%({\bf MIN: IS THIS CORRECT?})
-Red triangle denotes station KIS.
-(b)~Results for station KIS for the period range \trange{24}{120}.
-Vertical (Z), radial (R), and transverse (T) records of data (black, left column) and synthetics (red, left column), as well as the STA:LTA records (right column) used to produce the window picks.
-(c)~Results for station KIS for the period range \trange{6}{30}.
-}
-\end{figure}
-
-\clearpage
-\begin{figure}
-%\center
-\includegraphics[width=5.7in]{figures/japan/SHR_BO_200511211536A}
-\caption{\label{fg:SHR_BO_200511211536A}
-Window selection results for event 20051121536A from Table~\ref{tb:events} recorded at station SHR ($\Delta=17.47$\deg).
-%(a)~Event and station map: event 20051121536A is indicated by the beach ball with the CMT focal mechanism, station SHR is marked by the red triangle and all the other stations which recorded this event are marked by grey triangles.
-(a)~Map showing all stations with at least one measurement window for the period range \trange{24}{120} for this event.
-%({\bf MIN: IS THIS CORRECT?})
-Red triangle denotes station SHR.
-(b)~Results for station SHR for the period range \trange{24}{120}.
-Vertical (Z), radial (R), and transverse (T) records of data (black, left column) and synthetics (red, left column), as well as the STA:LTA records (right column) used to produce the window picks.
-(c)~Results for station SHR for the period range \trange{6}{30}.
-Note that the corresponding low-frequency bandpassed filtered version (b) has longer record length (800~s).
-}
-\end{figure}
-
-\clearpage
-\begin{figure}
-%\center
-\includegraphics[width=6in]{figures/japan/200511211536A_T06_rs}
-\caption{\label{fg:200511211536A_T06_rs}
-Summary plots of windowing results for event 200511211536A in Table~\ref{tb:events}, for the period range \trange{6}{30}.
-(a)~Map showing paths to each station with at least one measurement window.
-(b)-(d)~Histograms of number of windows as a function of normalised cross-correlation $\mathrm{CC}$, time-lag $\tau$ and amplitude ratio $\Delta \ln A$.
-(e)-(g)~Record sections of selected windows for the vertical, radial and transverse components.
-}
-\end{figure}
-
-\clearpage
-\begin{figure}
-%\center
-\includegraphics[width=6in]{figures/japan/200511211536A_T24_rs}
-\caption{\label{fg:200511211536A_T24_rs}
-Summary plots of windowing results for event 200511211536A in Table~\ref{tb:events}, for the period range \trange{24}{120}.
-}
-\end{figure}
-
-\clearpage
-\begin{figure}
-%\center
-\includegraphics[width=6in]{figures/japan/stats_T06}
-\caption{\label{fg:T06_rs}
-Summary statistics of windowing results for events 051502B, 200511211536A and 091502B in Table~\ref{tb:events}, for the period range \trange{6}{30}.
-}
-\end{figure}
-
-
-%
-%\clearpage
-%\begin{figure}
-%%\center
-%\includegraphics[width=6in]{figures/japan/051502B_T06_rs}
-%\caption{\label{fg:051502B_T06_rs}
-%Summary plots of windowing results for event 051502B in Table~\ref{tb:events}, for the period range \trange{6}{30}.
-%Same as Figure~\ref{fg:200511211536A_T06_rs}.
-%}
-%\end{figure}
-%
-%\clearpage
-%\begin{figure}
-%%\center
-%\includegraphics[width=6in]{figures/japan/091502B_T06_rs}
-%\caption{\label{fg:091502B_T06_rs}
-%Summary plots of windowing results for event 091502B in Table~\ref{tb:events}, for the period range \trange{6}{30}.
-%Same as Figure~\ref{fg:200511211536A_T06_rs}.
-%}
-%\end{figure}
-
-%\clearpage
-%\begin{figure}
-%%\center
-%\includegraphics[width=6in]{figures/japan/091502B_T06_rs}
-%\caption{\label{fg:091502B_T06_rs}
-%Summary plots of windowing results for event 051502B in Table~\ref{tb:events},
-%for the period range \trange{6}{30}. Same as Figure~\ref{fg:200511211536A_T06_rs).
-%}
-%\end{figure}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% SOUTHERN CALIFORNIA
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\clearpage
-\begin{figure}
-%\center
-\includegraphics[width=6in]{figures/socal/9818433_CLC_window.pdf}
-\caption{\label{fg:socal_CLC}
-Window selection results for event 9818433 from Table~\ref{tb:events} recorded at station CLC ($\Delta = 211.7$~km).
-%(a)~Source and station information for event 9818433 and station CLC.
-%(b)~Paths to each station with at least one measurement window for the period range \trange{6}{30}.
-%There are a total of 341 windows picked within 310 records.
-%Triangle denotes station CLC.
-%(c)~Paths to each station with at least one measurement window for the period range \trange{2}{30}.
-%There are a total of 190 windows picked within 193 records.
-%Triangle denotes station CLC.
-(a)~Map showing all stations with at least one measurement window for the period range \trange{6}{30} for this event.
-Red triangle denotes station CLC.
-(b)~Results for station CLC for the period range \trange{6}{30}.
-Vertical (Z), radial (R), and transverse (T) records of data (black, left column) and synthetics (red, left column), as well as the STA:LTA records (right column) used to produce the window picks.
-(c)~Results for station CLC for the period range \trange{2}{30}.
-Note that corresponding lower-passed filtered versions are shown in (b).
-}
-\end{figure}
-
-\clearpage
-\begin{figure}
-%\center
-\includegraphics[width=6in]{figures/socal/9818433_FMP_window.pdf}
-\caption{\label{fg:socal_FMP}
-Window selection results for event 9818433 from Table~\ref{tb:events} recorded at station FMP ($\Delta = 52.2$~km).
-Same caption as Figure~\ref{fg:socal_CLC}, only for a different station.
-}
-\end{figure}
-
-\clearpage
-\begin{figure}
-%\center
-\includegraphics[width=6in]{figures/socal/9983429_T06_rs.pdf}
-\caption{\label{fg:socal_rs_T06}
-Summary plots of windowing results for event 9983429 in Table~\ref{tb:events}, for the period range \trange{6}{30}.
-(a)~Map showing paths to each station with at least one measurement window.
-(b)-(d)~Histograms of number of windows as a function of normalised cross-correlation $\mathrm{CC}$, time-lag $\tau$ and amplitude ratio $\Delta \ln A$.
-(e)-(g)~Record sections of selected windows for the vertical, radial and transverse components.
-The two branches observed on the vertical and radial components correspond to the body-wave arrivals and the Rayleigh wave arrivals.
-}
-\end{figure}
-
-%\clearpage
-%\begin{figure}
-%%\center
-%\includegraphics[width=7in]{figures/socal/9983429_T02_rs.pdf}
-%\caption{\label{fg:socal_rs_T02}
-%(THIS FIGURE COULD IN THEORY BE CUT OUT, IF SPACE IS SHORT.)
-%Summary plots of windowing results for event 9983429 in Table~\ref{tb:events}, for the period range \trange{2}{30}.
-%Same as Figure~\ref{fg:socal_rs_T06}, only the windowing code has been run using a different set of parameters (Table~\ref{tb:example_params}), so that primarily only the body-wave arrivals are selected.
-%}
-%\end{figure}
-
-
-%\clearpage
-%\begin{figure}
-%%\center
-%\includegraphics[width=7in]{figures/socal/9818433_T06_CLC_adj.pdf}
-%\caption{\label{fg:socal_adj}
-%Adjoint sources constructed based on the windows picked in Figure~\ref{fg:socal_CLC}d, with the specification of a cross-correlation traveltime measurement. The adjoint sources for this measurement are simply a weighted version of the synthetic velocity traces. The number to the left of each subplot is the $\pm$ height of the $y$-axis. The cross-correlation measurements for traveltime ($\Delta T$) and amplitude ($\Delta \ln A$) are listed above each time window.
-%}
-%\end{figure}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Table captions
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Tables
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\newpage
+\begin{table}
+\begin{tabular}{lp{0.8\linewidth}}
+\hline
+\multicolumn{2}{l}{Standard tuning parameters:} \\[5pt]
+$T_{0,1}$ & bandpass filter corner periods \\
+$r_{P,A}$ & signal to noise ratios for whole waveform \\
+$r_0(t)$ & signal to noise ratios single windows \\
+$w_E(t)$ & water level on short-term:long-term ratio \\
+$\mathrm{CC}_0(t)$ & acceptance level for normalized cross-correlation\\
+$\Delta\tau_0(t)$ & acceptance level for time lag \\
+$\Delta\ln{A}_0(t)$ & acceptance level for amplitude ratio \\
+$\Delta\tau_{\rm ref}$ & reference time lag \\
+$\Delta\ln{A}_{\rm ref}$ & reference amplitude ratio \\
+\hline
+\multicolumn{2}{l}{Fine tuning parameters:} \\ [5pt]
+$c_0$ & for rejection of internal minima \\
+$c_1$ & for rejection of short windows \\
+$c_2$ & for rejection of un-prominent windows \\
+$c_{3a,b}$ & for rejection of multiple distinct arrivals \\
+$c_{4a,b}$ & for curtailing of windows with emergent starts and/or codas \\
+$w_{\mathrm{CC}}\quad w_{\rm len}\quad w_{\rm nwin}$ & for selection of best non-overlapping window combination \\
+\hline
+\end{tabular}
+\caption{\label{tb:params}
+Overview of standard tuning parameters, and of fine
+tuning parameters. Values are defined in a parameter file, and the
+time dependence of those that depend on time is described by user-defined functions.
