[cig-commits] r13277 - seismo/3D/ADJOINT_TOMO/flexwin/latex
alessia at geodynamics.org
alessia at geodynamics.org
Mon Nov 10 09:43:23 PST 2008
Author: alessia
Date: 2008-11-10 09:43:22 -0800 (Mon, 10 Nov 2008)
New Revision: 13277
Modified:
seismo/3D/ADJOINT_TOMO/flexwin/latex/AM-allcitations.bib
seismo/3D/ADJOINT_TOMO/flexwin/latex/abstract.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
seismo/3D/ADJOINT_TOMO/flexwin/latex/results.tex
Log:
Revisions continued
Modified: seismo/3D/ADJOINT_TOMO/flexwin/latex/AM-allcitations.bib
===================================================================
--- seismo/3D/ADJOINT_TOMO/flexwin/latex/AM-allcitations.bib 2008-11-09 01:46:02 UTC (rev 13276)
+++ seismo/3D/ADJOINT_TOMO/flexwin/latex/AM-allcitations.bib 2008-11-10 17:43:22 UTC (rev 13277)
@@ -1,8 +1,8 @@
-%% Created for alessia at 2008-04-07 12:51:26 +0200
+%% Created for alessia at 2008-11-10 18:23:32 +0100
-%% Saved with string encoding Occidental (ASCII)
+%% Saved with string encoding Unicode (UTF-8)
@string{ag = {Ann. Geophys.}}
@@ -94,6 +94,159 @@
@string{tectphys = {Tectonophysics}}
+ at article{LawrenceShearer2008,
+ Author = {Lawrence, J.F. and Shearer, P.M.},
+ Date-Added = {2008-11-10 18:18:29 +0100},
+ Date-Modified = {2008-11-10 18:21:30 +0100},
+ Journal = {Geophys. J. Int.},
+ Title = {Imaging mantle transition zone thickness with SdS-SS finite-frequency sensitivity kernels},
+ Year = {2008}}
+
+ at article{SiglochNolet2006,
+ Author = {Sigloch, K. and Nolet, G.},
+ Date-Added = {2008-11-10 18:15:44 +0100},
+ Date-Modified = {2008-11-10 18:17:27 +0100},
+ Journal = {Geophys. J. Int.},
+ Pages = {271--287},
+ Title = {Measuring finite-frequency body-wave amplitudes and traveltimes},
+ Volume = {167},
+ Year = {2006}}
+
+ at article{HouserEtal2008,
+ Author = {Houser, C. and Masters, G. and Laske, G.},
+ Date-Added = {2008-11-10 18:14:20 +0100},
+ Date-Modified = {2008-11-10 18:15:24 +0100},
+ Journal = {Geophys. J. Int.},
+ Pages = {195--212},
+ Title = {Shear and compressional velocity models of the mantle from cluster analysis of long-period waveforms},
+ Volume = {174},
+ Year = {2008}}
+
+ at article{vanDecarCrosson1990,
+ Author = {vanDecar, J.C. and Crosson, R.S.},
+ Date-Added = {2008-11-10 18:12:39 +0100},
+ Date-Modified = {2008-11-10 18:14:04 +0100},
+ Journal = {B. Seismol. Soc. Am.},
+ Number = {1},
+ Pages = {150--169},
+ Title = {Determination of teleseismic relative phase arrival times using multi-channel cross-correlation and least squares},
+ Volume = {80},
+ Year = {1990}}
+
+ at article{LawrenceEtal2006,
+ Author = {Lawrence, J.F. and Shearer, P.M. and Masters, G.},
+ Date-Added = {2008-11-10 18:10:44 +0100},
+ Date-Modified = {2008-11-10 18:12:25 +0100},
+ Journal = {Geophy. Res. Lett.},
+ Number = {L07315},
+ Title = {Mapping attenuation beneath North America using waveform cross-correlation and cluster analysis},
+ Volume = {33},
+ Year = {2006}}
+
+ at article{vanHeijstWoodhouse1997,
+ Author = {Van Heijst, H.J. and Woodhouse, J.H.},
+ Date-Added = {2008-11-10 18:08:11 +0100},
+ Date-Modified = {2008-11-10 18:09:27 +0100},
+ Journal = {Geophys. J. Int.},
+ Pages = {209--220},
+ Title = {Measuring surface-wave overtone phase velocities using a mode-branch stripping technique},
