[cig-commits] r12026 - seismo/3D/automeasure/latex
alessia at geodynamics.org
alessia at geodynamics.org
Sun May 25 05:03:33 PDT 2008
Author: alessia
Date: 2008-05-25 05:03:33 -0700 (Sun, 25 May 2008)
New Revision: 12026
Modified:
seismo/3D/automeasure/latex/abstract.tex
seismo/3D/automeasure/latex/acknowledgements.tex
seismo/3D/automeasure/latex/appendix.tex
seismo/3D/automeasure/latex/def_base.tex
seismo/3D/automeasure/latex/discussion.tex
seismo/3D/automeasure/latex/figures_paper.tex
seismo/3D/automeasure/latex/flexwin_paper.pdf
seismo/3D/automeasure/latex/flexwin_paper.tex
seismo/3D/automeasure/latex/introduction.tex
seismo/3D/automeasure/latex/method.tex
seismo/3D/automeasure/latex/results.tex
Log:
With Jeoren's modifications
Modified: seismo/3D/automeasure/latex/abstract.tex
===================================================================
--- seismo/3D/automeasure/latex/abstract.tex 2008-05-25 11:56:50 UTC (rev 12025)
+++ seismo/3D/automeasure/latex/abstract.tex 2008-05-25 12:03:33 UTC (rev 12026)
@@ -1,3 +1,3 @@
\begin{abstract}
-We present an algorithm for the automated selection of time windows on pairs of observed and synthetic seismograms. The algorithm was designed specifically to automate window selection and measurement for adjoint tomography studies, but is sufficiently flexible to be adapted to most tomographic applications and seismological scenarios. Adjoint tomography utilizes 3D wavefield simulations that capture complex phases that do not exist in 1D simulations or traditional travel-time curves. It therefore needs a data selection method that maximizes the number of measurements made on each seismic record while avoiding seismic noise. It must also be automated in order to adapt to changes in the synthetic seismograms after each iteration of the tomographic inversion. These considerations led us to favor a signal processing approach to the time-window selection problem, and to the development of the FLEXWIN algorithm we present here. We illustrate the algorithm using datasets from three distinct regions: the full Earth, the Japan subduction zone, and the southern California crust.
+We present an algorithm for the automated selection of time windows on pairs of observed and synthetic seismograms. The algorithm was designed specifically to automate window selection and measurement for adjoint tomography studies, but is sufficiently flexible to be adapted to most tomographic applications and seismological scenarios. Adjoint tomography utilizes 3D wavefield simulations that capture complex phases that do not necessarily exist in 1D simulations or traditional travel-time curves. It therefore needs a data selection method that maximizes the number of measurements made on each seismic record while avoiding seismic noise. It must also be automated in order to adapt to changes in the synthetic seismograms after each iteration of the tomographic inversion. These considerations led us to favor a signal processing approach to the time-window selection problem, and to the development of the FLEXWIN algorithm we present here. We illustrate the algorithm using datasets from three distinct regions: the entire globe, the Japan subduction zone, and southern California.
\end{abstract}
Modified: seismo/3D/automeasure/latex/acknowledgements.tex
===================================================================
--- seismo/3D/automeasure/latex/acknowledgements.tex 2008-05-25 11:56:50 UTC (rev 12025)
+++ seismo/3D/automeasure/latex/acknowledgements.tex 2008-05-25 12:03:33 UTC (rev 12026)
@@ -1 +1,8 @@
\section*{Acknowledgements}
+This is contribution No.~?? of the Division of Geological
+\& Planetary Sciences (GPS) of the California Institute of Technology.
+We acknowledge support by the
+National Science Foundation under grant EAR-0711177.
+The numerical simulations for this research were performed
+on the GPS Dell cluster.
+
Modified: seismo/3D/automeasure/latex/appendix.tex
===================================================================
--- seismo/3D/automeasure/latex/appendix.tex 2008-05-25 11:56:50 UTC (rev 12025)
+++ seismo/3D/automeasure/latex/appendix.tex 2008-05-25 12:03:33 UTC (rev 12026)
@@ -4,44 +4,44 @@
\subsection{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, we raise the water level on the STA:LTA waveform and impose stricter criteria on the waveform similarity after the approximate end of the surface wave arrivals. We allow greater flexibility in cross-correlation time lag $\Delta\tau_0$ for intermediate depth and deep earthquakes.
+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, we raise the water level on the STA:LTA waveform and impose stricter criteria on the waveform similarity after the approximate end of the surface wave arrivals. We allow greater flexibility in cross-correlation time lag $\Delta\tau_0$ for intermediate depth and deep earthquakes.
