[cig-commits] r11488 - seismo/3D/automeasure/latex

[alessia at geodynamics.org]

Author: alessia
Date: 2008-03-19 23:20:56 -0700 (Wed, 19 Mar 2008)
New Revision: 11488

Modified:
   seismo/3D/automeasure/latex/AM-allcitations.bib
   seismo/3D/automeasure/latex/introduction.tex
Log:
modified intro

Modified: seismo/3D/automeasure/latex/AM-allcitations.bib
===================================================================
--- seismo/3D/automeasure/latex/AM-allcitations.bib	2008-03-19 19:00:30 UTC (rev 11487)
+++ seismo/3D/automeasure/latex/AM-allcitations.bib	2008-03-20 06:20:56 UTC (rev 11488)
@@ -1042,6 +1042,15 @@
     year = 2005
 }
 
+ at article{CapdevilleEtal2003,
+  author = {Capdeville, Y. and Chaljub, E. and Vilotte, J.P. and Montagner, J.P.},
+  title = {Coupling the spectral element method with a modal solution for elastic wave propagation in global earth models},
+  journal = gji,
+  volume = 152,
+  pages = {34--67},
+  year = 2003
+  }
+
 @article{CaraLeveque1987,
     author = {Cara, M. and L\'ev\^eque, J.J.},
     title = {Waveform inversion using secondary observables},
@@ -3326,6 +3335,15 @@
     pages = {17,587--17,602}
 }
 
+ at article{KomatitschVilotte1998,
+  author = {Komatitsch, D. and Vilotte, J.-P.},
+  title = {The spectral element method: {A}n efficient tool to simulate the seismic response of 2D and 3D geological structures},
+  journal = bssa,
+  volume=88,
+  pages={368--392},
+  year = 1998
+}
+
 @article{KomatitschTromp2002a,
     author = {Komatitsch, D. and Tromp, J.},
     title = {Spectral-element simulations of global seismic wave propagation --- I.  Validation}, 
@@ -4286,7 +4304,7 @@
     pages = {837--851}
 }
 
- at article{MarqueringSN1996,
+ at article{MarqueringEtal1996,
     author = {Marquering, H. and Snieder, R. and Nolet, G.},
     title = {Waveform inversion and the significance of surface-wave mode coupling},
     journal = gji,
@@ -4295,6 +4313,15 @@
     year = 1996
 }
 
+ at article{MarqueringEtal1999,
+  author = {Marquering, H. and Dahlen, F.A. and Nolet, G.},
+  title = {Three-dimensional sensitivity kernels for finite-frequency traveltimes: the banana-doghnut paradox},
+  journal = gji,
+  volume = 137,
+  pages = {805-815},
+  year = 1999
+}
+
 @article{MartyCazenave1989,
     author = {Marty, J.C. and Cazenave, A.},
     title = {Regional variations in subsidence rate of oceanic plates: a global analysis},
@@ -7335,6 +7362,16 @@
     pages = {412--420}
 }
 
+ at article{ZhaoEtal2000,
+  author = {Zhao, L. and Jordan, T.H. and Chapman, C.H.},
+  title = {Three dimensional Fr\'echet differential kernels for seismic delay
+  times},
+  journal = gji,
+  volume = 141,
+  pages = {558-576},
+  year = 2000
+}
+
 @article{Zhao2004,
     author = {Zhao, D.P.},
     title = {Global tomographic images of mantle plumes and subducting slabs: insight into deep {E}arth dynamics},

Modified: seismo/3D/automeasure/latex/introduction.tex
===================================================================
--- seismo/3D/automeasure/latex/introduction.tex	2008-03-19 19:00:30 UTC (rev 11487)
+++ seismo/3D/automeasure/latex/introduction.tex	2008-03-20 06:20:56 UTC (rev 11488)
@@ -1,54 +1,81 @@
 \section{Introduction}
 