+ Volume = {131},
+ Year = {1997}}
+
+ at article{LebedevEtal2005,
+ Author = {Lebedev, S. and Nolet, G. and Meier, T. and van der Hilst, R.D.},
+ Date-Added = {2008-11-10 18:05:10 +0100},
+ Date-Modified = {2008-11-10 18:06:39 +0100},
+ Journal = {Geophys. J. Int.},
+ Pages = {951--964},
+ Title = {Automated multimode inversion of surface and S waveforms},
+ Volume = {162},
+ Year = {2005}}
+
+ at article{VisserEtal2007,
+ Author = {Visser, K and Lebedev, S. and Trampert, J. and Kennett, B.L.N.},
+ Date-Added = {2008-11-10 18:02:23 +0100},
+ Date-Modified = {2008-11-10 18:04:11 +0100},
+ Journal = {Geophy. Res. Lett.},
+ Number = {L03302},
+ Title = {Global Love wave overtone measurements},
+ Volume = {34},
+ Year = {2007}}
+
+ at article{WithersEtal1998,
+ Author = {Withers, M. and Aster, R. and Young, C. and Beiriger, J. and Harris, M. and Moore, S. and Trujillo, J.},
+ Date-Added = {2008-11-07 13:24:26 +0100},
+ Date-Modified = {2008-11-07 13:25:59 +0100},
+ Journal = {B. Seismol. Soc. Am.},
+ Number = {1},
+ Pages = {96--106},
+ Title = {A comparison of select trigger algorithms for automated global seismic phase and event detection},
+ Volume = {88},
+ Year = {1998}}
+
+ at incollection{SleemanVanEck2003,
+ Author = {Sleeman, R. and van Eck, T.},
+ Booktitle = {Methods and Applications of Signal Processing in Seismic Network Operations},
+ Date-Added = {2008-11-07 13:05:30 +0100},
+ Date-Modified = {2008-11-07 13:07:47 +0100},
+ Editor = {Takami, T. and Kitagawa, G.},
+ Pages = {173--194},
+ Publisher = {Springer},
+ Series = {Lecture Notes in Earth Sciences},
+ Title = {Single station real-time P and S phase pickers for seismic observatories},
+ Volume = {98},
+ Year = {2003}}
+
+ at article{EarleShearer1994,
+ Author = {Earle, P.S. and Shearer, P.M.},
+ Date-Added = {2008-11-07 13:03:47 +0100},
+ Date-Modified = {2008-11-07 13:04:48 +0100},
+ Journal = {B. Seismol. Soc. Am.},
+ Pages = {366--376},
+ Title = {Characterization of global seismograms using an automatic picking algorithm},
+ Volume = {84},
+ Year = {1994}}
+
+ at article{BaiKennett2000,
+ Author = {Bai, C.Y. and Kennett, B.L.N.},
+ Date-Added = {2008-11-07 13:02:09 +0100},
+ Date-Modified = {2008-11-07 13:03:30 +0100},
+ Journal = {B. Seismol. Soc. Am.},
+ Pages = {187--198},
+ Title = {Automatic phase detection and identification by full use of a single three component broadband seismogram},
+ Volume = {90},
+ Year = {2000}}
+
+ at incollection{AsterRowe2000,
+ Author = {Aster, R. and Rowe, A.},
+ Booktitle = {Advances in seismic event location},
+ Date-Added = {2008-11-07 12:59:16 +0100},
+ Date-Modified = {2008-11-07 13:01:35 +0100},
+ Pages = {231--263},
+ Publisher = {Kluwer Academic Publishers},
+ Title = {Automatic phase pick refinement and similar event association in large seismic datasets},
+ Year = {2000}}
+
+ at article{Allen1982,
+ Author = {Allen, R.V.},
+ Date-Added = {2008-11-07 12:57:53 +0100},
+ Date-Modified = {2008-11-07 12:58:57 +0100},
+ Journal = {B. Seismol. Soc. Am.},
+ Pages = {S225--S242},
+ Title = {Automatic phase pickers: their present use and future prospects},
+ Volume = {72},
+ Year = {1982}}
+
+ at article{Allen1978,
+ Author = {Allen, R.V.},