-
+We use the following parameters:
\begin{align}
w_E(t) & =
\begin{cases}
- w_E \text{$t \leq t_R$} \\
- 2 w_E \text{$t > t_R$}
+ 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{$t > t_R$}
+ r_0 & \text{$t \leq t_R$}, \\
+ 10r_0 & \text{$t > t_R$} ,
\end{cases}
\\
-CC_0(t) & =
+\mathrm{CC}_0(t) & =
\begin{cases}
- CC_0 & \text{$t \leq t_R$} \\
- 0.9 CC_0 & \text{$t_Q < t \leq t_R$} \\
- 0.95 & \text{$t > t_R$}
+ \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{$t > t_R$}
+ \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}
+ 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{$t > t_R$}
+ \Delta \ln A_0 & \text{$t \leq t_R$}, \\
+ \Delta \ln A_0/3 & \text{$t > t_R$} .
\end{cases}
\end{align}
@@ -57,9 +57,9 @@
\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{$t > t_{R1}$}
+ 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}
@@ -68,9 +68,9 @@
\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{$t > t_S$}
+ 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}
@@ -78,9 +78,9 @@
\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}
+ 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}
%--------------------------
@@ -88,29 +88,29 @@
\pagebreak
\subsection{Southern California scenario\label{ap:user_socal}}
-Below $t_P$ 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 \citep{Wald95}. The start and finish 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 computed from the formulas in \cite{KomatitschEtal2004}. The source-receiver distance (in km) is denoted by $\Delta$.
+Below $t_P$ 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 \citep{Wald95}. The start and finish 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 computed from the formulas in \cite{KomatitschEtal2004}. The source-receiver distance (in km) is denoted by $\Delta$.
For the \trange{6}{40} data, we 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{$t > t_{R1}$}
+ 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}
\\
-r_0(t) & = r_0
+r_0(t) & = r_0,
\\
-CC_0(t) & = CC_0
+\mathrm{CC}_0(t) & = \mathrm{CC}_0,
\\
\Delta\tau_0(t) & =
\begin{cases}
- 3.0 + \Delta/80.0 & \text{$t \le t_{R0}$} \\
- 3.0 + \Delta/50.0 & \text{$t > t_{R0}$}
+ 3.0 + \Delta/80.0 & \text{$t \le t_{R0}$}, \\
+ 3.0 + \Delta/50.0 & \text{$t > t_{R0}$},
\end{cases}
\\
-\Delta \ln A_0(t) & = \Delta \ln A_0
+\Delta \ln A_0(t) & = \Delta \ln A_0 .
\end{align}
For the \trange{2}{40} data, we avoid selecting surface-wave arrivals, and therefore we make the modifications
@@ -118,12 +118,12 @@
\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{$t > t_S$}
+ 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
+\Delta\tau_0(t) & = \Delta\tau_0.
\end{align}
%--------------------------
Modified: seismo/3D/automeasure/latex/def_base.tex
===================================================================
--- seismo/3D/automeasure/latex/def_base.tex 2008-05-25 11:56:50 UTC (rev 12025)
+++ seismo/3D/automeasure/latex/def_base.tex 2008-05-25 12:03:33 UTC (rev 12026)
@@ -27,3 +27,4 @@
\def\degcpkm{${\rm ^{\circ}C\; km}^{-1}$}
\newcommand{\trange}[2]{\mbox{{#1}--{#2}~s}}
+\newcommand{\rmd}{\mathrm{d}}
Modified: seismo/3D/automeasure/latex/discussion.tex
===================================================================
--- seismo/3D/automeasure/latex/discussion.tex 2008-05-25 11:56:50 UTC (rev 12025)
+++ seismo/3D/automeasure/latex/discussion.tex 2008-05-25 12:03:33 UTC (rev 12026)
@@ -2,17 +2,17 @@
\label{sec:discuss}
The window selection algorithm we describe in this paper was designed to solve the problem of automatically picking windows for tomographic problems, specifically for 3D-3D adjoint tomography as described by \cite{TrompEtal2005} and \cite{TapeEtal2007}.
-Once the time windows are picked, the user is faced with choosing a type of measurement within each time window, for example, waveform difference, cross-correlation time-lags, multi-taper phase and amplitude anomalies.
-The specificity of adjoint methods is to turn measurements of the differences between observed and synthetic waveforms into adjoint sources that are subsequently used to determine the sensitivity kernels of the measurements themselves to the Earth model parameters. The manner in which the adjoint source is created is specific to each type of measurement, but once formulated can be applied indifferently to any part of the seismogram. Adjoint methods have been used to calculate kernels of various body and surface-wave phases with respect to isotropic elastic parameters and interface depths \citep{LiuTromp2006}, and with respect to anisotropic elastic parameters \citep{SieminskiEtal2007a,SieminskiEtal2007b}. Adjoint methods allow us to calculate kernels for each and every wiggle on a given seismic record, thereby giving access to virtually all the information contained within.
+Once the time windows are picked, the user is faced with choosing a type of measurement within each time window, for example, waveform differences, cross-correlation time-lags, multi-taper phase and amplitude anomalies.