+}
+\end{table}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\clearpage
+\begin{table}
+\begin{tabular}{lrrrrrl}
+\hline
+Identifier & Latitude & Longitude & Depth, km & Moment, N m & $M_w$ & Location \\
+\hline
+\multicolumn{7}{c}{Global} \\ \hline
+% CHECK THAT THE MOMENT IS LISTED IN N-M, NOT DYNE-CM
+% CARL HAS FORMULAS TO CONVERT FROM A MOMENT TENSOR TO M0 TO MW
+101895B & 28.06 & 130.18 & 18.5 & 5.68e19 & 7.1 & Ryukyu Islands \\
+200808270646A & -10.49 & 41.44 & 24.0 & 4.68e17 & 5.7 & Comoros Region \\
+050295B & -3.77 & -77.07 & 112.8 & 1.27e19 & 6.7 & Northern Peru \\
+060994A & -13.82 & -67.25 & 647.1 & 2.63e21 & 8.2 & Northern Bolivia \\
+\hline
+\multicolumn{7}{c}{Japan} \\ \hline
+051502B & 24.66 & 121.66 & 22.4 & 1.91e18 & 6.1 & Taiwan \\
+200511211536A & 30.97 & 130.31 & 155.0 & 2.13e18 & 6.2 & Kyuhu, Japan \\
+091502B & 44.77 & 130.04 & 589.4 & 4.24e18 & 6.4 & Northeastern China \\
+\hline
+\multicolumn{7}{c}{Southern California} \\ \hline
+9983429 & 35.01 & -119.14 & 13.5 & 9.19e15 & 4.6 & Wheeler Ridge, California \\
+9818433 & 33.91 & -117.78 & 9.4 & 3.89e15 & 4.3 & Yorba Linda, California \\
+\hline
+\end{tabular}
+\caption{\label{tb:events}
+Example events used in this study. The identifier refers to the CMT catalog for global events and Japan events, and refers to the Southern California Earthquake Data Center catalog for southern California events.
+}
+\end{table}
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\clearpage
+\begin{table}
+\begin{center}
+\begin{tabular}{lcccccc}
+\hline
+ & Global & \multicolumn{2}{c}{Japan} & \multicolumn{3}{c}{S. California} \\
+\hline
+$T_{0,1}$ & 50, 150 & 24, 120 & 6, 30 & 6, 30 & 3, 30 & 2, 30 \\
+$r_{P,A}$ & 3.5, 3.0 & 3.5, 3.0 & 3.5, 3.0 & 3.0, 2.5 & 2.5, 3.5 & 2.5, 3.5 \\
+$r_0$ & 2.5 & 1.5 & 3.0 & 3.0 & 4.0 & 4.0 \\
+$w_E$ & 0.08 & 0.10 & 0.12 & 0.18 & 0.11 & 0.07 \\
+$\mathrm{CC}_0$ & 0.85 & 0.70 & 0.73 & 0.71 & 0.80 & 0.85 \\
+$\Delta\tau_0$ & 15 & 12.0 & 3.0 & 8.0 & 4.0 & 3.0 \\
+$\Delta\ln{A}_0$ & 1.0 & 1.0 & 1.5 & 1.5 & 1.0 & 1.0 \\
+$\Delta\tau_{\rm ref}$ & 0.0 & 0.0 & 0.0 & 4.0 & 2.0 & 1.0 \\
+$\Delta\ln{A}_{\rm ref}$& 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\
+\hline
+$c_0$ & 0.7 & 0.7 & 0.7 & 0.7 & 1.3 & 1.0 \\
+$c_1$ & 4.0 & 3.0 & 3.0 & 2.0 & 4.0 & 5.0 \\
+$c_2$ & 0.3 & 0.0 & 0.6 & 0.0 & 0.0 & 0.0 \\
+$c_{3a,b}$ & 1.0, 2.0 & 1.0, 2.0 & 1.0, 2.0 & 3.0, 2.0 & 4.0, 2.5 & 4.0, 2.5 \\
+$c_{4a,b}$ & 3.0, 10.0 & 3.0, 25.0 & 3.0, 12.0 & 2.5, 12.0 & 2.0, 6.0 & 2.0, 6.0 \\
+$w_{\mathrm{CC}}, w_{\rm len}, w_{\rm nwin}$
+ & 1, 1, 1 & 1, 1, 1 & 1, 1, 1 & 0.5,1.0,0.7 & 0.70,0.25,0.05 & 1,1,1 \\
+\hline
+\end{tabular}
+\caption{\label{tb:example_params}
+Values of standard and fine-tuning parameters for the three seismological
+scenarios discussed in this study.
+}
+\end{center}
+\end{table}
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Figure captions
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Figures
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\clearpage
+\begin{figure}
+\center \includegraphics[width=6in]{figures/050295B.050-150/ABKT_II_LHZ_seis_nowin.pdf}
+\caption{\label{fg:stalta}
+Synthetic seismogram and its corresponding envelope and STA:LTA timeseries.
+The seismogram was calculated using SPECFEM3D and the
+Earth model S20RTS \citep{RitsemaEtal2004} for the CMT catalog event
+050295B, whose details can be found in Table~\ref{tb:events}. The
+station, ABKT, is at an epicentral distance of 14100~km and at an azimuth of 44
+degrees from the event. The top panel shows the vertical component synthetic
+seismogram, filtered between periods of 50 and 150 seconds. The center panel shows its envelope, and the bottom panel
+shows the corresponding STA:LTA waveform. The dashed line overlaid on
+the STA:LTA waveform is the water level $w_E(t)$.
+}
+
+\end{figure}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\clearpage
+\begin{figure}
+\center \includegraphics[width=6in]{figures/fig/window_composite.pdf}
+\caption{\label{fg:win_composite}
+(a)~Window creation process. The thick black line represents the STA:LTA
+waveform $E(t)$, and the thick horizontal dashed line its water level $w_E(t)$.
+Local maxima are indicated by alternating red and blue dots, windows are
+indicated by two-headed horizontal arrows. The time of the local maximum used
+as the window seed $t_M$ is denoted by the position of the dot. Only windows for the fourth local maximum are shown. (b)~Rejection of candidate windows based on the amplitude of the local minima. The two deep
+local minima indicated by the grey arrows form virtual barriers. All candidate
+windows that cross these barriers are rejected.
+(c)~Rejection of candidate
+windows based on the prominence of the seed maximum. The local maxima
+indicated by the grey arrows are too low compared to the local minima
+adjacent to them. All windows that have these local maxima as their seed are
+rejected (black crosses over the window segments below the timeseries).
+(d)~Shortening of long coda windows. The grey bar indicates the maximum coda
+duration $c_{4b} T_0$. Note that after the rejection based on prominence represented in (c) and before shortening of long coda windows represented in (d), the algorithm rejects candidate windows based on the separation of distinct phases, a process that is illustrated in Figure~\ref{fg:separation}.
+}
+\end{figure}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\clearpage
+\begin{figure}
+\center \includegraphics[width=5in]{figures/fig/window_rejection_separation.pdf}
+\caption{\label{fg:separation}
+Rejection of candidate windows based on the separation of distinct phases.
+(a)~Heights of pairs of local maxima above their intervening minimum.
+(b)~The black line represents $f(\Delta T/T_0)$ from
+equation~(\ref{eq:sep}) with $c_{3a}=c_{3b}=1$. Vertical bars represent
+$h/h_M$ for each pair of maxima. Their position along the horizontal axis is
+given by the time separation $\Delta T$ between the maxima of each pair. The
+color of the bar is given by the color of the seed maximum corresponding to $h_M$. Bars whose height
+exceeds the $f(\Delta T/T_0)$ line represent windows to be rejected.
+(c)~The windows that have been rejected by this criterion are indicated by black
+crosses.
+}
+\end{figure}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\clearpage
+\begin{figure}
+\center \includegraphics[width=6in]{figures/fig/window_rejection_global_data.pdf}
+\caption{\label{fg:win_rej_data}
+Window rejection applied to real data.
+Top panel: observed (black) and synthetic (red) seismograms for the 050295B event
+recorded at ABKT (see Figure~\ref{fg:stalta}).
+Subsequent panels: candidate windows at different stages, separated into \stgc\ (shape based rejection) and
+\stgd\ (fit based rejection). Each candidate window is indicated by a black
+segment. The number of windows at each stage is shown to the left of the
+panel.
+}
+\end{figure}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\clearpage
+\begin{figure}
+\center \includegraphics[width=6in]{figures/050295B.050-150/ABKT_II_LHZ_criteria.pdf}
+\caption{\label{fg:criteria}
+Time-dependent fit based criteria
+for the 050295B event recorded at ABKT. The time-dependence of these criteria
+is given by the formulas in Appendix~\ref{ap:user_global}. The lower limit on
+acceptable cross-correlation value, $\mathrm{CC}_0$ (solid line), is
+0.85 for most of the duration of the seismogram; it is lowered to 0.75 during
+the approximate surface-wave window defined by the group velocities 4.2\kmps\
+and 3.2\kmps, and is raised to 0.95 thereafter. The upper limit on time lag,
+$\tau_0$ (dotted line), is 21~s for the whole seismogram. The upper limit on amplitude
+ratio, $\Delta \ln A_0$ (dashed line), is 1.0 for most of the seismogram; it is reduced to
+1/3 of this value after the end of the surface-waves.
+}
+\end{figure}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\clearpage
+\begin{figure}
+\center \includegraphics[width=5in]{figures/fig/window_overlap.pdf}
+\caption{\label{fg:stageE}
+The selection of the best non-overlapping window
+combinations. Each grey box represents a distinct group of windows.
+Non-overlapping subsets of windows are shown on separate lines. Only one
+line from within each group will be chosen, the one corresponding to the
+highest score obtained in equation~(\ref{eq:score}). The resulting optimal set
+of data windows is shown by thick arrows.}
+\end{figure}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\clearpage
+\begin{figure}
+\center \includegraphics[width=6in]{figures/fig/window_results.pdf}
+\caption{\label{fg:res_abkt}
+Window selection results for event 050295B
+from Table~\ref{tb:events} recorded at ABKT ($37.93$\degN,
+$58.11$\degE, $\Delta=127$\deg, vertical
+component).
