[cig-commits] r11954 - seismo/3D/automeasure/latex
alessia at geodynamics.org
alessia at geodynamics.org
Mon May 12 05:56:10 PDT 2008
Author: alessia
Date: 2008-05-12 05:56:10 -0700 (Mon, 12 May 2008)
New Revision: 11954
Modified:
seismo/3D/automeasure/latex/abstract.tex
seismo/3D/automeasure/latex/appendix.tex
seismo/3D/automeasure/latex/discussion.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
Log:
Slight modifications to abstract. Moved first few paragraphs of methods section into the introduction. Moved a few sentences from summary to introduction. Fixed global section of appendix.
Modified: seismo/3D/automeasure/latex/abstract.tex
===================================================================
--- seismo/3D/automeasure/latex/abstract.tex 2008-05-11 23:23:03 UTC (rev 11953)
+++ seismo/3D/automeasure/latex/abstract.tex 2008-05-12 12:56:10 UTC (rev 11954)
@@ -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 requires a data selection method that maximizes the number of measurements made on each seismic record while avoiding seismic noise. The method must adapt 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. The method 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 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 requires a data selection method that maximizes the number of measurements made on each seismic record while avoiding seismic noise. Such a method must adapt 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. 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.
\end{abstract}
Modified: seismo/3D/automeasure/latex/appendix.tex
===================================================================
--- seismo/3D/automeasure/latex/appendix.tex 2008-05-11 23:23:03 UTC (rev 11953)
+++ seismo/3D/automeasure/latex/appendix.tex 2008-05-12 12:56:10 UTC (rev 11954)
@@ -3,9 +3,9 @@
\subsection{Global scenario\label{ap:user_global}}
-ALESSIA: Please explain $t_Q$ and $t_R$.
-%Below $t_Q$ and $t_R$ denote the arrival times of the Love wave and Rayleigh wave, resepctively, computed using a 1D spherically symmetric earth model.
+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.
+
\begin{align}
w_E(t) & =
\begin{cases}
Modified: seismo/3D/automeasure/latex/discussion.tex
===================================================================
--- seismo/3D/automeasure/latex/discussion.tex 2008-05-11 23:23:03 UTC (rev 11953)
+++ seismo/3D/automeasure/latex/discussion.tex 2008-05-12 12:56:10 UTC (rev 11954)
@@ -9,14 +9,14 @@
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.
-Finally, we note that the design of FLEXWIN is predicated 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 noise in the observed seismograms is described well, which is rare. Without an adequate description of the spectral characteristics of the noise, it is prudent to resort to the selection of time-windows even for waveform difference measurements.
+Finally, we note that the design of this algorithm is predicated 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 noise in the observed seismograms is described well, which is rare. Without an adequate description of the spectral characteristics of the noise, it is prudent to resort to the selection of time-windows even for waveform difference measurements.
%------------------------------
\section{Summary
\label{sec:summary}}
-The FLEXWIN algorithm is independent of input model, geographic scale and frequency range. Use of the FLEXWIN algorithm need not be limited to tomography studies, nor to studies using 3D synthetics. It is a configurable process that can be applied to different seismic scenarios by changing the parameters in Table~\ref{tb:params}. We have configured the algorithm separately for each of the tomographic scenarios presented in Section~\ref{sec:results}. The configuration process is data-driven: starting from the description of how each parameter influences the window selection (Section~\ref{sec:algorithm}), the user tunes the parameters using a representative subset of the full dataset until the algorithm produces an adequate set of windows, then applies the tuned algorithm to the full dataset. The choice of what makes an adequate set of windows remains subjective, as it depends strongly on the quality of the input model, the quality of the data, and the region of the Earth the tomographic inversion aims to constrain. We consider the algorithm to be correctly tuned when false positives (windows around undesirable features of the seismogram) are minimized, and true positives (window around desirable features) are maximized. For a given dataset, the set of tuned parameters (Table~\ref{tb:params}) and their user-defined time dependencies completely determine the window selection results. Finally, we envision that successive iterations of a particular tomographic model may require minor adjustments to the tuning parameters, as the fits improve between the synthetic and observed seismograms, permitting higher frequency information to be used.