+The specificity of adjoint methods is to turn measurements of the differences between observed and synthetic waveforms into adjoint sources that are subsequently used to determine the sensitivity kernels of the measurements themselves to the Earth model parameters. The manner in which the adjoint source is created is specific to each type of measurement, but once formulated can be applied indifferently to any part of the seismogram. Adjoint methods have been used to calculate kernels of various body- and surface-wave phases with respect to isotropic elastic parameters and interface depths \citep{LiuTromp2006}, and with respect to anisotropic elastic parameters \citep{SieminskiEtal2007a,SieminskiEtal2007b}. Adjoint methods allow us to calculate kernels for each and every wiggle on a given seismic record, thereby giving access to virtually all the information contained within.
It is becoming clear, as more finite-frequency tomography models are published, that better kernels on their own are not the answer to the problem of improving the resolution of tomographic studies. \cite{TrampertSpetzler2006} and \cite{BoschiEtal2007} investigate the factors limiting the quality of finite-frequency tomography images, and conclude that incomplete and inhomogeneous data coverage limit in practice the improvement in resolution that accurate finite-frequency kernels can provide. The current frustration with the data-induced limitations to the improvements in wave-propagation theory is well summarized by \cite{Romanowicz2008}. The ability of adjoint methods to deal with all parts of the seismogram indifferently means we can incorporate more information from each seismogram into a tomographic problem, thereby improving data coverage.
The computational cost of constructing an adjoint kernel is independent of the number of time windows on each seismogram we choose to measure, and also of the number of records of a given event we choose to work with. It is therefore to our advantage to make measurements on as many records as possible, while covering as much as possible of each record. There are, however, certain limits we must be aware of. As mentioned in the introduction, there is nothing in the adjoint method itself that prevents us from constructing a kernel from noise-dominated portions of the data. As the purpose of 3D-3D tomography is to improve the fine details of Earth models, it would be counterproductive to pollute the inversion process with such kernels.
-The use of adjoint methods for tomography requires a method of selecting and windowing seismograms that avoids seismic noise while at the same time extracting as much information as possible from the signals. The method must be automated in order to adapt to the changing synthetic seismograms at each iteration of the tomographic inversion. The method must also be adaptable to the features that exist in the seismograms themselves, because 3D wavefield simulations are able to synthesize phases that do not exist in 1D simulations or traditional travel-time curves. These considerations led us to favor a signal processing approach to the problem of data selection, approach which in turn led to the development of the FLEXWIN algorithm we have presented here.
+The use of adjoint methods for tomography requires a strategy for selecting and windowing seismograms that avoids seismic noise while at the same time extracting as much information as possible from the signals. The method must be automated in order to adapt to the changing synthetic seismograms at each iteration of the tomographic inversion. The method must also be adaptable to the features that exist in the seismograms themselves, because 3D wavefield simulations are able to synthesize phases that do not exist in 1D simulations or traditional travel-time curves. These considerations led us to favor a signal processing approach to the problem of data selection, an approach which in turn led to the development of the FLEXWIN algorithm we have presented here.
Finally, we note that the design of this algorithm is based on the desire {\em not} to use the entire time series of each event when making a measurement between data and synthetics. If one were to simply take the waveform difference between two time series, then there would be no need for selecting time windows of interest. However, this ideal approach \citep[e.g.,][]{GauthierEtal1986} may only work in real applications if the
-statistical properties of the noise is well known, which is rare.
+statistical properties of the noise are well known, which is rare.
%noise in the observed seismograms is described well, which is rare.
Without an adequate description of the noise, it is prudent to resort to the selection of time windows even for waveform difference measurements.
Modified: seismo/3D/automeasure/latex/figures_paper.tex
===================================================================
--- seismo/3D/automeasure/latex/figures_paper.tex 2008-05-25 11:56:50 UTC (rev 12025)
+++ seismo/3D/automeasure/latex/figures_paper.tex 2008-05-25 12:03:33 UTC (rev 12026)
@@ -13,7 +13,7 @@
$r_{P,A}$ & 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 \\
-$CC_0(t)$ & acceptance level for normalized cross-correlation\\
+$\mathrm{CC}_0(t)$ & 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 \\
\hline
@@ -23,7 +23,7 @@
$c_2$ & 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 \\
-$w_{CC}\quad w_{\rm len}\quad w_{\rm nwin}$ & for selection of best non-overlapping window combination \\
+$w_{\mathrm{CC}}\quad w_{\rm len}\quad w_{\rm nwin}$ & for selection of best non-overlapping window combination \\
\hline
\end{tabular}
\caption{\label{tb:params}
@@ -75,7 +75,7 @@
$r_{P,A}$ & 3.5, 3.0 & 3.5, 3.0 & 3.5, 3.0 & 3.5, 3.0 & 3.5, 2.5 \\
$r_0$ & 2.5 & 1.5 & 3.0 & 2.5 & 4.0 \\
$w_E$ & 0.08 & 0.10 & 0.12 & 0.22 & 0.07 \\
-$CC_0$ & 0.85 & 0.70 & 0.70 & 0.74 & 0.85 \\
+$\mathrm{CC}_0$ & 0.85 & 0.70 & 0.70 & 0.74 & 0.85 \\
$\Delta\tau_0$ & 15 & 12.0 & 3.0 & 3.0 & 2.0 \\
$\Delta\ln{A}_0$& 1.0 & 1.0 & 1.0 & 1.5 & 1.0 \\
\hline
@@ -84,7 +84,7 @@
$c_2$ & 0.3 & 0.0 & 1.0 & 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 \\
$c_{4a,b}$ & 3.0, 10.0 & 3.0, 25.0 & 3.0, 12.0 & 2.5, 12.0 & 2.0, 6.0 \\
-$w_{CC}, w_{\rm len}, w_{\rm nwin}$
+$w_{\mathrm{CC}}, w_{\rm len}, w_{\rm nwin}$
& 1, 1, 1 & 1, 1, 1 & 1, 1, 1 & 1, 0, 0 & 1, 0, 0.5 \\
\hline
\end{tabular}
@@ -182,7 +182,7 @@
Time dependent fit based criteria
for the 050295B event recorded at ABKT. The time-dependence of these criteria
is given by the formulae in Appendix~\ref{ap:user_global}. The lower limit on
-acceptable cross-correlation value, $CC_0$ (solid line), is
+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,
@@ -229,10 +229,10 @@
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).