+(a)~Top: observed and synthetic seismograms (black and red
+traces); bottom: STA:LTA timeseries $E(t)$. Windows chosen by the algorithm
+are shown using light blue shading. The phases contained these windows are:
+(1)~$PP$, (2)~$PS+SP$, (3)~$SS$, (4)~$SSS$, (5)~$S5$, (6)~$S6$, (7)~fundamental
+mode Rayleigh wave.
+(b)~Ray paths corresponding to the body-wave phases present in the data windows in~(a).
+(c)~Window selection results for event 200808270646A from Table~\ref{tb:events} recorded
+at OTAV ($0.24$\degN, $78.45$\degW, $\Delta=119$\deg, vertical component). Phases contained within selected windows:
+(1)~$S_{\rm diff}$ and~$PS+SP$, (2)~$SS$, (3)~fundamental mode Rayleigh wave.
+(d)~Ray paths corresponding to the body-wave phases present in the data windows in~(c).
+}
+\end{figure}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\clearpage
+\begin{figure}
+\center \includegraphics[width=6in]{figures/fig/examples_global.pdf}
+\caption{\label{fg:examples}
+(a)~Window selection results for event 101895B from Table~\ref{tb:events} recorded
+at LBTB ($25.01$\degS, $25.60$\degE, $\Delta=113$\deg, radial component).
+Phases contained within selected windows:
+(1)~$SKS$, (2)~$PS+SP$, (3)~$SS$, (4)~fundamental mode Rayleigh wave (5) unidentified late phase.
+(b)~Body-wave ray paths corresponding to data windows in (a).
+(c)~Window selection results for event 060994A from Table~\ref{tb:events} recorded at WUS ($41.20$\degN, $79.22$\degE, $\Delta=140$\deg, transverse component).
+Phases contained within selected windows: (1)~$S_{\rm diff}$, (2)~$sS_{\rm diff}$, (3)~$SS$, (4)~$sSS$ followed by $SSS$, (5)~$sS5+S6$, (6)~$sS6+S7$ followed by $sS7$, (7)~major arc $sS4$, (8)~major arc $sS6$.
+(d)~Body-wave ray paths corresponding to data windows in~(c).
+}
+\end{figure}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\clearpage
+\begin{figure}
+\center \includegraphics[width=6in]{figures/fig/composites_global.pdf}
+\caption{\label{fg:composites}
+(a)-(c)~Summary plots of windowing results for event 101895B in Table~\ref{tb:events}.
+(a)~Global map showing great-circle paths to stations.
+(b)~Histograms of number of windows as a function of normalised cross-correlation $\mathrm{CC}$, time-lag $\tau$ and amplitude ratio $\Delta \ln A$; these give information about systematic trends in time shift and amplitude scaling.
+(c)~Record sections of selected windows for the vertical, radial and transverse components. The filled portions of the each record in the section indicate where windows have been selected by the algorithm.
+(d)-(f)~Summary plots of windowing results for event 060994A in Table~\ref{tb:events}.
+}
+\end{figure}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% JAPAN
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%\clearpage
+%\begin{figure}
+%%\center
+%\includegraphics[width=5.7in]{figures/japan/ERM_II_051502B}
+%\caption{\label{fg:ERM_II_051502B}
+%Window selection results for event 051502B from Table~\ref{tb:events} recorded at station ERM ($42.01$\degN, $143.16$\degE, $\Delta=24.83$\deg).
+%(a)~Event and station map: event is 051502B indicated by the beach ball with the
+%CMT focal mechanism, station ERM is marked as red triangles and all the other stations
+%which recorded this event are marked by grey triangles.
+%(b)~Results for station ERM for the period range \trange{24}{120}.
+%Vertical (Z), radial (R), and transverse (T) records of data (black, left column) and synthetics (red, left column), as well as the STA:LTA records (right column) used to produce the window picks.
+%(c)~Results for station ERM for the period range \trange{6}{30}.
+%}
+%\end{figure}
+%\clearpage
+
+
+\begin{figure}
+%\center
+\includegraphics[width=5.7in]{figures/japan/KIS_BO_091502B}
+\caption{\label{fg:KIS_BO_091502B}
+Window selection results for event 091502B from Table~\ref{tb:events} recorded at station KIS ($\Delta=11.79$\deg).
+%(a)~Event and station map: event 091502B is indicated by the beach ball with the CMT focal mechanism, station KIS is marked by the red triangle and all the other stations which recorded this event are marked by grey triangles.
+(a)~Map showing all stations with at least one measurement window for the period range \trange{24}{120} for this event.
+%({\bf MIN: IS THIS CORRECT?})
+Red triangle denotes station KIS.
+(b)~Results for station KIS for the period range \trange{24}{120}.
+Vertical (Z), radial (R), and transverse (T) records of data (black, left column) and synthetics (red, left column), as well as the STA:LTA records (right column) used to produce the window picks.
+(c)~Results for station KIS for the period range \trange{6}{30}.
+}
+\end{figure}
+
+\clearpage
+\begin{figure}
+%\center
+\includegraphics[width=5.7in]{figures/japan/SHR_BO_200511211536A}
+\caption{\label{fg:SHR_BO_200511211536A}
+Window selection results for event 20051121536A from Table~\ref{tb:events} recorded at station SHR ($\Delta=17.47$\deg).
+%(a)~Event and station map: event 20051121536A is indicated by the beach ball with the CMT focal mechanism, station SHR is marked by the red triangle and all the other stations which recorded this event are marked by grey triangles.
+(a)~Map showing all stations with at least one measurement window for the period range \trange{24}{120} for this event.
+%({\bf MIN: IS THIS CORRECT?})
+Red triangle denotes station SHR.
+(b)~Results for station SHR for the period range \trange{24}{120}.
+Vertical (Z), radial (R), and transverse (T) records of data (black, left column) and synthetics (red, left column), as well as the STA:LTA records (right column) used to produce the window picks.
+(c)~Results for station SHR for the period range \trange{6}{30}.
+}
+\end{figure}
+
+\clearpage
+\begin{figure}
+%\center
+\includegraphics[width=6in]{figures/japan/200511211536A_T06_rs}
+\caption{\label{fg:200511211536A_T06_rs}
+Summary plots of windowing results for event 200511211536A in Table~\ref{tb:events}, for the period range \trange{6}{30}.
+(a)~Map showing paths to each station with at least one measurement window.
+(b)-(d)~Histograms of number of windows as a function of normalised cross-correlation $\mathrm{CC}$, time-lag $\tau$ and amplitude ratio $\Delta \ln A$.
+(e)-(g)~Record sections of selected windows for the vertical, radial and transverse components.
+}
+\end{figure}
+
+\clearpage
+\begin{figure}
+%\center
+\includegraphics[width=6in]{figures/japan/200511211536A_T24_rs}
+\caption{\label{fg:200511211536A_T24_rs}
+Summary plots of windowing results for event 200511211536A in Table~\ref{tb:events}, for the period range \trange{24}{120}.
+}
+\end{figure}
+
+\clearpage
+\begin{figure}
+%\center
+\includegraphics[width=6in]{figures/japan/stats_T06}
+\caption{\label{fg:T06_rs}
+Summary statistics of windowing results for events 051502B, 200511211536A and 091502B in Table~\ref{tb:events}, for the period range \trange{6}{30}.
+}
+\end{figure}
+
+
+%
+%\clearpage
+%\begin{figure}
+%%\center
+%\includegraphics[width=6in]{figures/japan/051502B_T06_rs}
+%\caption{\label{fg:051502B_T06_rs}
+%Summary plots of windowing results for event 051502B in Table~\ref{tb:events}, for the period range \trange{6}{30}.
+%Same as Figure~\ref{fg:200511211536A_T06_rs}.
+%}
+%\end{figure}
+%
+%\clearpage
+%\begin{figure}
+%%\center
+%\includegraphics[width=6in]{figures/japan/091502B_T06_rs}
+%\caption{\label{fg:091502B_T06_rs}
+%Summary plots of windowing results for event 091502B in Table~\ref{tb:events}, for the period range \trange{6}{30}.
+%Same as Figure~\ref{fg:200511211536A_T06_rs}.
+%}
+%\end{figure}
+
+%\clearpage
+%\begin{figure}
+%%\center
+%\includegraphics[width=6in]{figures/japan/091502B_T06_rs}
+%\caption{\label{fg:091502B_T06_rs}
+%Summary plots of windowing results for event 051502B in Table~\ref{tb:events},
+%for the period range \trange{6}{30}. Same as Figure~\ref{fg:200511211536A_T06_rs).
+%}
+%\end{figure}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% SOUTHERN CALIFORNIA
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\clearpage
+\begin{figure}
+%\center
+\includegraphics[width=6in]{figures/socal/9818433_CLC_window.pdf}
+\caption{\label{fg:socal_CLC}
+Window selection results for event 9818433 from Table~\ref{tb:events} recorded at station CLC ($\Delta = 211.7$~km).
+%(a)~Source and station information for event 9818433 and station CLC.
+%(b)~Paths to each station with at least one measurement window for the period range \trange{6}{30}.
+%There are a total of 341 windows picked within 310 records.
+%Triangle denotes station CLC.
+%(c)~Paths to each station with at least one measurement window for the period range \trange{2}{30}.
+%There are a total of 190 windows picked within 193 records.
+%Triangle denotes station CLC.
+(a)~Map showing all stations with at least one measurement window for the period range \trange{6}{30} for this event.
+Red triangle denotes station CLC.
+(b)~Results for station CLC for the period range \trange{6}{30}.
+Vertical (Z), radial (R), and transverse (T) records of data (black, left column) and synthetics (red, left column), as well as the STA:LTA records (right column) used to produce the window picks.
+(c)~Results for station CLC for the period range \trange{2}{30}.
+Note that corresponding lower-passed filtered versions are shown in (b).
+}
+\end{figure}
+
+\clearpage
+\begin{figure}
+%\center
+\includegraphics[width=6in]{figures/socal/9818433_FMP_window.pdf}
+\caption{\label{fg:socal_FMP}
+Window selection results for event 9818433 from Table~\ref{tb:events} recorded at station FMP ($\Delta = 52.2$~km).
