[cig-commits] r13301 - seismo/3D/ADJOINT_TOMO/flexwin/latex
alessia at geodynamics.org
alessia at geodynamics.org
Thu Nov 13 14:32:41 PST 2008
Author: alessia
Date: 2008-11-13 14:32:40 -0800 (Thu, 13 Nov 2008)
New Revision: 13301
Modified:
seismo/3D/ADJOINT_TOMO/flexwin/latex/AM-allcitations.bib
seismo/3D/ADJOINT_TOMO/flexwin/latex/discussion.tex
seismo/3D/ADJOINT_TOMO/flexwin/latex/flexwin_paper.pdf
seismo/3D/ADJOINT_TOMO/flexwin/latex/introduction.tex
seismo/3D/ADJOINT_TOMO/flexwin/latex/method.tex
Log:
More modifications
Modified: seismo/3D/ADJOINT_TOMO/flexwin/latex/AM-allcitations.bib
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--- seismo/3D/ADJOINT_TOMO/flexwin/latex/AM-allcitations.bib 2008-11-13 12:23:48 UTC (rev 13300)
+++ seismo/3D/ADJOINT_TOMO/flexwin/latex/AM-allcitations.bib 2008-11-13 22:32:40 UTC (rev 13301)
@@ -1,5 +1,5 @@
-%% Created for alessia at 2008-11-10 18:23:32 +0100
+%% Created for alessia at 2008-11-12 13:26:00 +0100
%% Saved with string encoding Unicode (UTF-8)
@@ -94,6 +94,16 @@
@string{tectphys = {Tectonophysics}}
+ at article{PanningRomanowicz2006,
+ Author = {Panning, M. and Romanowicz, B.},
+ Date-Added = {2008-11-12 13:24:58 +0100},
+ Date-Modified = {2008-11-12 13:25:58 +0100},
+ Journal = {Geophys. J. Int.},
+ Pages = {361--379},
+ Title = {A three-dimensional radially anisotropic model of shear velocity in the whole mantle},
+ Volume = {167},
+ Year = {2006}}
+
@article{LawrenceShearer2008,
Author = {Lawrence, J.F. and Shearer, P.M.},
Date-Added = {2008-11-10 18:18:29 +0100},
Modified: seismo/3D/ADJOINT_TOMO/flexwin/latex/discussion.tex
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--- seismo/3D/ADJOINT_TOMO/flexwin/latex/discussion.tex 2008-11-13 12:23:48 UTC (rev 13300)
+++ seismo/3D/ADJOINT_TOMO/flexwin/latex/discussion.tex 2008-11-13 22:32:40 UTC (rev 13301)
@@ -2,27 +2,25 @@
\section{Using FLEXWIN for tomography}
\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 in which phase separation and/or identification are not necessary: 3D-3D numerical tomography, of which the adjoint tomography proposed by \cite{TrompEtal2005} and \cite{TapeEtal2007} is an example. For these problems, our algorithm provides a window-selection solution that is midway between full-waveform selection -- which carries the risk of including high-noise portions of the waveform that would contaminate the tomography -- and the selection of known phases or phase-groups based on a-priori arrival times -- which carries the risk of missing the information contained in the non-traditional phases produced by fully 3D structures. We discuss later in this section and in some detail the relevance of this window selection method to adjoint tomography.
+The window selection algorithm we describe in this paper was designed to solve the problem of automatically picking windows for tomographic problems in which phase separation and identification are not necessary: 3D-3D numerical tomography, of which the adjoint tomography proposed by \cite{TrompEtal2005} and \cite{TapeEtal2007} is an example. For these problems, our algorithm provides a window-selection solution that is midway between full-waveform selection -- which carries the risk of including high-noise portions of the waveform that would contaminate the tomography -- and the selection of known phases or phase-groups based on a-priori arrival times -- which carries the risk of missing the information contained in the non-traditional phases produced by fully 3D structures.
-Our windowing algorithm may also be used to select windows for more traditional tomographic problems in which phase separation is necessary (e.g. body wave tomography or fundamental-mode surface wave tomography), but only for frequencies and epicentral distances for which these phases are naturally separated by virtue of their travel-times. SENTENCE ON HOW THIS SELECTION IS USUALLY PERFORMED. For these natural phase separation problems, the user would start by modulating the $w_E(t)$ water-level to exclude those portions of the waveform where the travel-time curves run together or cross. Portions of the waveform that contain phases not of interest for a given tomographic inversion should also be excluded in the same manner. For this class of tomographic problem, the advantages of using FLEXWIN over manual or ad-hoc automated selection would be the encapsulation of the selection criteria entirely within the parameters of Table~\ref{tb:params} (and their time-dependent modulation), leading to greater clarity and portability between studies using different inversion methods.