+(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).
+(d)~Body-wave ray paths corresponding to data windows in~(c).
}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -242,7 +242,7 @@
\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 $CC$, time-lag $\tau$ and amplitude ratio $\Delta \ln A$; these give information about systematic trends in time shift and amplitude scaling.
+(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}.
}
@@ -275,8 +275,8 @@
\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 ($33.87$\degN, $135.89$\degE, $\Delta=11.79$\deg).
-(a)~Event and station map: event is 091502B indicated by the beach ball with the
-CMT focal mechanism, station KIS is marked as red triangles and all the other stations
+(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.
(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.
@@ -291,12 +291,12 @@
\caption{\label{fg:SHR_BO_200511211536A}
Window selection results for event 20051121536A from Table~\ref{tb:events} recorded at station SHR ($44.06$\degN, $144.99$\degE, $\Delta=17.47$\deg).
(a)~Event and station map: event 20051121536A is indicated by the beach ball with the
-CMT focal mechanism, station SHR is marked as red triangles and all the other stations
+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.
(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 corresponding low-frequency band-passed filtered version (b) has longer record length (800~s).
+Note that the corresponding low-frequency band-passed filtered version (b) has longer record length (800~s).
}
\end{figure}
@@ -307,7 +307,7 @@
\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 $CC$, time-lag $\tau$ and amplitude ratio $\Delta \ln A$.
+(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}
@@ -402,7 +402,7 @@
\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}{40}.
(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 $CC$, time-lag $\tau$ and amplitude ratio $\Delta \ln A$.
+(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.
}
Modified: seismo/3D/automeasure/latex/flexwin_paper.pdf
===================================================================
(Binary files differ)
Modified: seismo/3D/automeasure/latex/flexwin_paper.tex
===================================================================
--- seismo/3D/automeasure/latex/flexwin_paper.tex 2008-05-25 11:56:50 UTC (rev 12025)
+++ seismo/3D/automeasure/latex/flexwin_paper.tex 2008-05-25 12:03:33 UTC (rev 12026)
@@ -18,14 +18,13 @@
\input{def_base}
-%\newcommand{\trange}[2]{\mbox{{#1}--{#2}~s}}
%=============================================
\begin{document}
%\title{An automated data-window selection algorithm for adjoint tomography}
\title{An automated time-window selection algorithm for seismic tomography}
-\author{Alessia Maggi, Carl Tape, Min Chen, Daniel Chao, Jeoren Tromp}
+\author{Alessia Maggi, Carl Tape, Min Chen, Daniel Chao, and Jeroen Tromp}
\date{}
\maketitle
@@ -36,7 +35,7 @@
\input{results}
\input{discussion}
%\input{conclusion}
-%\input{acknowledgements}
+\input{acknowledgements}
\pagebreak
\input{appendix}
\pagebreak
Modified: seismo/3D/automeasure/latex/introduction.tex
===================================================================
--- seismo/3D/automeasure/latex/introduction.tex 2008-05-25 11:56:50 UTC (rev 12025)
+++ seismo/3D/automeasure/latex/introduction.tex 2008-05-25 12:03:33 UTC (rev 12026)
@@ -1,8 +1,8 @@
\section{Introduction}
-Seismic tomography - the process of imaging the 3D structure of the Earth using
-seismic recordings - has been transformed by recent advances in methodology.
-Finite-frequency approaches are been used instead of ray-based approaches, and 3D reference models instead of 1D reference models.
+Seismic tomography --- the process of imaging the 3D structure of the Earth using
+seismic recordings --- has been transformed by recent advances in methodology.