+Same caption as Figure~\ref{fg:socal_CLC}, only for a different station.
+}
+\end{figure}
+
+\clearpage
+\begin{figure}
+%\center
+\includegraphics[width=6in]{figures/socal/9983429_T06_rs.pdf}
+\caption{\label{fg:socal_rs_T06}
+Summary plots of windowing results for event 9983429 in Table~\ref{tb:events}, for the period range \trange{6}{30}.
+(a)~Map showing paths to each station with at least one measurement window.
+(b)-(d)~Histograms of number of windows as a function of normalised cross-correlation $\mathrm{CC}$, time-lag $\tau$ and amplitude ratio $\Delta \ln A$.
+(e)-(g)~Record sections of selected windows for the vertical, radial and transverse components.
+The two branches observed on the vertical and radial components correspond to the body-wave arrivals and the Rayleigh wave arrivals.
+}
+\end{figure}
+
+%\clearpage
+%\begin{figure}
+%%\center
+%\includegraphics[width=7in]{figures/socal/9983429_T02_rs.pdf}
+%\caption{\label{fg:socal_rs_T02}
+%(THIS FIGURE COULD IN THEORY BE CUT OUT, IF SPACE IS SHORT.)
+%Summary plots of windowing results for event 9983429 in Table~\ref{tb:events}, for the period range \trange{2}{30}.
+%Same as Figure~\ref{fg:socal_rs_T06}, only the windowing code has been run using a different set of parameters (Table~\ref{tb:example_params}), so that primarily only the body-wave arrivals are selected.
+%}
+%\end{figure}
+
+
+%\clearpage
+%\begin{figure}
+%%\center
+%\includegraphics[width=7in]{figures/socal/9818433_T06_CLC_adj.pdf}
+%\caption{\label{fg:socal_adj}
+%Adjoint sources constructed based on the windows picked in Figure~\ref{fg:socal_CLC}d, with the specification of a cross-correlation traveltime measurement. The adjoint sources for this measurement are simply a weighted version of the synthetic velocity traces. The number to the left of each subplot is the $\pm$ height of the $y$-axis. The cross-correlation measurements for traveltime ($\Delta T$) and amplitude ($\Delta \ln A$) are listed above each time window.
+%}
+%\end{figure}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Modified: seismo/3D/ADJOINT_TOMO/flexwin/latex/flexwin_paper.pdf
===================================================================
(Binary files differ)
Modified: seismo/3D/ADJOINT_TOMO/flexwin/latex/results.tex
===================================================================
--- seismo/3D/ADJOINT_TOMO/flexwin/latex/results.tex 2008-12-11 17:22:51 UTC (rev 13653)
+++ seismo/3D/ADJOINT_TOMO/flexwin/latex/results.tex 2008-12-11 19:27:20 UTC (rev 13654)
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-\section{Windowing Examples \label{sec:results}}
-
-We present a set of examples showing the results of the FLEXWIN algorithm
-applied to real data. These examples illustrate the robustness and flexibility of the
-algorithm. We have applied the algorithm to three
-tomographic scenarios, with very different geographical extents and distinct period ranges:
-long-period global tomography (\trange{50}{150}),
-regional tomography of the Japan subduction zone, down to 700~km (\trange{6}{120}), and
-regional tomography of southern California, down to 60~km (\trange{2}{40}).
-For each of these scenarios, we compare
-observed seismograms to spectral-element synthetics, using our
-algorithm to select time windows on the pairs of timeseries.
-
-The windowing algorithm
-itself has little prior knowledge of seismology, other than in the most general
-terms: it considers a seismogram to be a succession of seismic phases indicated
-by changes in amplitude and frequency of the signal with time; it is based upon
-the idea that the short-term to long-term average ratio STA:LTA is a good
-indicator of the arrival of such phases;
-it has a notion of the characteristics of an optimal set of data windows.
-All other prior information --- the frequency range to be considered, the
-portions of the seismogram to be excluded, the acceptable signal-to-noise
-ratios, the tolerance of dissimilarity between the observed and synthetic
-seismogram --- varies greatly between any two seismological studies. In order
-to ensure maximum flexibility of our windowing algorithm, all such
-scenario-dependent information is encapsulated in the tuning parameters of
-Table~\ref{tb:params}.
-
-We tuned the windowing algorithm separately for each of the three scenarios we present here, and we present examples based on the events listed in Table~\ref{tb:events}. Tuning parameter values for each scenario can be found in Table~\ref{tb:example_params}, while the functional forms of the time-dependent parameters can be found in Appendix~\ref{ap:user_fn}. Once tuned for a given scenario, the algorithm is applied to all its events without further modification.
-
-
-\subsection{Global tomography}
-\label{sec:globe}
-
-Our first scenario is a global scale, long-period tomographic study.
-We calculate spectral-element synthetic seismograms through an Earth model for
-which the mantle is given by the S20RTS model of \citet{RitsemaEtal2004},
-and the crust by the CRUST2.0 model of \citet{BassinEtal2000}.
-The degree-20 $S$-wave velocity model S20RTS defines isotropic perturbations to
-radially anisotropic PREM \citep{DziewonskiAnderson1981}; the SPECFEM3D implementation of S20RTS takes
-$P$-wave velocity anomalies from the degree-12 $P$-wave velocity model of \citet{RitsemaVanHeijst2002}.
-CRUST2.0 specifies a
-seven-layer crustal seismic velocity and density profile for each cell on a
-2\deg\ grid. The S20RTS+CRUST2.0 combination produces synthetics that are a
-good match to observed seismograms for periods longer than \trange{35}{40}. For our
-examples, we shall be working in the period range \trange{50}{150}.
-
-Here we discuss windowing results for shadow-zone seismograms of four earthquakes listed
-in Table~\ref{tb:events}: a shallow event in the Ryukyu Islands, Japan (101895B),
-a smaller magnitude shallow event in the
-Comoros region, between Mozambique and Madagascar (200808270646A),
-an intermediate depth event in northern Peru (050295B), and a strong
-deep event in northern Bolivia (060994A). We focus on shadow zone
-seismograms as these contain a large number of often poorly time-separated
-phases, and pose a greater windowing challenge than more commonly used
-teleseismic seismograms.
-
-Windowing results for these seismograms (one example per earthquake) are shown
-in Figures~\ref{fg:res_abkt}a,c and~\ref{fg:examples}a,c. The first observation
-we make when looking at these examples is that the synthetics match the data
-well, indicating that the Earth model S20RTS+CRUST2.0 provides a good 3D image
-of how the Earth is seen by \trange{50}{150} seismic waves. The fit is far from
-perfect, though, as is attested by the shape differences, time-lags and
-amplitude differences visible on many seismic phases; these indicate that there is
-room for improving the Earth model and possibly certain
-earthquake parameters even at these low frequencies.
-
-The second observation we make is that our algorithm has placed time windows
-around most of the significant features that stand out in the STA:LTA
-timeseries $E(t)$ and in the seismograms themselves, and that the window limits
-also seem to be sensibly placed. These windows were selected according to the
-purely signal processing algorithm described in the previous section, which has no
-knowledge of Earth structure or of seismic phases and their traveltime curves.
-In order to demonstrate the ability of such an Earth-blind algorithm to set
-windows around actual seismic phases, we have identified the
-seismic arrivals contained within the chosen data windows, using standard
-PREM-based traveltime curves. We have found that most of the features within
-the windows in Figures~\ref{fg:res_abkt}a,c and~\ref{fg:examples}a,c correspond
-to known seismic phases, which are listed in the
-corresponding figure captions. We have also traced the body-wave ray paths
-corresponding to these phases and show them in Figures~\ref{fg:res_abkt}b,d and~\ref{fg:examples}b,d;
-these ray path plots serve to illustrate the considerable
-amount of information contained in a single seismogram, even a long period
-seismogram, when all the usable seismic phases are considered. Fewer useable seismic phases are windowed for the smaller magnitude event in Figure~\ref{fg:res_abkt}c.
-
-Not all the features within a given seismogram are identifiable as seismic
-phases. For example, the second window in Figure~\ref{fg:examples}b seems to
-contain two features. When we look at periods shorter than 50~s, the first
-feature retains its character and is clearly identifiable as $sS_{\rm diff}$,
-while the second feature looses its character entirely and is more readily
-assimilated to a generic $S$ wave coda than to a distinct seismic phase.
-This feature is present in both observed and synthetic seismograms, and
-undoubtedly contains information. The particularity of our windowing algorithm
-is to treat such features as information, without trying to identify their
-sources. A scheme that permits the computation of
-sensitivity kernels for such features (e.g. the adjoint scheme), would allow measurements made
-on them to be interpreted and inverted correctly. Other methods of determining
-measurement sensitivities may have more difficulty dealing with them. These
-considerations illustrate the strong ties that exist between the selection,
-measurement and interpretation stages of any study using seismological data.
-
-We have described those seismic phases and other features in the seismograms
-that have been selected by our windowing algorithm. Equally important are the
-phases that have been rejected. Two such phases are $P_{\rm diff}$ and $S4$ on the
-vertical component seismogram in Figure~\ref{fg:res_abkt}a. We can identify
-the reasons for the rejection of these phases by comparing the selected time windows with the candidate windows at each stage in the rejection process
-(Figure~\ref{fg:win_rej_data}). The $P_{\rm diff}$ phase, though small on the
-long period seismogram, gives rise to a strong maximum on the $E(t)$ timeseries
-and therefore to at least one candidate window. Candidate windows
-containing $P_{\rm diff}$ disappear from Figure~\ref{fg:win_rej_data} at the
-${\rm SNR}_W$ based rejection stage, indicating that this phase was rejected
-for its low signal-to-noise ratio. The $S4$ phase also gives rise to a
-distinct maximum in $E(t)$, and to its own candidate window that is still
-present at the end of both window rejection stages (it corresponds to the
-fourth window from the right at the bottom of Figure~\ref{fg:win_rej_data}).