+ Date-Added = {2008-11-07 12:56:07 +0100},
+ Date-Modified = {2008-11-07 12:57:37 +0100},
+ Journal = {B. Seismol. Soc. Am.},
+ Pages = {1521-1531},
+ Title = {Automatic earthquake recognition and timing from single traces},
+ Volume = {68},
+ Year = {1987}}
+
@article{LiTanimoto1993,
Author = {Li, X.D. and Tanimoto, T.},
Date-Added = {2008-04-07 12:36:02 +0200},
@@ -234,14 +387,14 @@
Year = {1991}}
@article{KomatitschEtal2004,
- Author = {Komatitsch, D. and Liu, Q. and Tromp, J. and S\"uss, P. and Stidham, C. and Shaw J.H.},
- Date-Added = {2008-03-22 19:38:39 +0100},
- Date-Modified = {2008-03-22 19:41:12 +0100},
- Journal = {B. Seismol. Soc. Am.},
- Pages = {187--206},
- Title = {{Simulations of ground motion in the Los Angeles basin based upon the spectral-element method}},
- Volume = {94},
- Year = {2004}}
+ Author = {Komatitsch, D. and Liu, Q. and Tromp, J. and S\"uss, P. and Stidham, C. and Shaw J.H.},
+ Date-Added = {2008-03-22 19:38:39 +0100},
+ Date-Modified = {2008-03-22 19:41:12 +0100},
+ Journal = {B. Seismol. Soc. Am.},
+ Pages = {187--206},
+ Title = {{Simulations of ground motion in the Los Angeles basin based upon the spectral-element method}},
+ Volume = {94},
+ Year = {2004}}
@article{ChenEtal2007,
Author = {Chen, M. and Tromp, J. and Helmberger, D. and Kanamori, H.},
@@ -362,8 +515,8 @@
Date-Modified = {2008-03-22 15:50:46 +0100},
Doi = {10.1029/2005JB003677},
Journal = {J. Geophys. Res.},
+ Title = {Global upper-mantle structure from finite-frequency surface-wave tomography},
Volume = {111},
- Title = {Global upper-mantle structure from finite-frequency surface-wave tomography},
Year = {2006},
Bdsk-Url-1 = {http://dx.doi.org/10.1029/2005JB003677}}
@@ -3996,13 +4149,11 @@
Year = 2006}
@article{MaggiEtal2008,
- author = {Maggi, A. and Tape, C. and Chen, M. and Chao, D. and Tromp, J.},
- journal = gji,
- pages = {},
- title = {An automated time-window selection algorithm for seismic tomography},
- volume = XX,
- year = 2008
- }
+ Author = {Maggi, A. and Tape, C. and Chen, M. and Chao, D. and Tromp, J.},
+ Journal = gji,
+ Title = {An automated time-window selection algorithm for seismic tomography},
+ Volume = XX,
+ Year = 2008}
@article{MJJ99,
Author = {Mahatsente, R. and Jentzsch, G. and Jahr, T.},
@@ -6301,15 +6452,14 @@
Year = 1979}
@article{Wald95,
- AUTHOR = {Wald, L. A. and Hutton, L. K. and Given, D. D.},
- JOURNAL = srl,
- PAGES = {9--19},
- TITLE = {{The Southern California Network Bulletin: 1990--1993 summary}},
- VOLUME = 66,
- NUMBER = 1,
- YEAR = 1995}
+ Author = {Wald, L. A. and Hutton, L. K. and Given, D. D.},
+ Journal = srl,
+ Number = 1,
+ Pages = {9--19},
+ Title = {{The Southern California Network Bulletin: 1990--1993 summary}},
+ Volume = 66,
+ Year = 1995}
-
@article{WalkerJB2003,
Author = {Walker, R. and Jackson, J. and Baker, C.},
Journal = gji,
Modified: seismo/3D/ADJOINT_TOMO/flexwin/latex/abstract.tex
===================================================================
--- seismo/3D/ADJOINT_TOMO/flexwin/latex/abstract.tex 2008-11-09 01:46:02 UTC (rev 13276)
+++ seismo/3D/ADJOINT_TOMO/flexwin/latex/abstract.tex 2008-11-10 17:43:22 UTC (rev 13277)
@@ -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 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.