+The FLEXWIN algorithm is independent of input model, geographic scale and frequency range. Its use need not be limited to tomography studies, nor to studies using 3D synthetics. It is a configurable process that can be applied to different seismic scenarios by changing the parameters in Table~\ref{tb:params}. We have configured the algorithm separately for each of the tomographic scenarios presented in Section~\ref{sec:results}. The configuration process is data-driven: starting from the description of how each parameter influences the window selection (Section~\ref{sec:algorithm}), the user tunes the parameters using a representative subset of the full dataset until the algorithm produces an adequate set of windows, then applies the tuned algorithm to the full dataset. The choice of what makes an adequate set of windows remains subjective, as it depends strongly on the quality of the input model, the quality of the data, and the region of the Earth the tomographic inversion aims to constrain. We consider the algorithm to be correctly tuned when false positives (windows around undesirable features of the seismogram) are minimized, and true positives (window around desirable features) are maximized. For a given dataset, the set of tuned parameters (Table~\ref{tb:params}) and their user-defined time dependencies completely determine the window selection results. Finally, we envision that successive iterations of a particular tomographic model may require minor adjustments to the tuning parameters, as the fits improve between the synthetic and observed seismograms, permitting higher frequency information to be used.
-The desire to study regions of detailed structure and to examine the effects of finite source processes leads seismology researchers to deal with increasingly complex seismic records. Furthermore, with increasing coverage and sampling rate, the available data becomes voluminous and challenging to manage. Our hope is that the FLEXWIN software package will become a standard seismological tool for picking time windows for measurements between complex synthetic and observed seismograms. In using this package, the onus would still be on the seismologist to tune the algorithm parameters so as to pick time-windows appropriate for each specific study target. For a given data-set and a given set of tuning parameters, the time-window picking is entirely reproducible. The automated and signal processing nature of the procedure should eliminate some of the human bias involved in picking measurement windows, while expediting the process of analyzing tens to hundreds of thousands of records.
+The desire to study regions of detailed structure and to examine the effects of finite source processes requires seismologists to deal with increasingly complex seismic records. Furthermore, with increasing coverage and sampling rate, the available data becomes voluminous and challenging to manage. In using the FLEXWIN package, the onus would still be on the seismologist to tune the algorithm parameters so as to pick time-windows appropriate for each specific study target. For a given data-set and a given set of tuning parameters, the time-window picking is entirely reproducible. The automated and signal processing nature of the procedure should eliminate some of the human bias involved in picking measurement windows, while expediting the process of analyzing tens to hundreds of thousands of records.
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 2008-05-11 23:23:03 UTC (rev 11953)
+++ seismo/3D/automeasure/latex/flexwin_paper.tex 2008-05-12 12:56:10 UTC (rev 11954)
@@ -31,7 +31,7 @@
\input{abstract}
-\pagebreak \input{introduction}
+\input{introduction}
\input{method}
\input{results}
\input{discussion}
Modified: seismo/3D/automeasure/latex/introduction.tex
===================================================================
--- seismo/3D/automeasure/latex/introduction.tex 2008-05-11 23:23:03 UTC (rev 11953)
+++ seismo/3D/automeasure/latex/introduction.tex 2008-05-12 12:56:10 UTC (rev 11954)
@@ -19,25 +19,24 @@
observable from this guess (a travel-time, a dispersion curve, a full
waveform); measure the difference (misfit) between the prediction and the
observation; improve on the original guess. This vague description of the
-tomographic problem hides a number of important assumptions, common to all
-tomographic approaches: firstly, that we are able to predict observables
+tomographic problem hides a number of important assumptions: firstly, that we are able to predict observables
correctly (we can solve the forward problem); secondly, that the misfit is due
to inadequacies in the values of our initial model parameters, and is not caused
by a misunderstanding of the physics, our solution to the forward problem, or
the presence of noise in the observations; lastly, that we know the
relation between the measured misfit and the model parameters
-(partial derivatives or sensitivity kernel).