+Finite-frequency approaches are being used instead of ray-based approaches, and 3D reference models instead of 1D reference models.
These transitions are motivated by a greater understanding of the volumetric sensitivity of
seismic measurements \citep{MarqueringEtal1999,ZhaoEtal2000,DahlenEtal2000} and by computational advances in the forward
modelling of seismic wave propagation in fully 3D media \citep{KomatitschVilotte1998,KomatitschEtal2002,CapdevilleEtal2003}.
@@ -30,8 +30,8 @@
available seismic data. The choices made in selecting these subsets are
inextricably linked to the assumptions made in the tomographic method. For example, ray-based
travel-time tomography deals
-only with high frequency body wave arrivals, while great-circle
-surface wave tomography must satisfy the path-integral approximation,
+only with high-frequency body wave arrivals, while great-circle
+surface-wave tomography must satisfy the path-integral approximation,
and only considers surface waves that present no evidence of multipathing.
In both these examples, a large proportion of the information contained within the seismograms goes to waste.
The emerging 3D-3D tomographic methods take advantage of
@@ -62,7 +62,7 @@
contains a distinct energy arrival, then require an adequate correspondence
between observed and synthetic waveforms within these windows. This selection paradigm is general, and can be applied to synthetic seismograms regardless of how they have been obtained. It is clear, however, that a synthetic seismogram obtained by 3D propagation through a good 3D Earth model will provide a better fit to the observed seismogram over a greater proportion of its length than will be the case for a more approximate synthetic seismogram.
-In order to the isolate changes in amplitude or frequency content susceptible of being
+In order to isolate changes in amplitude or frequency content potentially
associated with distinct energy arrivals, we need to analyse the character of the synthetic waveform itself. This analysis is similar to that used on observed waveforms
in automated phase detection algorithms for the routine location of
earthquakes. In designing our time-window selection algorithm, we have taken a tool used in this detection process ---
@@ -94,4 +94,4 @@
%These considerations on the acceptability of composite phases in tomographic inversions illustrate one of the major difficulties in defining a data selection strategy: the great range of choices open to the tomographer. We have therefore designed a configurable data selection process that can be adapted to different tomographic scenarios by tuning a handful of parameters (see Table~\ref{tb:params}). Although we have designed the algorithm for use in adjoint tomography, its inherent flexibility should make it useful in many data-selection applications.
-We have successfully applied our windowing algorithm, the details of which are described in Section~\ref{sec:algorithm}, to diverse seismological scenarios: local and near regional tomography in Southern California, regional subduction-zone tomography in Japan, and global tomography. We present examples from each of these scenarios in Section~\ref{sec:results}, and we discuss the use of the algorithm in the context of adjoint tomography in Section~\ref{sec:discuss}. We hope that the time-window selection algorithm we present here will become a standard tool in seismic tomography studies.
+We have successfully applied our windowing algorithm, the details of which are described in Section~\ref{sec:algorithm}, to diverse seismological scenarios: local and near regional tomography in Southern California, regional subduction-zone tomography in Japan, and global tomography. We present examples from each of these scenarios in Section~\ref{sec:results}, and we discuss the use of the algorithm in the context of adjoint tomography in Section~\ref{sec:discuss}.
Modified: seismo/3D/automeasure/latex/method.tex
===================================================================
--- seismo/3D/automeasure/latex/method.tex 2008-05-25 11:56:50 UTC (rev 12025)
+++ seismo/3D/automeasure/latex/method.tex 2008-05-25 12:03:33 UTC (rev 12026)
@@ -16,7 +16,7 @@
seismograms; {\em phase D:} resolution of preliminary window overlaps. The parameters that permit tuning of the
window selection towards a specific tomographic scenario are all contained in a
simple parameter file (see Table~\ref{tb:params}). More complexity and finer
-tuning can be obtained by rendering some of these parameters time dependent, via user defined functions that can depend on the source parameters (e.g. event location or depth).
+tuning can be obtained by rendering some of these parameters time dependent via user defined functions that can depend on the source parameters (e.g. event location or depth).
%----------------------
@@ -33,7 +33,7 @@
We apply minimal and identical pre-processing to both observed and synthetic
seismograms: band-pass filtering with a non-causal Butterworth
filter, whose
-short and long period corners we denote as $T_0$ and $T_1$ respectively.
+short and long period corners we denote by $T_0$ and $T_1$ respectively.
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.
All further references to ``seismograms'' in this paper will refer to these filtered waveforms.