+We present an algorithm for the automated selection of time windows on pairs of observed and synthetic seismograms. {\bf The algorithm was designed specifically to automate window selection and measurement for adjoint tomography studies, but is sufficiently flexible to be adapted to many 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. {\bf It requires a data selection method that includes these new phases, maximizes the number of measurements made on each seismic record, while avoiding seismic noise. This selection method must also be automated in order to adapt to changes in the synthetic seismograms after each iteration of the tomographic inversion. These considerations have 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/ADJOINT_TOMO/flexwin/latex/flexwin_paper.pdf
===================================================================
(Binary files differ)
Modified: seismo/3D/ADJOINT_TOMO/flexwin/latex/introduction.tex
===================================================================
--- seismo/3D/ADJOINT_TOMO/flexwin/latex/introduction.tex 2008-11-09 01:46:02 UTC (rev 13276)
+++ seismo/3D/ADJOINT_TOMO/flexwin/latex/introduction.tex 2008-11-10 17:43:22 UTC (rev 13277)
@@ -12,20 +12,6 @@
produce new 3D Earth models \citep[e.g.][]{MontelliEtal2004a,ZhouEtal2006}. 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 \citep{TrompEtal2005,ChenEtal2007b}.
-%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: 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, by inaccuracies in our solution to the forward problem, or by
-%the presence of noise in the observations; lastly, that we know the
-%relation between the measured misfit and the model parameters
-%(in terms of partial derivatives or a sensitivity kernel).
-
It is common practice in tomography to work only with certain subsets of the
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
@@ -41,6 +27,8 @@
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. }
+
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
in Earth model parameters to variations in the misfit are obtained by
interaction bewteen the wavefield used to generate the synthetic seismograms (the
@@ -52,22 +40,20 @@
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, there is nothing in the adjoint method itself that prevents us from constructing an adjoint kernel from noise-dominated data, and thereby polluting our inversion process.
-Our data selection strategy therefore 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.
+{\bf An appropriate data selection strategy for adjoint tomography should therefore 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.}
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. We therefore select time windows on the synthetic seismogram within which the waveform
-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.
+seismology correspond to seismic arrivals.
+{\bf Our strategy is therefore to select time windows on the synthetic seismogram within which the waveform contains a distinct energy arrival, then require to 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 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 ---
-the long-term / short-term ratio --- and applied it to the definition of
-time windows around distinct seismic phases.
+earthquakes.
+{\bf In designing our time-window selection algorithm, we have taken a tool used in this detection process -- the long-term / short-term average ratio -- and applied it to the definition of time windows around distinct seismic phases.}
The choices made in time-window selection for tomography are
interconnected with all aspects of the tomographic inversion process,
@@ -75,23 +61,4 @@
measurement method, to the method
used to obtain sensitivity kernels. One of the major difficulties in defining a general data selection strategy is the great range of possible choices open to the tomographer. We have 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 our algorithm for use in adjoint tomography, its inherent flexibility should make it useful in many data-selection applications.
-%Let us take as an example the case of composite seismic arrivals. 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 more 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 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 {\bf we discuss the use of the algorithm in the context of tomography -- and more specifically adjoint tomography -- in Section~\ref{sec:discuss}.}
Modified: seismo/3D/ADJOINT_TOMO/flexwin/latex/method.tex
===================================================================
--- seismo/3D/ADJOINT_TOMO/flexwin/latex/method.tex 2008-11-09 01:46:02 UTC (rev 13276)
+++ seismo/3D/ADJOINT_TOMO/flexwin/latex/method.tex 2008-11-10 17:43:22 UTC (rev 13277)
@@ -21,15 +21,12 @@
%----------------------
\subsection{Phase 0 \label{sec:phase0}}
-%{\em Parameters used: $T_{0,1}$.}
The purpose of this phase is to pre-process input seismograms, to reject
noisy records, and to set up a secondary waveform (the short-term / long-term average ratio) derived from the envelope of the synthetic seismogram. This STA:LTA waveform will be used later to define preliminary
measurement windows.
%----------------------
-%\subsubsection{Pre-processing}
-
We apply minimal and identical pre-processing to both observed and synthetic
seismograms: {\bf removal of any linear trend, tapering, and} band-pass filtering with a non-causal Butterworth
filter, whose
@@ -40,8 +37,6 @@
%----------------------
-%\subsubsection{Seismogram rejection on the basis of noise in observed seismogram}
-
Our next step is to reject seismograms that are dominated by noise. This rejection is based on two signal-to-noise criteria that compare the power and amplitude of the signal to those of the background noise (given by the observed waveform before the first $P$-wave arrival). The power signal-to-noise ratio is defined as
${\rm SNR}_P = P_{\rm signal}/P_{\rm noise},$
where the time-normalized power in the signal and noise portions of the data are defined respectively by
@@ -61,13 +56,13 @@
%----------------------
-%\subsubsection{Construction of STA:LTA timeseries}
+{\bf Detection and identification of seismic phase arrivals is routinely performed by automated
+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. }
-Detection of seismic phase arrivals is routinely performed by automated
-earthquake location algorithms. We have taken a tool used in this
-standard detection process --- the short-term long-term average ratio (STA:LTA)
---- and adapted it to the task of defining time windows around seismic phases. Given a synthetic seismogram $s(t)$, we derive its
-STA:LTA timeseries using an iterative algorithm.