-FLEXWIN was designed to provide automated window selection for adjoint
-tomography studies, in a way that mimics the choices that
-would be made by a competent seismologist.  The purpose of adjoint tomography is
-to improve 3D Earth models by minimizing the misfit between observed
-seismograms and predictions (synthetic seismograms) made by full wavefield
-propagation. In adjoint tomography, the sensitivity kernels that tie variations
+Seismic tomography - the process of imaging the 3D structure of the Earth using
+seismic recordings - has been tranformed by recent advances in methodology.
+Ray-based approaches are being superseded by finite-frequency kernel-based
+approaches, and 1D reference models by 3D 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 propagaion in fully 3D media \citep{KomatitschVilotte1998,KomatitschEtal2002,CapdevilleEtal2003}.  
+In the past decade we have learnt how to calculate analytic sensitivity kernels
+in 1D media \citep{FavierEtal2003,ZhouEtal2004,SieminskiEtal2004,CalvetChevrot2005,DahlenEtal2006,CalvetEtal2006} and numeric sensitivity kernels in 3D media \citep{Capdeville2005,TrompEtal2005,ZhaoEtal2005,ZhaoEtal2006,LiuTromp2006,SieminskiEtal2007a,SieminskiEtal2007b}.
+The analytic kernels have been taken up rapidly by tomographers, and used to
+produce new 3D Earth models (REFs).  The numeric kernels have
+opened up the possibility of `3D-3D' tomography, i.e.~seismic tomography based upon a 3D reference model, 3D numerical simulations of the seismic wavefield and finite-frequency sensitivity kernels (REFs).
+
+The growing number of competing tomographic techniques all have at their core
+the following `standard operating procedure', which they share with all inverse
+problems in physics: make a guess about a set of model parameters; predict an
+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: fristly, 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 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.  For example, ray-based travel-time tomography deals
+only with well identified 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.
+Data choices are therefore inextricably linked to tomographic method.  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
+accuracy of which releases tomographers from many of the data restrictions
+required when using approximate forward modelling and simplified descriptions
+of sensitivity.  
+
+In this paper we present an automated data selection method for the 3D-3D adjoint tomography approach of \cite{TrompEtal2005,LiuTromp2006} and \cite{TapeEtal2007}.  In adjoint tomography, the sensitivity kernels that tie variations
 in Earth model parameters to variations in the misfit are obtained by
 interference of the wavefield used to generate the synthetic seismograms (the
-direct wavefield) with an adjoint wavefield, which obeys the same wave equation
+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 \citep{TrompEtal2005,LiuTromp2006,TapeEtal2007}.  
+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 stations or on the number measurements made.  It is therefore to our advantage to use the greatest amount of information from each seismogram.
 The adjoint kernel calculation procedure allows us to measure and use for
-tomographic inversion almost any part of the seismogram.  We do not even need
-to know what the phases are, as the adjoint kernel calculation will take care of
-defining their sensitivities.  There is, however, one important limitation to
-the choice of measurement windows: {\em measurements should only be made on
-seismic arrivals that are physically related to the model parameters}.  This
-limitation is common to all physical measurement problems involving some
-modeling or simulation, and can be simply restated as: {\em do not measure
-noise}.  When quantifying the misfit between observed data and predictions,
-noise is defined as any signal not physically related to the system being
-simulated.  In earthquake seismology, seismic energy which is not caused
-directly or indirectly by the earthquake being simulated is considered to be
-noise.
+tomographic inversion almost any part of the seismic signal.  We do not even
+need to identify specific seismic phases, as the kernel will take care of
+defining the 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
+inversion process.  When quantifying the misfit between observed data and
+predictions, noise is usually defined as any signal not physically related to
+the system being simulated.  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
+avoided in the choice of the portions of the seismogram to be measured. 
 
-Most large scale seismological studies have some component of automization in
-their data selection process.  A reasonably straightforward procedure to select
-data is to estimate the arrival time of the phases of interest using a
-simplified Earth structure, cut the seismogram around these times, and compare
-the recorded ground motion with that predicted from the simplified structure.
-If the similarity between the two waveforms is high enough, the data is deemed
-acceptable.
-
-FLEXWIN turns this procedure on its head, eliminating Earth-model based step of
-pre-defining the arrival times of phases of interest.  Seismic phases are none
-other than distinctive arrivals in seismograms, so we use the records
-themselves to define when the seismic phases arrive.  Our window selection
-strategy proceds in two steps : (1) select windows on the seismogram in which
-the waveform contains a distinct energy arrival; (2) require an adequate
-correspondance between observed and synthetic seismograms within these windows.
-
+From a signal processing point of view, the simplest way to avoid serious
+contamination by noise is to select and measure strong signals, which in
+seismology correspond to seismic arrivals.  Our data selection strategy
+therefore selects windows on the synthetic seismogram in which the waveform
+contains a distinct energy arrival, then requires an adequate correspondance
+between observed and synthetic waveforms within these windows.  
 During the first step we need to analyse the character of the waveform itself, in
 order to isolate changes in amplitude or frequency content susceptible of being
 associated with distinct seismic phases.  This analysis is similar to that used
 in automated phase detection algorithms used in the routine location of
 earthquakes.  We have therefore taken a tool used in the detection process ---
 the long-term / short-term ratio --- and applied it to the definition of
-time-windows around disticnt seismic phases.  Once these time-windows have been
+time-windows around distinct seismic phases.  Once these time-windows have been
 defined, we proceed to the second step, during which we reject those windows in
 which the observed and synthetic seismograms fail a set of quality criteria
 based on their cross-correlation, time-lag, amplitude ratio and signal-to-noise
@@ -60,52 +87,23 @@
 global propagation) simply by tuning the parameters for each scenario.  These
 three scenarios will be used as examples.
 