@@ -46,8 +46,8 @@
${\rm SNR}_P = P_{\rm signal}/P_{\rm noise},$
where the time-normalized power in the signal and noise portions of the data are defined respectively by
\begin{align}
-P_{\rm signal} & = \frac{1}{t_E-t_A} \int_{t_A}^{t_E}d^2(t)dt, \\
-P_{\rm noise} & = \frac{1}{t_A-t_0} \int_{t_0}^{t_A}d^2(t)dt, \label{eq:noise}
+P_{\rm signal} & = \frac{1}{t_E-t_A} \int_{t_A}^{t_E}d^2(t)\,\,\rmd t, \\
+P_{\rm noise} & = \frac{1}{t_A-t_0} \int_{t_0}^{t_A}d^2(t)\,\,\rmd t, \label{eq:noise}
\end{align}
where $d(t)$ denotes the observed seismogram, $t_0$ is its start time, $t_A$ is
set to be slightly before the time of the first arrival, and $t_E$ is the end
@@ -77,7 +77,7 @@
series with timestep $\delta t$, calculate its short term average
$S(t_i)$ and its long term average $L(t_i)$ as follows,
\begin{align}
-S(t_i) & = C_S \; S(t_{i-1}) + e(t_i) \\
+S(t_i) & = C_S \; S(t_{i-1}) + e(t_i) , \\
L(t_i) & = C_L \; L(t_{i-1}) + e(t_i) ,
\end{align}
and obtain their ratio:
@@ -198,7 +198,7 @@
\begin{equation}
f(\Delta T) =
\begin{cases}
-c_{3a} & \text{ $\Delta T/T_0 \leq c_{3b}$} \\
+c_{3a} & \text{ $\Delta T/T_0 \leq c_{3b}$,} \\
c_{3a}\exp{[-(\Delta T/T_0-c_{3b})^2/c_{3b}^2]} & \text{ $\Delta T/T_0 > c_{3b}$.}
\end{cases}
\label{eq:sep}
@@ -206,7 +206,7 @@
If we take
as an example $c_{3a}=1$, this criterion leads to the automatic rejection of
windows containing a local maximum that is higher than the seed maximum; it also leads to the rejection of windows containing a local maximum that is
-lower than the seed maximum if it is also sufficiently distant in time from
+lower than the seed maximum if it is sufficiently distant in time from
$t_M$. This criterion allows us to distinguish unseparable phase groups from
distinct seismic phases that arrive close in time.
@@ -225,14 +225,14 @@
before their first local maximum, and on the right if they end later than
$c_{4b} T_0$ after their last local maximum (see Figure~\ref{fg:win_composite}d).
-Figures~\ref{fg:win_composite} and~\ref{fg:separation} illustrate the shape based
+Figures~\ref{fg:win_composite} and~\ref{fg:separation} illustrate the shape-based
rejection procedure (Phase B) on a schematic $E(t)$ time series. Each
successive criterion reduces the number of acceptable candidate windows. A
similar reduction occurs when this procedure is applied to real $E(t)$ time series, as shown
by the upper portion of Figure~\ref{fg:win_rej_data}.
\subsection{Phase C \label{sec:phaseC}}
-%{\bf User parameters: $CC_0(t)$, $\Delta\tau_0(t)$, $\Delta\ln{A}_0(t)$}
+%{\bf User parameters: $\mathrm{CC}_0(t)$, $\Delta\tau_0(t)$, $\Delta\ln{A}_0(t)$}
After having greatly reduced the number of candidate windows by rejection based
on the shape of the STA:LTA time series $E(t)$, we are now left with a set of
@@ -244,36 +244,35 @@
performed by most windowing schemes.
The quantities we use to define well-behavedness of data within a window are
-signal
-to noise ratio ${\rm SNR}_W$, normalised cross-correlation value between
-observed and synthetic seismograms $CC$,
+signal-to-noise ratio ${\rm SNR}_W$, normalised cross-correlation value between
+observed and synthetic seismograms $\mathrm{CC}$,
cross-correlation time lag $\Delta \tau$, and amplitude ratio $\Delta \ln
-A$. The signal to noise ratio for single windows is defined as an amplitude
+A$. The signal-to-noise ratio for single windows is defined as an amplitude
ratio, ${\rm SNR}_W=A_{\rm window}/A_{\rm noise}$, where $A_{\rm window}$ and
$A_{\rm noise}$ are the maximum absolute values of the observed seismogram $|d(t)|$ in the window
-and in the noise time-span respectively (see equation~\ref{eq:noise}). The cross-correlation value $CC$ is defined as the maximum value of the
-cross-correlation function ${\rm CC}={\rm max}[\Gamma(t^\prime)]$, where
+and in the noise time-span respectively (see equation~\ref{eq:noise}). The cross-correlation value $\mathrm{CC}$ is defined as the maximum value of the
+cross-correlation function $\mathrm{CC}={\rm max}[\Gamma(t)]$, where
\begin{equation}
-\Gamma(t^\prime) = \int s(t-t^\prime)d(t)dt,
+\Gamma(t) = \int s(t'-t)d(t')\,\rmd t',
\end{equation}
and
quantifies the similarity in shape between the $s(t)$ and $d(t)$
-waveforms. The time lag $\Delta \tau$ is defined as the value of $t^\prime$
+waveforms. The time lag $\Delta \tau$ is defined as the value of $t$
at which $\Gamma$ is maximal, and quantifies the delay in time between a
synthetic and observed phase arrival. The amplitude ratio $\Delta \ln A$ is
defined as the amplitude ratio between observed and synthetic
seismograms \citep{DahlenBaig2002}
\begin{equation}
-\Delta\ln{A} = \left[ \frac{\int d(t)^2 dt}{\int s(t)^2 dt} \right]^{1/2} - 1. \label{eq:dlnA_def}
+\Delta\ln{A} = \left[ \frac{\int d(t)^2 \,\rmd t}{\int s(t)^2 \,\rmd t} \right]^{1/2} - 1. \label{eq:dlnA_def}
\end{equation}
The limits that trigger rejection of windows based on the values of these four
-quantities are the time dependent parameters $r_0(t)$, $CC_0(t)$, $\Delta
+quantities are the time dependent parameters $r_0(t)$, $\mathrm{CC}_0(t)$, $\Delta
\tau_0(t)$ and $\Delta \ln A_0(t)$ in Table~\ref{tb:params}.