-As the $S4$ candidate and its neighbour the $S5$ candidate overlap, the
-algorithm has to choose between them using equation~(\ref{eq:score}). The fit
-to the shape of $S4$ is worse than that to $S5$, therefore the $S4$ window is
-discarded. It is helpful, when setting and tuning the values of the
-parameters in Table~\ref{tb:params}, to analyse the rejection and overlap
-resolution steps as we have done here for a number of representative
-seismograms, seeking to avoid the acceptance of unreasonable candidate windows,
-and to minimize the rejection of acceptable ones.
-
-A further appreciation of the windowing results is given by event-based
-summaries such as those in Figure~\ref{fg:composites}, which show at a glance
-the geographical path distribution of records containing acceptable windows,
-the distribution of $\mathrm{CC}$, $\Delta\tau$ and $\Delta\ln A$ values within the
-accepted time windows, and time-window record sections. Comparison of the
-summary plots for the shallow Ryukyu Islands event and the deep
-Bolivia event (Figure~\ref{fg:composites}b and~e respectively) shows that both
-have similar one-sided distributions of $\mathrm{CC}$ values, strongly biased towards
-the higher degrees of similarity $\mathrm{CC}>0.95$. The two events also have similar
-two-sided $\Delta\ln A$ distributions that peak at $\Delta\ln A\simeq0.25$,
-indicating that on average the synthetics underestimate the amplitude of the
-observed waveforms by 25\%. We cannot know at this stage if this
-anomaly is due to an underestimation of the seismic moments of the events, or to an
-overestimation of attenuation. The $\Delta\tau$ distributions for the two
-events are also two-sided. The shallow event $\Delta\tau$ values
-peak between 0 and 4~s, indicating that the synthetics are moderately faster
-than the observed records; the deep event $\Delta\tau$ distribution peaks at
-much higher time lags of 8--10~s. Possible explanations for these large average
-time lags include an origin time error, and/or an overestimation of the seismic
-velocity at the source location.
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\subsection{Regional tomography of the Japan subduction zone}
-\label{sec:japan}
-Our second scenario is a regional-scale tomographic study of the Japan subduction zone, using a set of local events within the depth range 0--600~km.
-The lateral dimensions of the domain are
-44$^\circ$(EW)$\times$33$^\circ$(NS) (108--152$^\circ$E
-and 18--51$^\circ$N).
-The initial model is constructed using the southeast Asia model of
-\cite{LebedevNolet2003} as the background model, with
-$P$-wave velocity anomalies added from
-a high-resolution Japan $P$-wave model \citep{ZhaoEtal1994}
-and $S$-wave velocity anomalies
-scaled to $P$ by a factor of 1.5 \citep{ChenEtal2007}.
-Two different crustal
-models are implemented in the spectral-element mesh: inside the region of the
-high-resolution model (32--45$^\circ$N, 130--145$^\circ$E
-and down to 500~km), the crustal model is derived from
-the arrival times of local shallow earthquakes \citep{ZhaoEtal1992};
-outside this region, the crustal model is CRUST2.0 \citep{BassinEtal2000}.
-
-We collected data for more than 200 events with $M_w$ 4.5--8 that
-occurred between 2000 and 2006. The source locations and focal
-mechanisms are the centroid-moment tensor (CMT) solutions.
-We used a total of 818 stations from three different networks
-(GSN, F-net and Hi-net): the 119 stations of the GSN and F-net
-provide broadband records,
-whereas the 699 Hi-net stations provide only high-frequency records.
-We use the one-chunk version of spectral-element code to calculate
-synthetic seismograms accurate at periods of $\sim$6~s and
-longer \citep{ChenEtal2007}, and present results for two period ranges:
-\trange{6}{30}, using all the records, and \trange{24}{120}, using the broadband records only.
-
-Figures~\ref{fg:KIS_BO_091502B} and \ref{fg:SHR_BO_200511211536A} show windowing results for two events at two different depths (Table~\ref{tb:events}): 091502B, 589.4~km deep, northeastern China; 200511211536A, 155~km deep, Kyushu, Japan. We have tuned the windowing algorithm using different sets of parameters for the two period ranges (see Table~\ref{tb:example_params}). In the period range \trange{24}{120}, the water level is raised after the surface-wave arrivals to exclude the later arrivals that are not sensitive to upper mantle structure. In the period range \trange{6}{30}, the water level is raised after the $S$-wave arrivals to exclude the surface-waves, as the current crustal model is not detailed enough to predict the short-period surface-waves.
-
-%Figures~\ref{fg:ERM_II_051502B}, \ref{fg:KIS_BO_091502B} and \ref{fg:SHR_BO_200511211536A} show windowing results for three events at different depths (Table~\ref{tb:events}): 051502B, 22.4~km deep, Taiwan; 091502B, 589.4~km deep, northeastern China; 200511211536A, 155~km deep, Kyushu, Japan. We have tuned the windowing algorithm using different sets of parameters for the two period ranges (see Table~\ref{tb:example_params}). In the period range \trange{24}{120}, the water level is raised after the surface-wave arrivals to exclude the later arrivals that are not sensitive to upper mantle structure. In the period range \trange{6}{30}, the water level is raised after the $S$-wave arrivals to exclude the surface-waves, as the current crustal model is not detailed enough to predict the short-period surface-waves.
-
-%For the shallow event beneath Taiwan recorded at station ERM (Figure~\ref{fg:ERM_II_051502B}), the observed and synthetic seismograms in \trange{24}{120} are similar in shape, and the algorithm picks not only the long-period $P$- and $S$-wave arrivals, but also the Rayleigh-wave on the vertical and radial components and the Love-wave on the transverse component (Figure~\ref{fg:ERM_II_051502B}b). In the short-period range (\trange{6}{30}), the synthetics are a poorer fit to the data than in the long-period range (\trange{24}{120}). The synthetics capture only the major $P$-wave arrival on the vertical component (Figure~\ref{fg:ERM_II_051502B}c), which is also the only arrival picked by the windowing algorithm. As the depth sensitivity of surface-waves is frequency dependent, the good fits at long periods (\trange{24}{120}) indicate that the starting model structure below the Moho is adequate for tomography.
-
-Figure~\ref{fg:KIS_BO_091502B} shows an example of window picks for a deep event
-beneath northeastern China (091502B) recorded at station KIS.
-%Compared to the shallow event above,
-The seismograms from this event are relatively simple, containing only two major body-wave arrivals ($P$ and $S$). The windowing algorithm's similarity criterion comes into play here, causing it
-not to pick the short-period $S$ arrival
-on the vertical component (Figure~\ref{fg:KIS_BO_091502B}c) as
-the distorted $S$-wave waveform of the data is quite
-different from the Gaussian shaped synthetics.
-The long-period $S$-wave arrival on the
-same component is selected due to higher data-synthetic
-waveform similarity (Figure~\ref{fg:KIS_BO_091502B}b).
-
-The records of the intermediate-depth event (200511211536A) recorded by station SHR (Figure~\ref{fg:SHR_BO_200511211536A}) contain more seismic phases
-than the previous two examples.
-On the vertical component of the short-period
- seismogram (Figure~\ref{fg:SHR_BO_200511211536A}c), the $P$-wave
-arrives at $\sim$230~s, immediately followed by $pP$ and $sPn$,
-and the $S$-wave arrives at $\sim$420~s, followed by $sS$ and
-$PcP$. The windowing algorithm selects separate windows for the $P$, $S$ and $sS$ arrivals
-on the vertical component, and selects only the $P$ arrival on the radial component.
-In the period range \trange{24}{120} (Figure~\ref{fg:SHR_BO_200511211536A}b), the $P$ and $S$ waves merge with the arrivals that follow them, causing the windowing algorithm to select wave packets instead of single phases: $P+pP+sPn$ and $S+sS+PcP$ on the vertical and radial components, and $S+sS$ on
-the transverse component.
-%Note that the surface-wave signals of this intermediate-depth event are not as clearly defined as those of the shallow event (Figure~\ref{fg:ERM_II_051502B}).
-
-Summary plots of window picks for event 200511211536A in the two
-period ranges \trange{6}{30} and \trange{24}{120} are shown in Figures~\ref{fg:200511211536A_T06_rs} and~\ref{fg:200511211536A_T24_rs} respectively.
-On the short-period window record sections, the windows picked by the algorithm form two main branches
-that correspond to $P$ and $S$ arrivals. Some $P$ arrivals are visible even on the transverse component (Figure~\ref{fg:200511211536A_T06_rs}g).
-The number and width of windows for each trace varies with epicentral distance.
-On the vertical and radial components
-(Figure~\ref{fg:200511211536A_T06_rs}ef),
-beyond a distance of 14\deg\ and after the $P$-arrival branch,
-there are two small branches corresponding to $pP$ and $sPn$, while
-after the $S$-arrival branch there is another branch
-corresponding to $sS$. The summary plot for the \trange{24}{120} period range shows a single branch of windows on the vertical component, that splits up into separate $P$- and $S$-wave packets at distances greater than 15\deg. The same split is visible on the radial component, but occurs earlier (around 10\deg), while the transverse component windows form a single branch containing the merged $S+sS$ arrivals.
-
-Comparison of the histograms in Figures~\ref{fg:200511211536A_T06_rs} and~\ref{fg:200511211536A_T24_rs} shows that windows selected on the \trange{24}{120} seismograms tend to have higher degrees of waveform similarity than those selected on the \trange{6}{30} records.
-$\Delta\tau$ values peak between $-5$~s and $0$~s in both period ranges, indicating that
-the synthetics are slower than the observed records.
-The particularly large peak at $-2$~s in the $\Delta\tau$ distribution
-of Figure~\ref{fg:200511211536A_T06_rs}c is probably due to
-the large number of Hi-net recordings that make up the
-short-period range records.