+{\bf Finish this introduction properly}
+
 \pagebreak
 
-\subsection{BASIC POINTS FROM CARL}
+%\subsection{BASIC POINTS FROM CARL}
 
-\begin{itemize}
-\item Statistical properties of ``noise'' in seismograms is not well known.
-\item Full waveform tomography was not a successful in practice as in theory.
-\item We are interested in regions with complex tectonics, which lead to complex structures, and complex seismograms.
-\item We are interested in matching the seismograms ``wiggle for wiggle'', not other quanta, for example, spectral content, peak acceleration (WHAT ELSE?).
-\end{itemize}
+%\begin{itemize}
+%\item Statistical properties of ``noise'' in seismograms is not well known.
+%\item Full waveform tomography was not a successful in practice as in theory.
+%\item We are interested in regions with complex tectonics, which lead to complex structures, and complex seismograms.
+%\item We are interested in matching the seismograms ``wiggle for wiggle'', not other quanta, for example, spectral content, peak acceleration (WHAT ELSE?).
+%\end{itemize}
 
-\subsection{EXTRA ALESSIA TEXT -- WHERE DOES THIS FIT IN?}
+%\subsection{EXTRA ALESSIA TEXT -- WHERE DOES THIS FIT IN?}
 
-Once noise-dominated data have been rejected, we are ready to consider defining
-preliminary measurement windows.  We choose to define these windows around
-seismic phase arrivals, for two reasons: (1) the presence of a phase arrival in
-a window reduces the impact of residual noise on any measurement; (2) distinct
-phase arrivals tend to have well-defined sensitivity kernels which are
-intuitively easier to interpret.  
+%Once noise-dominated data have been rejected, we are ready to consider defining preliminary measurement windows.  We choose to define these windows around seismic phase arrivals, for two reasons: (1) the presence of a phase arrival in a window reduces the impact of residual noise on any measurement; (2) distinct phase arrivals tend to have well-defined sensitivity kernels which are intuitively easier to interpret.  
 
-A reasonably straightforward procedure to
-define data windows around seismic phases is to estimate their arrival time
-using a simplified Earth model, and to define windows around these times,
-allowing for the uncertainty in the travel time and the width of the seismic
-phase itself.  This kind of procedure is simple to implement when
-the phases of interest are well spaced on the seismogram, and forms the basis
-of window selection for many tomographic studies that use cross-correlation
-measurements of travel time delays (REFs).  When the phases of interest are
-spaced closely enough on the seismogram that the ideal windows for each phase
-overlap, different strategies have to be applied.  One such strategy is that
-implemented by {\bf Panning et al?}, and involves using the predicted
-travel-time curves in a reference Earth model to pre-define the extend and
-position of data windows as a function of epicentral distance.
+%A reasonably straightforward procedure to define data windows around seismic phases is to estimate their arrival time using a simplified Earth model, and to define windows around these times, allowing for the uncertainty in the travel time and the width of the seismic phase itself.  This kind of procedure is simple to implement when the phases of interest are well spaced on the seismogram, and forms the basis of window selection for many tomographic studies that use cross-correlation measurements of travel time delays (REFs).  When the phases of interest are spaced closely enough on the seismogram that the ideal windows for each phase overlap, different strategies have to be applied.  One such strategy is that implemented by {\bf Panning et al?}, and involves using the predicted travel-time curves in a reference Earth model to pre-define the extend and position of data windows as a function of epicentral distance.
 
-Windowing strategies of this type have one major drawback, tied to the fact
-that the prominence of seismic phases depends
-strongly on focal mechanism and frequency
-range, and to a lesser extent on 3D Earth structure.  In order to avoid placing
-empty and or unnecessary windows, these travel-time based schemes may have to
-be modified to take at least focal mechanism and frequency range into account.
-As the importance of these two factors varies as a function of the seismic
-phases of interest, taking them into account is more or less equivalent to
-calculating a full synthetic seismogram, and analyzing the shape and amplitude
-of the synthetic signal.  
-We argue that since a full synthetic seismogram contains all the travel time,
-frequency range and focal mechanism information required to assess the
-usefulness of a particular data window, the seismogram itself should be used to
-define the data windows.  Instead of using travel times, we choose to detect
-seismic phase arrivals directly on the synthetic seismograms. 
+%Windowing strategies of this type have one major drawback, tied to the fact that the prominence of seismic phases depends strongly on focal mechanism and frequency range, and to a lesser extent on 3D Earth structure.  In order to avoid placing empty and or unnecessary windows, these travel-time based schemes may have to be modified to take at least focal mechanism and frequency range into account.  As the importance of these two factors varies as a function of the seismic phases of interest, taking them into account is more or less equivalent to calculating a full synthetic seismogram, and analyzing the shape and amplitude of the synthetic signal.  We argue that since a full synthetic seismogram contains all the travel time, frequency range and focal mechanism information required to assess the usefulness of a particular data window, the seismogram itself should be used to define the data windows.  Instead of using travel times, we choose to detect seismic phase arrivals directly on the synthetic seismograms.