+FLEXWIN may also be used to select windows for tomographic problems in which separation of seismic arrivals is necessary and occurs naturally (with certain frequency and epicentral distance conditions) by virtue of differences in travel-times. It can straightforwardly be adapted to studies of distinct body wave phases \citep[e.g.][]{RitsemaVanHeijst2002} or to emulate the wavepacket selection of \cite{PanningRomanowicz2006} by modulating the $w_E(t)$ water-level using predicted phase arrival times, and selecting appropriate values for the signal-to-noise, cross-correlation and amplitude limits. The method can also be used to pre-select windows for studies of fundamental mode surface waves \citep[e.g. those based on the methods of][]{TrampertWoodhouse1995, EkstromEtal1997, LevshinRitzwoller2001} by modulating $w_E(t)$ to exclude portions of the waveform that do not correspond to the correct group velocity window or epicentral distance range. Given the dispersed nature of surface waves, synthetics produced by 1D starting models often are considerably different in shape from the data, so the $CC$ and $\Delta T$ conditions (but not the signal-to-noise or $\Delta \ln A$ conditions) should relaxed in the window selection. These windows should then be passed on to specific algorithms used to extract the dispersion information.
+For this class of natural separation tomographic problems, the advantages of using FLEXWIN over manual or specifically designed automated windowing would be the encapsulation of the selection criteria entirely within the parameters of Table~\ref{tb:params} (and their time-dependent modulation), leading to greater clarity and portability between studies using different inversion methods.
-PARAGRAPH ON WHERE FLEXWIN IS NOT RECOMMENDED TO BE USED: WHEN SEPARATION OF OVERLAPPING INFORMATION IS REQUIRED, EG FOR HIGHER MODE SURFACE WAVE STUDIES WHERE MODE BRANCH STRIPPING OR DETAILED AUTOMATED MULTIMODE ANALYSIS (AMI OR SECONDARY VARIABLES A LA DEBAYLE) ARE MORE INDICATED.
+FLEXWIN is not indicated for tomographic problems in which the extraction and separation of information from overlapping portions of a single timeseries is required, for example studies of higher mode surface wave dispersion for which specific methods -- mode branch stripping \citep{vanHeijstWoodhouse1997}, separation of secondary observables \citep{CaraLeveque1987, Debayle1999}, partitioned waveform and automated multimode inversion \citep{Nolet1990, LebedevEtal2005}, non-linear direct search \citep{YoshizawaKennett2002b, VisserEtal2007} -- have been developed.
-
\subsection{Relevance to adjoint tomography}
-PARAGRAPH DESCRIBING BRIEFLY ADJOINT METHODS, REWRITING THE PARAGRAPH BELOW IN A MORE COMPREHENSIBLE MANNER
-
-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 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.
+The full power of FLEXWIN can only be unleashed for problems -- such as adjoint tomography -- which do not require the separation (natural or otherwise) of seismic phases. The specificity of adjoint tomography, among the 3D-3D tomographic methods, is to calculate the sensitivity kernels by interaction between the wavefield used to generate the synthetic seismograms and an adjoint wavefield whose source term is derived from measurements of misfit between the synthetic and observed seismograms \cite{TrompEtal2005, LiuTromp2006}. The manner in which the adjoint sources are constructed is specific to each type of measurement (e.g. waveform difference, cross-correlation time-lag, multi-taper phase and amplitude anomaly), 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 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 computationally advantageous to make measurements on as many records as possible for each event, 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.
+It is clear that 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 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.
+{\bf The adjoint kernels are only strictly valid for the 3D Earth model they were constructed in, and therefore need to be re-computed at each iteration of the tomographic inversion \citep{TapeEtal2007}. At each iteration, the similarities between the synthetic and observed seismograms improve, such that for later iterations a greater proportion of the waveform is adequate for measurement. In order to take advantage of this extra information, the windowing method used to isolate the portions of the waveform to be measured needs to be automated.}
+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. All 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 are well known, which is rare.
@@ -33,9 +31,15 @@
\section{Summary
\label{sec:summary}}
-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 this paper (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 was designed to automatically pick time windows for tomographic problems in which phase separation and identification are not necessary, however it can also be applied to problems in which phase separation is necessary and occurs naturally. It provides an automated window-selection solution that is midway between full-waveform selection and the selection of known phases or phase-groups based on a-priori arrival times.
-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.
+FLEXWIN has no a-priori knowledge related to input model, geographic scale or frequency range.
+It is a configurable process that can be applied to different seismic scenarios by changing the handful of parameters in Table~\ref{tb:params}. The configuration process is data-driven: starting from the description of how each parameter influences the window selection (Section~\ref{sec:algorithm} and Appendix~\ref{ap:tuning}), 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, which are therefore entirely reproducible.
+
+The desire to study regions with strong 3D variations in Earth structure requires seismologists to deal with increasingly complex seismic records, and to use methods that take advantage of full wavefield simulations. Only by using all available information will tomographic inversions produce more accurate and higher resolution images of the Earth's interior. A window selection method such as FLEXWIN is necessary in order to fully unleash the potential of recent tomographic methods -- and specifically of adjoint tomography -- to exploit information from all parts of the waveform.