-The $\Delta\ln A$ distribution peaks at $\Delta\ln A\simeq0$
-for \trange{24}{120} (Figure~\ref{fg:200511211536A_T24_rs}d),
-indicating the amplitude of the synthetics matches the amplitude of the data
-at long periods. The peak at $\Delta\ln A\simeq-0.3$
-in Figure~\ref{fg:200511211536A_T06_rs}d indicates that, on average,
-the synthetics overestimate the amplitude of the
-observed waveforms by $30\%$ at short-periods. We cannot know at this stage
-if this anomaly is due to an overestimation short-period energy in the source spectra of the events,
-or to an underestimation of the seismic attenuation.
-
-Figure~\ref{fg:T06_rs}
-shows summary plots of the
-window pick statistics for the shallow (051502B), intermediate (200511211536A) and deep
-events (091502B) for the period range \trange{6}{30}. Notice the very large numbers of
-measurement windows picked due to the over 600
-Hi-net stations: 1243 windows for event 051502B, 1356 windows
-for event 200511211536A, and 1880 windows for
-event 091502B.
-Comparing the statistics for these three events, we see that
-the degree of similarity, $\mathrm{CC}$, improves with increasing event
-depth, implying that the representation
-of mantle structure is better than that of crustal structure
-in the initial model.
-The $\Delta\ln A$ distributions of these three events
-have similar shapes, with peaks in the
-range of $-0.5$ -- $-0.3.$
-However, the $\Delta\tau$ distributions have very different features:
-the shallow event (051502B) has a large peak
-at $-10$~s and another smaller peak at $8$~s; the intermediate-depth
-event (200511211536A) has sharp peak at $-2$~s; the deep event(091502B) has a more
-distributed $\Delta\tau$ in the range $-2$ to $-10$~s.
-Possible explanations for these large average
-time lags include an origin time error,
-and/or an overestimation of the seismic
-velocity at the source location.
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\subsection{Local tomography in Southern California}
-\label{sec:socal}
-
-Our last scenario is a local tomographic study of southern California. We apply the windowing algorithm to a set of 140 events within southern California, for which we have computed synthetic seismograms using the spectral-element method and a regional 3D crustal and upper mantle model \citep{KomatitschEtal2004}. This model contains three discontinuities: the surface topography (included in the mesh), the basement layer that separates the sedimentary basins from the bedrock, and the Moho, separating the lower crust from the upper mantle. The model includes several sedimentary basins, such as the Ventura basin, the Los Angeles basin, and the Salton trough \citep{KomatitschEtal2004,LovelyEtal2006}. The smooth 3D background velocity model used in \citet{KomatitschEtal2004} was determined by \citet{Hauksson2000}; we use an updated version provided by \citet{LinEtal2007}. The physical domain of the model is approximately 600~km by 500~km at the surface, and extends to a depth of 60~km. Our simulations of seismic waves are numerically accurate down to a period of 2~s.
-
-%The 140 events, with $M_w$ magnitudes between 3.5 and 5.5, were recorded between 1999 and 2007 and constitute a subset of the focal mechanisms presented by \citet{ClintonEtal2006}. The locations and origin times are primarily from \citet{LinEtal2008}, supplemented by the catalog of \citet{ThurberEtal2006} for events near Parkfield, and the catalog of \citet{McLarenEtal2008} for events near San Simeon. The Parkfield and San Simeon regions had $M_w > 6$ earthquakes within our time period of interest: 2004.09.28~$M_w$~6.0 (Parkfield) and 2003.12.22~$M_w$~6.5 (San Simeon). Aftershocks of both events are included in the dataset.
-The 140 events have $M_w$ magnitudes between 3.5 and 5.5 and were recorded between 1999 and 2007. The locations and origin times are primarily from \citet{LinEtal2008}, and the focal mechanisms are from \citet{ClintonEtal2006}, \citet{HardebeckShearer2003}, or \citet{YTan06}.
-
-We test the windowing code using three period ranges: \trange{6}{30}, \trange{3}{30}, and \trange{2}{30}. The parameters we use for the windowing code are listed in Table~\ref{tb:example_params}. Figures~\ref{fg:socal_CLC} and~\ref{fg:socal_FMP} show examples of the output from the windowing algorithm for event 9818433 listed in Table~\ref{tb:events} recorded at two different stations, while Figure~\ref{fg:socal_rs_T06} shows a summary plot for event 9983429 in the \trange{6}{30} period range.
-
-The windowing algorithm tends to identify five windows on each set of three-component \trange{6}{30} seismograms (Figures~\ref{fg:socal_CLC} and~\ref{fg:socal_rs_T06}): on the vertical and radial components the first window corresponds to the body-wave arrival and the second to the Rayleigh wave, while windows on the transverse component capture the Love wave.
-The \trange{2}{30}
- synthetic seismograms do not agree well with the observed seismograms, especially in the later part of the signal, leading to fewer picked windows. In Figure~\ref{fg:socal_CLC}c, only three windows are selected by the algorithm: the $P$ arrival recorded on the radial component, the $S$ arrival on the transverse component, and the Love-wave arrival on the transverse component. The $P$ arrival ($PmP$ or $Pn$) in fact appears on all three components on both data and synthetics. On the vertical component it is rejected because the cross-correlation value within the time window did not exceed the specified minimum value of 0.85 (Table~\ref{tb:example_params}). On the transverse component it does not have a large enough signal-to-noise ratio to be picked, but it is evident as a small peak at 36~s in the STA:LTA curve, and more conspicuous when zooming into the synthetics and data. The presence of the $P$ arrival on the transverse component highlights the possibility of measuring subtle phases that may be present in 3D synthetics.
-
-Figure~\ref{fg:socal_FMP} shows results for the same event as Figure~\ref{fg:socal_CLC}, but for a different station, FMP, situated 52~km from the event and within the Los Angeles basin. Comparison of the two figures highlights the characteristic resonance caused by the thick sediments within the basin. This resonance is beautifully captured by the transverse component synthetics (Figure~\ref{fg:socal_FMP}b, record T), thanks to the inclusion of the basin in the model \citep{KomatitschEtal2004}. In order to pick such long time windows with substantial frequency-dependent measurement differences, we are forced to lower the minimum cross-correlation value $\mathrm{CC}_0$ for the entire dataset (0.71 in Table~\ref{tb:example_params}) and increase $c_{4b}$ to capture the slow decay in the STA:LTA curves (Figure~\ref{fg:socal_FMP}b, record T). It is striking that although these arrivals look nothing like the energy packets typical for the global case, the windowing algorithm is still able to determine the proper start and end times for the windows. In Figure~\ref{fg:socal_FMP}c the windowing algorithm selects three short-period body-wave time windows with superb agreement between data and synthetics.
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Windowing Examples \label{sec:results}}
+
+We present a set of examples showing the results of the FLEXWIN algorithm
+applied to real data. These examples illustrate the robustness and flexibility of the
+algorithm. We have applied the algorithm to three
+tomographic scenarios, with very different geographical extents and distinct period ranges:
+long-period global tomography (\trange{50}{150}),
+regional tomography of the Japan subduction zone, down to 700~km (\trange{6}{120}), and
+regional tomography of southern California, down to 60~km (\trange{2}{40}).
+For each of these scenarios, we compare
+observed seismograms to spectral-element synthetics, using our
+algorithm to select time windows on the pairs of timeseries.
+
+The windowing algorithm
+itself has little prior knowledge of seismology, other than in the most general
+terms: it considers a seismogram to be a succession of seismic phases indicated
+by changes in amplitude and frequency of the signal with time; it is based upon
+the idea that the short-term to long-term average ratio STA:LTA is a good
+indicator of the arrival of such phases;
+it has a notion of the characteristics of an optimal set of data windows.
+All other prior information --- the frequency range to be considered, the
+portions of the seismogram to be excluded, the acceptable signal-to-noise
+ratios, the tolerance of dissimilarity between the observed and synthetic
+seismogram --- varies greatly between any two seismological studies. In order
+to ensure maximum flexibility of our windowing algorithm, all such
+scenario-dependent information is encapsulated in the tuning parameters of
+Table~\ref{tb:params}.
+
+We tuned the windowing algorithm separately for each of the three scenarios we present here, and we present examples based on the events listed in Table~\ref{tb:events}. Tuning parameter values for each scenario can be found in Table~\ref{tb:example_params}, while the functional forms of the time-dependent parameters can be found in Appendix~\ref{ap:user_fn}. Once tuned for a given scenario, the algorithm is applied to all its events without further modification.
+
+
+\subsection{Global tomography}
+\label{sec:globe}
+
+Our first scenario is a global scale, long-period tomographic study.
+We calculate spectral-element synthetic seismograms through an Earth model for
+which the mantle is given by the S20RTS model of \citet{RitsemaEtal2004},
+and the crust by the CRUST2.0 model of \citet{BassinEtal2000}.
+The degree-20 $S$-wave velocity model S20RTS defines isotropic perturbations to
+radially anisotropic PREM \citep{DziewonskiAnderson1981}; the SPECFEM3D implementation of S20RTS takes
+$P$-wave velocity anomalies from the degree-12 $P$-wave velocity model of \citet{RitsemaVanHeijst2002}.
+CRUST2.0 specifies a
+seven-layer crustal seismic velocity and density profile for each cell on a
+2\deg\ grid. The S20RTS+CRUST2.0 combination produces synthetics that are a
+good match to observed seismograms for periods longer than \trange{35}{40}. For our
+examples, we shall be working in the period range \trange{50}{150}.
+
+Here we discuss windowing results for shadow-zone seismograms of four earthquakes listed
+in Table~\ref{tb:events}: a shallow event in the Ryukyu Islands, Japan (101895B),
+a smaller magnitude shallow event in the
+Comoros region, between Mozambique and Madagascar (200808270646A),
+an intermediate depth event in northern Peru (050295B), and a strong
+deep event in northern Bolivia (060994A). We focus on shadow zone
+seismograms as these contain a large number of often poorly time-separated
+phases, and pose a greater windowing challenge than more commonly used
+teleseismic seismograms.