+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
$\mathcal{H}[s(t)]$, its envelope $e(t)$ is given by:
\begin{equation}
@@ -75,7 +70,7 @@
\end{equation}
In order to create the STA:LTA waveform $E(t)$, we discretize the envelope time
series with timestep $\delta t$, calculate its short term average
-$S(t_i)$ and its long term average $L(t_i)$ as follows,
+$S(t_i)$ and its long term average $L(t_i)$ {\bf recursively} as follows,
\begin{align}
S(t_i) & = C_S \; S(t_{i-1}) + e(t_i) , \label{eq:sta}\\
L(t_i) & = C_L \; L(t_{i-1}) + e(t_i) , \label{eq:lta}
@@ -135,29 +130,27 @@
phases, we must determine rules for deciding when adjacent local maxima
should be part of a single window. From an algorithmic point
of view, it is simpler to create all possible combinations of adjacent windows
-and subsequently reject the unacceptable ones, than to consider expanding
+and subsequently reject the unacceptable ones, than to consider {\bf combining}
small, single-maximum windows into larger ones.
We start by defining a water level on $E(t)$ via the time dependent parameter
-$w_E(t)$ in Table~\ref{tb:params}. The water level shown in
+$w_E(t)$ in Table~\ref{tb:params}.
+{\bf All local maxima that lie above $w_E(t)$ are used for the creation of candidate time windows.}
+The water level shown in
Figure~\ref{fg:stalta} corresponds to $w_E=0.08$ for the duration of the main
seismic signal. Once set for typical seismograms for a given
seismological scenario, it is not necessary to change $w_E$ for each
seismogram. This is also true of all the other parameters in
Table~\ref{tb:params}: once the system has been tuned,
these parameters remain unchanged and are used for all seismic events in the same scenario.
-{\bf
-A summary of the main considerations the user should take into account to
-tune these parameters can be found in Appendix~\ref{ap:tuning}.
-}
+{\bf A summary of the main considerations the user should take into account to tune these parameters can be found in Appendix~\ref{ap:tuning}.}
The functional forms of the time-dependent parameters are defined by the user, can depend on
information about the earthquake source and the receiver, and also
-remain unchanged once the system has been tuned (see Appendix~\ref{ap:user_fn}).
+remain unchanged once the system has been tuned.
For the example in Figure~\ref{fg:stalta}, we have required the water level
$w_E(t)$ to double after the end of the surface wave arrivals (as defined by
the epicentral distance and a group velocity of $3.2$~\kmps) so as to avoid
-creating time windows after $R1$. All local maxima that lie above $w_E(t)$
-are used for the creation of candidate time windows.
+creating time windows after $R1$.
We take each acceptable local maximum in turn as a seed maximum, and create all
possible candidate windows that contain it, as illustrated by
@@ -197,14 +190,13 @@
rejecting short windows, we are requiring that time windows be long enough to
contain useful information.
Thirdly, we reject windows whose seed maximum $E(t_M)$ rises by less than
-$c_2 w_E(t)$ above either of its adjacent minima. Subdued local maxima of
+$c_2 w_E(t_M)$ above either of its adjacent minima. Subdued local maxima of
this kind represent minor changes in waveform character, and should not be used
to anchor time windows. They may, however, be considered as part of a time window with a more prominent maximum (see Figure~\ref{fg:win_composite}c).
Lastly, we reject windows that contain at least
one strong phase arrival that is well separated in time from $t_M$. The
rejection is performed using the following criterion:
\begin{equation}
-%h/h_M > f(\frac{\Delta T}{T_0}; c_{3a},c_{3b}),
h/h_M > f(\Delta T/T_0; c_{3a},c_{3b}),
\end{equation}
where $h_M$ is the height of the seed maximum $E(t_M)$ above the deepest
@@ -222,10 +214,9 @@
\end{equation}
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 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.