+(in terms of partial derivatives or a sensitivity kernel).
In order to remain within a domain in which these assumptions are still valid,
it is common practice in tomography to work only with certain subsets of the
-available seismic data. Data choices are inextricably linked to tomographic method. For example, ray-based travel-time tomography deals
+available seismic data. The choices made in selecting these subsets are inextricably linked to the choice of tomographic method. For example, ray-based travel-time tomography deals
only with high frequency body wave arrivals, while great-circle
surface wave tomography takes pains to satisfy the path-integral approximation,
and only deals with surface waves that present no evidence of multipathing.
The
-emerging 3D-3D methods seem to be the best candidates for tomographic studies
-of regions with complex tectonics or structure. These methods take advantage of
-full wavefield simulations and numeric 3D finite-frequency kernels, the
+emerging 3D-3D tomographic methods seem to be the best candidates for studying
+ regions with complex 3D structure. These methods take advantage of
+full wavefield simulations and numeric finite-frequency kernels, the
accuracy of which releases tomographers from many of the data restrictions
required when using approximate forward modelling and simplified descriptions
of sensitivity. 3D-3D tomographic methods require their own specific data selection strategies.
@@ -47,18 +46,25 @@
interference of the wavefield used to generate the synthetic seismograms (the
direct wavefield) with an adjoint wavefield that obeys the same wave equation
as the direct wavefield, but with a source term which is derived from the
-misfit measurements. The computational cost of such kernel computations for use in seismic tomography depends only on the number of events, and not on the number of receivers nor on the number of measurements made. It is therefore to our advantage to use the greatest amount of information from each seismogram.
+misfit measurements. The computational cost of such kernel computations for use in seismic tomography depends only on the number of events, and not on the number of receivers nor on the number of measurements made. It is therefore to our advantage to make the greatest number of measurements on each seismogram.
+Our data selection strategy aims to define measurement time-windows that
+cover as much of a given seismogram as possible, whilst avoiding portions of
+the waveform that are dominated by noise. We define noise as any signal that
+cannot be modeled using physically reasonable values of the simulation
+parameters. It is important to note that by this definition what we consider
+to be noise varies with our simulation abilities. For example: body waves are
+noise for surface wave simulations; short period signals are noise for long
+period simulations; multiple scattering and coda signals are noise for most
+waveform simulation methods, including the spectral element method \citep{KomatitschEtal2002} we use for adjoint tomography.
+
The adjoint kernel calculation procedure allows us to measure and use for
tomographic inversion almost any part of the seismic signal. We do not
need to identify specific seismic phases, as the kernel will take care of
-defining the relevant sensitivities. However, with great power comes great
-responsibility: there is nothing in the adjoint method itself that prevents us
-from constructing an adjoint kernel from noise, thereby polluting our
+defining the relevant sensitivities. However, there is nothing in the adjoint method itself that prevents us
+from constructing an adjoint kernel from noise, and thereby polluting our
inversion process.
-In earthquake seismology, we consider to be noise
-any seismic energy that is not caused directly or indirectly by the earthquake
-being simulated. It is up to the data selection method to ensure such noise is
+It is up to the data selection method to ensure such noise is
avoided in the choice of the portions of the seismogram to be measured.
From a signal processing point of view, the simplest way to avoid serious
@@ -72,6 +78,29 @@
earthquakes. We have taken a tool used in this detection process ---
the long-term / short-term ratio --- and applied it to the definition of
time-windows around distinct seismic phases.
-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 propagation in Southern California, regional subduction-zone propagation in Japan, and global propagation. 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}.