+
+Windowing results for these seismograms (one example per earthquake) are shown
+in Figures~\ref{fg:res_abkt}a,c and~\ref{fg:examples}a,c. The first observation
+we make when looking at these examples is that the synthetics match the data
+well, indicating that the Earth model S20RTS+CRUST2.0 provides a good 3D image
+of how the Earth is seen by \trange{50}{150} seismic waves. The fit is far from
+perfect, though, as is attested by the shape differences, time-lags and
+amplitude differences visible on many seismic phases; these indicate that there is
+room for improving the Earth model and possibly certain
+earthquake parameters even at these low frequencies.
+
+The second observation we make is that our algorithm has placed time windows
+around most of the significant features that stand out in the STA:LTA
+timeseries $E(t)$ and in the seismograms themselves, and that the window limits
+also seem to be sensibly placed. These windows were selected according to the
+purely signal processing algorithm described in the previous section, which has no
+knowledge of Earth structure or of seismic phases and their traveltime curves.
+In order to demonstrate the ability of such an Earth-blind algorithm to set
+windows around actual seismic phases, we have identified the
+seismic arrivals contained within the chosen data windows, using standard
+PREM-based traveltime curves. We have found that most of the features within
+the windows in Figures~\ref{fg:res_abkt}a,c and~\ref{fg:examples}a,c correspond
+to known seismic phases, which are listed in the
+corresponding figure captions. We have also traced the body-wave ray paths
+corresponding to these phases and show them in Figures~\ref{fg:res_abkt}b,d and~\ref{fg:examples}b,d;
+these ray path plots serve to illustrate the considerable
+amount of information contained in a single seismogram, even a long period
+seismogram, when all the usable seismic phases are considered. Fewer useable seismic phases are windowed for the smaller magnitude event in Figure~\ref{fg:res_abkt}c.
+
+Not all the features within a given seismogram are identifiable as seismic
+phases. For example, the second window in Figure~\ref{fg:examples}b seems to
+contain two features. When we look at periods shorter than 50~s, the first
+feature retains its character and is clearly identifiable as $sS_{\rm diff}$,
+while the second feature looses its character entirely and is more readily
+assimilated to a generic $S$ wave coda than to a distinct seismic phase.
+This feature is present in both observed and synthetic seismograms, and
+undoubtedly contains information. The particularity of our windowing algorithm
+is to treat such features as information, without trying to identify their
+sources. A scheme that permits the computation of
+sensitivity kernels for such features (e.g. the adjoint scheme), would allow measurements made
+on them to be interpreted and inverted correctly. Other methods of determining
+measurement sensitivities may have more difficulty dealing with them. These
+considerations illustrate the strong ties that exist between the selection,
+measurement and interpretation stages of any study using seismological data.
+
+We have described those seismic phases and other features in the seismograms
+that have been selected by our windowing algorithm. Equally important are the
+phases that have been rejected. Two such phases are $P_{\rm diff}$ and $S4$ on the
+vertical component seismogram in Figure~\ref{fg:res_abkt}a. We can identify
+the reasons for the rejection of these phases by comparing the selected time windows with the candidate windows at each stage in the rejection process
+(Figure~\ref{fg:win_rej_data}). The $P_{\rm diff}$ phase, though small on the
+long period seismogram, gives rise to a strong maximum on the $E(t)$ timeseries
+and therefore to at least one candidate window. Candidate windows
+containing $P_{\rm diff}$ disappear from Figure~\ref{fg:win_rej_data} at the
+${\rm SNR}_W$ based rejection stage, indicating that this phase was rejected
+for its low signal-to-noise ratio. The $S4$ phase also gives rise to a
+distinct maximum in $E(t)$, and to its own candidate window that is still
+present at the end of both window rejection stages (it corresponds to the
+fourth window from the right at the bottom of Figure~\ref{fg:win_rej_data}).
+As the $S4$ candidate and its neighbour the $S5$ candidate overlap, the
+algorithm has to choose between them using equation~(\ref{eq:score}). The fit
+to the shape of $S4$ is worse than that to $S5$, therefore the $S4$ window is
+discarded. It is helpful, when setting and tuning the values of the
+parameters in Table~\ref{tb:params}, to analyse the rejection and overlap
+resolution steps as we have done here for a number of representative
+seismograms, seeking to avoid the acceptance of unreasonable candidate windows,
+and to minimize the rejection of acceptable ones.
+
+A further appreciation of the windowing results is given by event-based
+summaries such as those in Figure~\ref{fg:composites}, which show at a glance
+the geographical path distribution of records containing acceptable windows,
+the distribution of $\mathrm{CC}$, $\Delta\tau$ and $\Delta\ln A$ values within the
+accepted time windows, and time-window record sections. Comparison of the
+summary plots for the shallow Ryukyu Islands event and the deep
+Bolivia event (Figure~\ref{fg:composites}b and~e respectively) shows that both
+have similar one-sided distributions of $\mathrm{CC}$ values, strongly biased towards
+the higher degrees of similarity $\mathrm{CC}>0.95$. The two events also have similar
+two-sided $\Delta\ln A$ distributions that peak at $\Delta\ln A\simeq0.25$,
+indicating that on average the synthetics underestimate the amplitude of the
+observed waveforms by 25\%. We cannot know at this stage if this
+anomaly is due to an underestimation of the seismic moments of the events, or to an
+overestimation of attenuation. The $\Delta\tau$ distributions for the two
+events are also two-sided. The shallow event $\Delta\tau$ values
+peak between 0 and 4~s, indicating that the synthetics are moderately faster
+than the observed records; the deep event $\Delta\tau$ distribution peaks at
+much higher time lags of 8--10~s. Possible explanations for these large average
+time lags include an origin time error, and/or an overestimation of the seismic
+velocity at the source location.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Regional tomography of the Japan subduction zone}
+\label{sec:japan}
+Our second scenario is a regional-scale tomographic study of the Japan subduction zone, using a set of local events within the depth range 0--600~km.
+The lateral dimensions of the domain are
+44$^\circ$(EW)$\times$33$^\circ$(NS) (108--152$^\circ$E
+and 18--51$^\circ$N).
+The initial model is constructed using the southeast Asia model of
+\cite{LebedevNolet2003} as the background model, with
+$P$-wave velocity anomalies added from
+a high-resolution Japan $P$-wave model \citep{ZhaoEtal1994}
+and $S$-wave velocity anomalies
+scaled to $P$ by a factor of 1.5 \citep{ChenEtal2007}.
+Two different crustal
+models are implemented in the spectral-element mesh: inside the region of the
+high-resolution model (32--45$^\circ$N, 130--145$^\circ$E
+and down to 500~km), the crustal model is derived from
+the arrival times of local shallow earthquakes \citep{ZhaoEtal1992};
+outside this region, the crustal model is CRUST2.0 \citep{BassinEtal2000}.
+
+We collected data for more than 200 events with $M_w$ 4.5--8 that
+occurred between 2000 and 2006. The source locations and focal
+mechanisms are the centroid-moment tensor (CMT) solutions.
+We used a total of 818 stations from three different networks
+(GSN, F-net and Hi-net): the 119 stations of the GSN and F-net
+provide broadband records,
+whereas the 699 Hi-net stations provide only high-frequency records.
+We use the one-chunk version of spectral-element code to calculate
+synthetic seismograms accurate at periods of $\sim$6~s and
+longer \citep{ChenEtal2007}, and present results for two period ranges:
+\trange{6}{30}, using all the records, and \trange{24}{120}, using the broadband records only.
+
+Figures~\ref{fg:KIS_BO_091502B} and \ref{fg:SHR_BO_200511211536A} show windowing results for two events at two different depths (Table~\ref{tb:events}): 091502B, 589.4~km deep, northeastern China; 200511211536A, 155~km deep, Kyushu, Japan. We have tuned the windowing algorithm using different sets of parameters for the two period ranges (see Table~\ref{tb:example_params}). In the period range \trange{24}{120}, the water level is raised after the surface-wave arrivals to exclude the later arrivals that are not sensitive to upper mantle structure. In the period range \trange{6}{30}, the water level is raised after the $S$-wave arrivals to exclude the surface-waves, as the current crustal model is not detailed enough to predict the short-period surface-waves.
+
+%Figures~\ref{fg:ERM_II_051502B}, \ref{fg:KIS_BO_091502B} and \ref{fg:SHR_BO_200511211536A} show windowing results for three events at different depths (Table~\ref{tb:events}): 051502B, 22.4~km deep, Taiwan; 091502B, 589.4~km deep, northeastern China; 200511211536A, 155~km deep, Kyushu, Japan. We have tuned the windowing algorithm using different sets of parameters for the two period ranges (see Table~\ref{tb:example_params}). In the period range \trange{24}{120}, the water level is raised after the surface-wave arrivals to exclude the later arrivals that are not sensitive to upper mantle structure. In the period range \trange{6}{30}, the water level is raised after the $S$-wave arrivals to exclude the surface-waves, as the current crustal model is not detailed enough to predict the short-period surface-waves.
+
+%For the shallow event beneath Taiwan recorded at station ERM (Figure~\ref{fg:ERM_II_051502B}), the observed and synthetic seismograms in \trange{24}{120} are similar in shape, and the algorithm picks not only the long-period $P$- and $S$-wave arrivals, but also the Rayleigh-wave on the vertical and radial components and the Love-wave on the transverse component (Figure~\ref{fg:ERM_II_051502B}b). In the short-period range (\trange{6}{30}), the synthetics are a poorer fit to the data than in the long-period range (\trange{24}{120}). The synthetics capture only the major $P$-wave arrival on the vertical component (Figure~\ref{fg:ERM_II_051502B}c), which is also the only arrival picked by the windowing algorithm. As the depth sensitivity of surface-waves is frequency dependent, the good fits at long periods (\trange{24}{120}) indicate that the starting model structure below the Moho is adequate for tomography.
+
+Figure~\ref{fg:KIS_BO_091502B} shows an example of window picks for a deep event
+beneath northeastern China (091502B) recorded at station KIS.
+%Compared to the shallow event above,
+The seismograms from this event are relatively simple, containing only two major body-wave arrivals ($P$ and $S$). The windowing algorithm's similarity criterion comes into play here, causing it
+not to pick the short-period $S$ arrival
+on the vertical component (Figure~\ref{fg:KIS_BO_091502B}c) as
+the distorted $S$-wave waveform of the data is quite
+different from the Gaussian shaped synthetics.