+windows containing a local maximum that is higher than {\bf their} seed maximum; it also leads to the rejection of windows containing a local maximum that is
+lower than {\bf their} seed maximum if {\bf this local maximum} is sufficiently distant in time from
+$t_M$. {\bf This criterion allows us to distinguish unseparable phase groups from distinct seismic phases.}
The candidate windows that remain after application of these four rejection
criteria are almost ready to be passed on to the next stage, in which they will
@@ -257,8 +248,7 @@
groups of phases on the synthetic seismogram.
The next stage is to evaluate the degree of similarity between the observed and
synthetic seismograms within these windows, and to reject
-those that fail basic fit-based criteria. A similar kind of rejection is
-performed by most windowing schemes.
+those that fail basic fit-based criteria.
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
@@ -287,9 +277,11 @@
\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.
+parameters such as epicentral distance and earthquake depth.
+{\bf Examples of functional forms for these parameters can be found in Appendix~\ref{ap:user_fn}.}
Figure~\ref{fg:criteria} shows the time
-dependence of $\mathrm{CC}_0$ , $\Delta \tau_0$ and $\Delta \ln A_0$ for an example seismogram.
+dependence of $\mathrm{CC}_0$ , $\Delta \tau_0$ and $\Delta \ln A_0$ for
+the example seismogram of Figure~\ref{fg:win_rej_data}.
We only accept candidate windows that satisfy all of the following:
\begin{align}
@@ -299,8 +291,8 @@
|\Delta\ln{A}| & \leq \Delta\ln{A}_0(t_M), \label{eq:dlnA}
\end{align}
where $t_M$ is the time of the window's seed maximum. In words, we only accept
-windows in which the observed signal is above the noise level, the observed and
-synthetic signals are reasonably similar in shape, their arrival times
+windows in which the observed signal is sufficiently above the noise level, the observed and
+synthetic signals are reasonably similar in shape, their arrival time
differences are small, and their amplitudes are broadly compatible. When the synthetic and observed
seismograms are similar, the fit-based criteria of
equations~(\ref{eq:cc})-(\ref{eq:dlnA}) reject only a few of the candidate data
@@ -350,9 +342,9 @@
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 $\mathrm{CC}$ 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
-$w_{\mathrm{CC}}$, $w_{\rm len}$ and $w_{\rm nwin}$ in Table~\ref{tb:params}.
+short ones have different time lags $\Delta\tau$. {\bf Weighting of the
+three scores is necessary, and is controlled by the three parameters
+$w_{\mathrm{CC}}$, $w_{\rm len}$ 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
@@ -374,9 +366,9 @@
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
-highest combined score $S$. The final, optimal set of windows is
+{\bf The best subset of candidate windows within each group is the one with the
+highest combined score $S$. The final set of windows is
given by concatenating the best subsets of candidate windows for each group.
-Figure~\ref{fg:res_abkt} shows an example of optimal windows selected on real
-data.
+Figure~\ref{fg:res_abkt} shows an example of final windows selected on real
+data.}
Modified: seismo/3D/ADJOINT_TOMO/flexwin/latex/results.tex
===================================================================
--- seismo/3D/ADJOINT_TOMO/flexwin/latex/results.tex 2008-11-09 01:46:02 UTC (rev 13276)
+++ seismo/3D/ADJOINT_TOMO/flexwin/latex/results.tex 2008-11-10 17:43:22 UTC (rev 13277)
@@ -26,7 +26,7 @@
scenario-dependent information is encapsulated in the tuning parameters of
Table~\ref{tb:params}.
-We tuned the windowing algorithm separately for each of the three scenarios we present here, and we present examples based on the events listed in Table~\ref{tb:events}. Tuning parameter values can be found in Table~\ref{tb:example_params}, while the functional forms of the time-dependent parameters can be found in Appendix~\ref{ap:user_fn}. Once tuned for a scenario, the algorithm is applied to all the events in that scenario without further modification.
+We tuned the windowing algorithm separately for each of the three scenarios we present here, and we present examples based on the events listed in Table~\ref{tb:events}. Tuning parameter values for each scenario can be found in Table~\ref{tb:example_params}, while the functional forms of the time-dependent parameters can be found in Appendix~\ref{ap:user_fn}. {\bf Once tuned for a given scenario, the algorithm is applied to all its events without further modification. }
\subsection{Global tomography}
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