+The choices made in time-window selection for tomography are
+interconnected with all other aspects of the tomographic inversion process,
+from the waveform simulation method (direct problem), through the choice of
+measurement, to the inversion itself which necessarily depends on the method
+of obtaining sensitivity kernels. For example, a glance at any plot of travel-time curves will reveal the presence of many
+time crossings and triplications. These indicate that seismic phases with
+often very different ray paths may arrive at similar times, resulting in
+composite arrivals on a seismogram. Whether or not such arrivals can be used
+in tomography depends on the choice of the forward simulation method (can
+this composite arrival be simulated?), on the type of measurement to be made
+(can the measurement method characterize the differences between observed
+and simulated signals accurately?), and on the capacity of the inverse method
+used to correctly account for the sensitivity of the composite phase. Most traditional tomographic methods tend to avoid using composite phases. Accurate sensitivity kernels for these phases can be calculated using adjoint methods
+\citep{LiuTromp2006}.
+ Their acceptance into adjoint tomography inversions depends on the
+choice of measurement method: waveform difference measurements can capture the
+full complexity of the difference between observed and simulated composite
+phases, but lead to highly non-linear tomographic inversions and are more
+sensitive to noise; measurements such as cross-correlation
+travel-times that lead to less non-linear tomographic inversions can deal with composite phases only when the simulated and
+observed signals are similar in shape.
+
+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.
\ No newline at end of file
Modified: seismo/3D/automeasure/latex/method.tex
===================================================================
--- seismo/3D/automeasure/latex/method.tex 2008-05-11 23:23:03 UTC (rev 11953)
+++ seismo/3D/automeasure/latex/method.tex 2008-05-12 12:56:10 UTC (rev 11954)
@@ -1,42 +1,5 @@
-\section{The selection algorithm\label{sec:algorithm}}
+\section{The selection algorithm\label{sec:algorithm}}
-Our selection strategy aims to define measurement time-windows that
-cover as much of a given seismogram as possible, whilst avoiding portions of
-the waveform that are dominated by noise. We define noise as any signal that
-cannot be modeled using physically reasonable values of the simulation
-parameters. It is important to note that by this definition what we consider
-to be noise varies with our simulation abilities. For example: body waves are
-noise for surface wave simulations; short period signals are noise for long
-period simulations; multiple scattering and coda signals are noise for most
-waveform simulation methods, though their intercorrelation can yield
-information, notably on surface wave group velocity dispersion \citep{CampilloPaul2003}.
-
-A glance at any plot of travel-time curves will reveal the presence of many
-time crossings and triplications. These indicate that seismic phases with
-often very different ray paths may arrive at similar times, resulting in
-composite arrivals on a seismogram. Whether or not such arrivals can be used
-in tomography depends on the choice of the forward simulation method (can
-this composite arrival be simulated?), on the type of measurement to be made
-(can the measurement method characterize the differences between observed
-and simulated signals accurately?), and on the capacity of the inverse method
-used to correctly account for the sensitivity of the composite phase. Most traditional tomographic methods tend to avoid using composite phases. Accurate sensitivity kernels for these phases can be calculated using adjoint methods
-\citep{LiuTromp2006}.
- Their acceptance into adjoint tomography inversions depends on the
-choice of measurement method: waveform difference measurements can capture the
-full complexity of the difference between observed and simulated composite
-phases, but lead to highly non-linear tomographic inversions and are more
-sensitive to noise; measurements such as cross-correlation
-travel-times that lead to less non-linear tomographic inversions can deal with composite phases only when the simulated and
-observed signals are similar in shape.
-
-These considerations illustrate how the choices made in time-window selection are
-interconnected with all other aspects of the tomographic inversion process,
-from the waveform simulation method (direct problem), through the choice of
-measurement, to the inversion itself which necessarily depends on the method
-of obtaining sensitivity kernels.
-
-% Therefore, we have built considerable flexibility into our windowing scheme, enabling it to function under a great variety of tomographic scenarios.
-
Our algorithm, called FLEXWIN to reflect its FLEXibility in picking time WINdows for measurement, operates on pairs of
observed and synthetic single component seismograms. There is no restriction
on the type of simulation used to generate the synthetics, though realistic
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