As for the STA:LTA water level $w_E(t)$ used in above, the functional form of
these parameters is defined by the user, and can depend on source and receiver
parameters such as epicentral distance and earthquake depth.
Figure~\ref{fg:criteria} shows the time
-dependence of $CC_0$ , $\Delta \tau_0$ and $\Delta \ln A_0$ for an example seismogram.
+dependence of $\mathrm{CC}_0$ , $\Delta \tau_0$ and $\Delta \ln A_0$ for an example seismogram.
We only accept candidate windows that satisfy all of the following:
\begin{align}
@@ -293,7 +292,7 @@
man-made), diffuse noise sources, or instrumental glitches.
\subsection{Phase D \label{sec:phaseD}}
-%{\em User parameters: $w_{CC}$, $w_{\rm len}$.}
+%{\em User parameters: $w_{\mathrm{CC}}$, $w_{\rm len}$.}
After having rejected candidate data windows that fail any of the shape or
similarity based criteria described above, we are left with a small number of
@@ -312,7 +311,7 @@
have passed all previous tests, that do not overlap with other windows in the set,
and that cover as much of the seismogram as possible. When choosing between
candidate windows, we favour those within which the
-observed and synthetic seismograms are most similar (high values of $CC$).
+observed and synthetic seismograms are most similar (high values of $\mathrm{CC}$).
Furthermore, should we have the choice between two short windows and a longer,
equally well-fitting one covering the same time-span, we may wish to favour
the longer window as this poses a stronger constraint on the tomographic inversion.
@@ -333,10 +332,10 @@
candidate windows, and scoring each subset on three criteria: length of
seismogram covered by the windows, average cross-correlation value for the windows,
and total number of windows. These criteria often work against each other. For
-example, a long window may have a lower $CC$ than two shorter ones, if the two
+example, a long window may have a lower $\mathrm{CC}$ than two shorter ones, if the two
short ones have different time lags $\Delta\tau$. An optimal weighting of the
three scores is necessary, and is controlled by the three weighting parameters
-$w_{CC}$, $w_{\rm len}$ and $w_{\rm nwin}$ in Table~\ref{tb:params}.
+$w_{\mathrm{CC}}$, $w_{\rm len}$ and $w_{\rm nwin}$ in Table~\ref{tb:params}.
As can be seen in Figure~\ref{fg:phaseD}, the generation of subsets is
facilitated by first grouping candidate windows such that no group overlaps
@@ -344,18 +343,18 @@
performed independently within each group. We score each non-overlapping
subset of windows within a group using the following three metrics:
\begin{align}
-S_{CC} &= \sum_i^{N_{\rm set}} CC_i / N_{\rm set},\\
-S_{\rm len} &= [\sum_i^{N_{\rm set}} t^e_i - t^s_i]/[t^e_g - t^s_g], \\
+S_{\mathrm{CC}} &= \sum_i^{N_{\rm set}} \mathrm{CC}_i / N_{\rm set},\\
+S_{\rm len} &= \left[\sum_i^{N_{\rm set}} t^e_i - t^s_i\right]/\left[t^e_g - t^s_g\right], \\
S_{\rm nwin} & = 1 - N_{\rm set}/N_{\rm group},
\end{align}
-where $CC_i$ is the cross-correlation value of the $i$th window in
+where $\mathrm{CC}_i$ is the cross-correlation value of the $i$th window in
the subset, $N_{\rm set}$ is the number of windows in the subset, $N_{\rm
group}$ is the number of windows in the group, and $t^s_i$, $t^e_i$, $t^s_g$
and $t^e_g$ are respectively the start and end times of the $i$th candidate
window in the set, and of the group itself. The three scores
are combined into one using the weighting parameters:
\begin{equation}
-S = \frac{w_{CC}S_{CC}+w_{\rm len}S_{\rm len}+w_{\rm nwin}S_{\rm nwin}}{w_{CC}+w_{\rm len}+w_{\rm nwin}}.