+
FLEXWIN is available as an open-source package through CIG (Computational
Infrastructure for Geodynamics, {\tt http://www.geodynamics.org}).
+
+
+
Modified: seismo/3D/ADJOINT_TOMO/flexwin/latex/flexwin_paper.pdf
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Modified: seismo/3D/ADJOINT_TOMO/flexwin/latex/introduction.tex
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--- seismo/3D/ADJOINT_TOMO/flexwin/latex/introduction.tex 2008-11-13 12:23:48 UTC (rev 13300)
+++ seismo/3D/ADJOINT_TOMO/flexwin/latex/introduction.tex 2008-11-13 22:32:40 UTC (rev 13301)
@@ -27,15 +27,14 @@
of sensitivity. These methods seem to be the best candidates for studying
regions with complex 3D structure as they permit the use of a larger proportion of the information contained within each seismogram, including complex arrivals not predicted by 1D approximations of Earth structure. In order to exploit the full power of 3D-3D tomographic methods, we require a new data selection strategy that does not exclude such complex arrivals.
-{\bf As data selection strategies for tomography depend so closely on the tomographic technique, there are nearly as many such strategies as there are tomographic methods. Furthermore, many of these strategies have been automated in some way, as larger and larger volumes of data have become available for tomographic studies. We shall not try to be exhaustive in the following short presentation of currently available data selection methods, but shall limit our discussion to a few representative examples. }
+{\bf As data selection strategies for tomography depend so closely on the tomographic technique, there are nearly as many such strategies as there are tomographic methods. Furthermore, many of these strategies have been automated in some way, as larger and larger volumes of data have become available for tomographic studies. We shall not try to be exhaustive in the following short presentation of currently available data selection methods, but shall limit our discussion to a few representative examples. Body wave studies that have moved away from using manual travel-time picks or catalog arrival times generally pick windows around specific arrivals defined by predicted arrival times, and include automated tests on arrival time separation and/or the fit of observed to synthetic pulses to reject inadequate data \cite[e.g.][]{RitsemaVanHeijst2002,LawrenceShearer2008}. Partial automation of the \cite{vanDecarCrosson1990} multi-channel cross-correlation method has led to efficient methods for obtaining highly accurate travel-time \citep{SiglochNolet2006,HouserEtal2008} and even attenuation \citep{LawrenceEtal2006} measurements. In the surface wave community, there has been much work done to automate methods for extracting dispersion characteristics of fundamental mode \citep{TrampertWoodhouse1995, LaskeMasters1996, EkstromEtal1997, LevshinRitzwoller2001} and higher mode \citep{vanHeijstWoodhouse1997, Debayle1999, YoshizawaKennett2002b, BeuclerEtal2003, LebedevEtal2005, VisserEtal2007} surface waves. Recently, \cite{PanningRomanowicz2006} have described an algorithm to semi-automatically pick body and surface wavepackets based on the predicted traveltimes of several phases.}
-In this paper we present an automated data selection method designed for the adjoint approach to 3D-3D tomography \citep{TrompEtal2005,LiuTromp2006,TapeEtal2007}, which builds upon \cite{Tarantola1984}. In adjoint tomography, the sensitivity kernels that tie variations
+{\bf The automated data selection method we present in this paper goes further than that of \cite{PanningRomanowicz2006}, as it not tied to arrival time predictions of known phases. Our algorithm is designed to integrate with} the adjoint approach to 3D-3D tomography \citep{TrompEtal2005,LiuTromp2006,TapeEtal2007}, which builds upon \cite{Tarantola1984}. In adjoint tomography, the sensitivity kernels that tie variations
in Earth model parameters to variations in the misfit are obtained by
interaction bewteen the wavefield used to generate the synthetic seismograms (the
direct wavefield) and 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 make the greatest number of measurements on each seismogram.
-
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
Modified: seismo/3D/ADJOINT_TOMO/flexwin/latex/method.tex
===================================================================
--- seismo/3D/ADJOINT_TOMO/flexwin/latex/method.tex 2008-11-13 12:23:48 UTC (rev 13300)
+++ seismo/3D/ADJOINT_TOMO/flexwin/latex/method.tex 2008-11-13 22:32:40 UTC (rev 13301)
@@ -60,7 +60,6 @@
earthquake location algorithms \citep[e.g.][]{Allen1982, EarleShearer1994, AsterRowe2000, BaiKennett2000, SleemanVanEck2003}. We have taken a tool used in most implementations of the
automated detection process -- the short-term long-term average ratio \citep[STA:LTA, e.g.][]{WithersEtal1998,BaiKennett2001}
-- and adapted it to the task of defining time windows around seismic phases. }
-
Given a synthetic seismogram $s(t)$, we derive an
STA:LTA timeseries using an iterative algorithm applied to the envelope of the synthetic.
If we denote the Hilbert transform of the synthetic seismogram by
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