+The long-period $S$-wave arrival on the
+same component is selected due to higher data-synthetic
+waveform similarity (Figure~\ref{fg:KIS_BO_091502B}b).
+
+The records of the intermediate-depth event (200511211536A) recorded by station SHR (Figure~\ref{fg:SHR_BO_200511211536A}) contain more seismic phases
+than the previous two examples.
+On the vertical component of the short-period
+ seismogram (Figure~\ref{fg:SHR_BO_200511211536A}c), the $P$-wave
+arrives at $\sim$230~s, immediately followed by $pP$ and $sPn$,
+and the $S$-wave arrives at $\sim$420~s, followed by $sS$ and
+$PcP$. The windowing algorithm selects separate windows for the $P$, $sPn$, $S$ and $sS$ arrivals
+on the vertical component, and selects only the $P$ and $sPn$ arrivals on the radial component.
+In the period range \trange{24}{120} (Figure~\ref{fg:SHR_BO_200511211536A}b), the $P$ and $S$ waves merge with the arrivals that follow them, causing the windowing algorithm to select wave packets instead of single phases: $P+pP+sPn$ and $S+sS+PcP$ on the vertical and radial components, and $S+sS$ on
+the transverse component.
+%Note that the surface-wave signals of this intermediate-depth event are not as clearly defined as those of the shallow event (Figure~\ref{fg:ERM_II_051502B}).
+
+Summary plots of window picks for event 200511211536A in the two
+period ranges \trange{6}{30} and \trange{24}{120} are shown in Figures~\ref{fg:200511211536A_T06_rs} and~\ref{fg:200511211536A_T24_rs} respectively.
+On the short-period window record sections, the windows picked by the algorithm form two main branches
+that correspond to $P$ and $S$ arrivals. Some $P$ arrivals are visible even on the transverse component (Figure~\ref{fg:200511211536A_T06_rs}g).
+The number and width of windows for each trace varies with epicentral distance.
+On the vertical and radial components
+(Figure~\ref{fg:200511211536A_T06_rs}ef),
+beyond a distance of 13\deg\ and after the $P$-arrival branch,
+there are two small branches corresponding to $pP$ and $sPn$, while
+after the $S$-arrival branch there is another branch
+corresponding to $sS$. The summary plot for the \trange{24}{120} period range shows a single branch of windows on the vertical component, that splits up into separate $P$- and $S$-wave packets at distances greater than 15\deg. The same split is visible on the radial component, but occurs earlier (around 10\deg), while the transverse component windows form a single branch containing the merged $S+sS$ arrivals.
+
+Comparison of the histograms in Figures~\ref{fg:200511211536A_T06_rs} and~\ref{fg:200511211536A_T24_rs} shows that windows selected on the \trange{24}{120} seismograms tend to have higher degrees of waveform similarity than those selected on the \trange{6}{30} records.
+$\Delta\tau$ values peak between $-5$~s and $0$~s in both period ranges, indicating that
+the synthetics are slower than the observed records.
+The particularly large peak at $-2$~s in the $\Delta\tau$ distribution
+of Figure~\ref{fg:200511211536A_T06_rs}c is probably due to
+the large number of Hi-net recordings that make up the
+short-period range records.
+The $\Delta\ln A$ distribution peaks at $\Delta\ln A\simeq0$
+for \trange{24}{120} (Figure~\ref{fg:200511211536A_T24_rs}d),
+indicating the amplitude of the synthetics matches the amplitude of the data
+at long periods. The peak at $\Delta\ln A\simeq-0.2$
+in Figure~\ref{fg:200511211536A_T06_rs}d indicates that, on average,
+the synthetics overestimate the amplitude of the
+observed waveforms by $20\%$ at short-periods. We cannot know at this stage
+if this anomaly is due to an overestimation short-period energy in the source spectra of the events,
+or to an underestimation of the seismic attenuation.
+
+Figure~\ref{fg:T06_rs}
+shows summary plots of the
+window pick statistics for the shallow (051502B), intermediate (200511211536A) and deep
+events (091502B) for the period range \trange{6}{30}. Notice the very large numbers of
+measurement windows picked due to the over 600
+Hi-net stations: 1361 windows for event 051502B, 1519 windows
+for event 200511211536A, and 2099 windows for
+event 091502B.
+Comparing the statistics for these three events, we see that
+the degree of similarity, $\mathrm{CC}$, improves with increasing event
+depth, implying that the representation
+of mantle structure is better than that of crustal structure
+in the initial model.
+The $\Delta\ln A$ distributions of these three events
+have similar shapes, with peaks in the
+range of $-0.5$ -- $0$
+However, the $\Delta\tau$ distributions have very different features:
+the shallow event (051502B) has a large peak
+at $-9$~s and another smaller peak at $8$~s; the intermediate-depth
+event (200511211536A) has sharp peak at $-2$~s; the deep event(091502B) has a more
+distributed $\Delta\tau$ in the range $-2$ to $-10$~s.
+Possible explanations for these large average
+time lags include an origin time error,
+and/or an overestimation of the seismic
+velocity at the source location.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Local tomography in Southern California}
+\label{sec:socal}
+
+Our last scenario is a local tomographic study of southern California. We apply the windowing algorithm to a set of 140 events within southern California, for which we have computed synthetic seismograms using the spectral-element method and a regional 3D crustal and upper mantle model \citep{KomatitschEtal2004}. This model contains three discontinuities: the surface topography (included in the mesh), the basement layer that separates the sedimentary basins from the bedrock, and the Moho, separating the lower crust from the upper mantle. The model includes several sedimentary basins, such as the Ventura basin, the Los Angeles basin, and the Salton trough \citep{KomatitschEtal2004,LovelyEtal2006}. The smooth 3D background velocity model used in \citet{KomatitschEtal2004} was determined by \citet{Hauksson2000}; we use an updated version provided by \citet{LinEtal2007}. The physical domain of the model is approximately 600~km by 500~km at the surface, and extends to a depth of 60~km. Our simulations of seismic waves are numerically accurate down to a period of 2~s.
+
+%The 140 events, with $M_w$ magnitudes between 3.5 and 5.5, were recorded between 1999 and 2007 and constitute a subset of the focal mechanisms presented by \citet{ClintonEtal2006}. The locations and origin times are primarily from \citet{LinEtal2008}, supplemented by the catalog of \citet{ThurberEtal2006} for events near Parkfield, and the catalog of \citet{McLarenEtal2008} for events near San Simeon. The Parkfield and San Simeon regions had $M_w > 6$ earthquakes within our time period of interest: 2004.09.28~$M_w$~6.0 (Parkfield) and 2003.12.22~$M_w$~6.5 (San Simeon). Aftershocks of both events are included in the dataset.
+The 140 events have $M_w$ magnitudes between 3.5 and 5.5 and were recorded between 1999 and 2007. The locations and origin times are primarily from \citet{LinEtal2008}, and the focal mechanisms are from \citet{ClintonEtal2006}, \citet{HardebeckShearer2003}, or \citet{YTan06}.
+
+We test the windowing code using three period ranges: \trange{6}{30}, \trange{3}{30}, and \trange{2}{30}. The parameters we use for the windowing code are listed in Table~\ref{tb:example_params}. Figures~\ref{fg:socal_CLC} and~\ref{fg:socal_FMP} show examples of the output from the windowing algorithm for event 9818433 listed in Table~\ref{tb:events} recorded at two different stations, while Figure~\ref{fg:socal_rs_T06} shows a summary plot for event 9983429 in the \trange{6}{30} period range.
+
+The windowing algorithm tends to identify five windows on each set of three-component \trange{6}{30} seismograms (Figures~\ref{fg:socal_CLC} and~\ref{fg:socal_rs_T06}): on the vertical and radial components the first window corresponds to the body-wave arrival and the second to the Rayleigh wave, while windows on the transverse component capture the Love wave.
+The \trange{2}{30}
+ synthetic seismograms do not agree well with the observed seismograms, especially in the later part of the signal, leading to fewer picked windows. In Figure~\ref{fg:socal_CLC}c, only three windows are selected by the algorithm: the $P$ arrival recorded on the radial component, the $S$ arrival on the transverse component, and the Love-wave arrival on the transverse component. The $P$ arrival ($PmP$ or $Pn$) in fact appears on all three components on both data and synthetics. On the vertical component it is rejected because the cross-correlation value within the time window did not exceed the specified minimum value of 0.85 (Table~\ref{tb:example_params}). On the transverse component it does not have a large enough signal-to-noise ratio to be picked, but it is evident as a small peak at 36~s in the STA:LTA curve, and more conspicuous when zooming into the synthetics and data. The presence of the $P$ arrival on the transverse component highlights the possibility of measuring subtle phases that may be present in 3D synthetics.
+
+Figure~\ref{fg:socal_FMP} shows results for the same event as Figure~\ref{fg:socal_CLC}, but for a different station, FMP, situated 52~km from the event and within the Los Angeles basin. Comparison of the two figures highlights the characteristic resonance caused by the thick sediments within the basin. This resonance is beautifully captured by the transverse component synthetics (Figure~\ref{fg:socal_FMP}b, record T), thanks to the inclusion of the basin in the model \citep{KomatitschEtal2004}. In order to pick such long time windows with substantial frequency-dependent measurement differences, we are forced to lower the minimum cross-correlation value $\mathrm{CC}_0$ for the entire dataset (0.71 in Table~\ref{tb:example_params}) and increase $c_{4b}$ to capture the slow decay in the STA:LTA curves (Figure~\ref{fg:socal_FMP}b, record T). It is striking that although these arrivals look nothing like the energy packets typical for the global case, the windowing algorithm is still able to determine the proper start and end times for the windows. In Figure~\ref{fg:socal_FMP}c the windowing algorithm selects three short-period body-wave time windows with superb agreement between data and synthetics.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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