+S = \frac{w_{\mathrm{CC}}S_{\mathrm{CC}}+w_{\rm len}S_{\rm len}+w_{\rm nwin}S_{\rm nwin}}{w_{\mathrm{CC}}+w_{\rm len}+w_{\rm nwin}}.
\label{eq:score}
\end{equation}
The best subset of candidate windows within each group is the one with the
Modified: seismo/3D/automeasure/latex/results.tex
===================================================================
--- seismo/3D/automeasure/latex/results.tex 2008-05-25 11:56:50 UTC (rev 12025)
+++ seismo/3D/automeasure/latex/results.tex 2008-05-25 12:03:33 UTC (rev 12026)
@@ -5,7 +5,7 @@
algorithm. We have applied the algorithm to three
tomographic scenarios, with very different geographical extents and distinct period ranges:
a global tomography (\trange{50}{150}),
-a regional tomography of the Japanese subduction zone, down to 700~km (\trange{6}{120}), and
+a regional tomography of the Japan subduction zone, down to 700~km (\trange{6}{120}), and
a 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
@@ -75,8 +75,8 @@
the windows in Figures~\ref{fg:res_abkt}a 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 and
-~\ref{fg:examples}b,d; these ray path plots serve to illustrate the considerable
+corresponding to these phases and show them in Figures~\ref{fg:res_abkt}b 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.
@@ -86,7 +86,7 @@
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.
-Although this feature is not a seismic phase in the high frequency sense, it is
+Although this feature is not a seismic phase in the high-frequency sense, it is
nevertheless 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
@@ -107,7 +107,7 @@
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
+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}).
@@ -123,17 +123,17 @@
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 $CC$, $\Delta\tau$ and $\Delta\ln A$ values within the
+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 $CC$ values, strongly biased towards
-the higher degrees of similarity $CC>0.95$. The two events also have similar
+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 seismic moment of the events, or to an
-overestimation of the attenuation. The $\Delta\tau$ distributions for the two
+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
@@ -142,9 +142,9 @@
velocity at the source location.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\subsection{Regional tomography of the Japanese subduction zone}
+\subsection{Regional tomography of the Japan subduction zone}
\label{sec:japan}
-Our second scenario is a regional-scale tomographic study of the Japanese subduction zone, using a set of local events within the depth range 0--600~km.
+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).
@@ -165,13 +165,13 @@
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 GSN and F-net
-provide broadband records,
+(GSN, F-net and Hi-net): the 119 stations of the GSN and F-net
+provide broad-band 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.
+\trange{6}{30}, using all the records, and \trange{24}{120}, using the broad-band 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.
@@ -199,7 +199,7 @@
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 wavepackets instead of single phases: $P+pP+sPn$ and $S+sS+PcP$ on the vertical and radial components, and $S+sS$ on
+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}).
@@ -210,10 +210,10 @@
The number and width of windows for each trace varies with epicentral distance.
On the vertical and radial component
window record sections (Figure~\ref{fg:200511211536A_T06_rs}ef),
-beyond the distance of 14\deg\ and after the $P$-arrival branch
+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 $S$-wavepackets 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.
+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
@@ -229,30 +229,30 @@
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,
+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}
-show summary plots of the
-window picks statistics for the shallow event (051502B), intermediate (200511211536A) and deep
+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 $CC$ improves with increasing event
-depth, implying that the estimation
-of mantle structure is better than the estimation of crustal structure
+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.
+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.
+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
@@ -262,15 +262,15 @@
\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 150 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 basement surface is essential for simulating the resonance of seismic waves within sedimentary basins, such as the Ventura basin, the L.A. basin, and the Salton trough \citep{KomatitschEtal2004,LovelyEtal2006}. The smooth 3D background velocity model used in \citet{KomatitschEtal2004} was \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.
+Our last scenario is a local tomographic study of southern California. We apply the windowing algorithm to a set of 150 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 basement surface is essential for simulating the resonance of seismic waves within 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 150 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 150 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.
We test the windowing code using two period ranges: \trange{6}{40} and \trange{2}{40}. 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}{40} period range.
-The windowing algorithm tends to identify five windows on each set of three component longer-period 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 windowing algorithm tends to identify five windows on each set of three-component longer-period 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 shorter-period 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}e, only two windows are selected by the algorithm: a P arrival recorded on the radial component, and the combined S and Love-wave arrival on the transverse component. The P-wave arrival on the vertical component 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}).
-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}d, record T), thanks to the inclusion of the basement layer in the crustal 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 $CC_0$ for the entire dataset (0.74 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}d, 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}e the windowing algorithm selects three short-period body-wave time windows with superb agreement between data and 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}d, record T), thanks to the inclusion of the basement layer in the crustal 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 (0.74 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}d, 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}e the windowing algorithm selects three short-period body-wave time windows with superb agreement between data and synthetics.
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