alessia at geodynamics.org alessia at geodynamics.org
Tue Nov 4 08:36:24 PST 2008

Author: alessia
Date: 2008-11-04 08:36:23 -0800 (Tue, 04 Nov 2008)
New Revision: 13253

Modified:
Log:
Appendix rewritten.  Added SAC acknowledgement to appendix. Draft of new discussion section.

===================================================================
--- seismo/3D/ADJOINT_TOMO/flexwin/latex/acknowledgements.tex	2008-11-04 09:49:03 UTC (rev 13252)
+++ seismo/3D/ADJOINT_TOMO/flexwin/latex/acknowledgements.tex	2008-11-04 16:36:23 UTC (rev 13253)
@@ -7,3 +7,4 @@
Additional global scale data were provided by the GEOSCOPE network.
We thank the Hi-net Data Center (NIED), especially Takuto Maeda and Kazushige Obara, for their help in providing the seismograms used in the Japan examples.
For the southern California examples, we used seismograms from the Southern California Seismic Network, operated by California Institute of Technology and U.S.G.S.
+{\bf The FLEXWIN code makes use of filtering and enveloping algorithms that are part of SAC (Seismic Analysis Code, Lawerence Livermore National Laboratory) provided for free to IRIS members.  We thank Brian Savage for adding interfaces to these algorithms in recent SAC distributions. }

===================================================================
--- seismo/3D/ADJOINT_TOMO/flexwin/latex/appendix.tex	2008-11-04 09:49:03 UTC (rev 13252)
+++ seismo/3D/ADJOINT_TOMO/flexwin/latex/appendix.tex	2008-11-04 16:36:23 UTC (rev 13253)
@@ -1,32 +1,31 @@
\appendix
+{\bf
\section{Tuning considerations\label{ap:tuning}}
FLEXWIN is not a black-box application, and as such cannot be blindly applied
to any given dataset or tomographic scenario.  The data windowing required by
any given problem will differ depending on the inversion method, the scale of
the problem (local, regional, global), the quality of the data-set and that of
the model and method used to calculate the synthetic seismograms.  The user
-must configure and tune FLEXWIN for the given problem.  In this appendix we
-shall discuss some general considerations the uesr should bear in mind during
+must configure and tune the algorithm for the given problem.  In this appendix we
+shall discuss some general considerations the user should bear in mind during
the tuning process.  For more detailed information on tuning, and for further
examples of tuning parameter sets, we refer the reader to the user manual that
-accomanies the FLEXWIN code distribution.
+accompanies the source code.

The order in which the parameters in Table~\ref{tb:params} are discussed in the
main text of this paper follows the order in which they are used by the
algorithm, but is not necessarily the best order in which to consider them for
tuning purposes.  We suggest the following as a practical starting sequence
-(the process will likely need to be repeated and refined several times before
+(the process will need to be repeated and refined several times before
converging on the optimal set of parameters for a given problem and data-set).

$T_{0,1}$ : In setting the corner periods of the band-pass filter, the
-user is deciding on the frequency content of the information to be used int he
+user is deciding on the frequency content of the information to be used in the
tomographic problem.  Values of these corner periods should reflect the
information content of the data, the quality of the Earth model and the
accuracy of the simulation used to generate the synthetic seismogram.  The
frequency content in the data depends on the spectral characteristics of the
-source (higher frequencies for small magnitude local events, lower frequencies
-for large magnitude events), on the instrument responses (flat to 120s for
-STS-2s, but xxxxxxxxx for Hi-Net instruments), and on the attenuation
+source, on the instrument responses, and on the attenuation
characteristics of the medium. As $T_{0,1}$ depend on the source and station
characteristics, which may be heterogeneous in any given data-set, these filter
periods can be modified dynamically by constructing an appropriate user
@@ -49,15 +48,13 @@
$w_E(t)$ should then be adjusted to exclude those portions of the waveform the
user is not interested in, by raising $w_E(t)$ (e.g. to exclude the fundamental
mode surface wave: {\em if t $>$ fundamental mode surface wave arrival time then set $w_E(t)=1$}).
-made to include or exclude low amplitude local maxima in $E(t)$ from the window
-creation process, but we suggest such adjustments be made after $r0(t)$,
+We suggest finer adjustments to $w_E(t)$ be made after $r0(t)$,
$CC_0(t)$, $\Delta T_0(t)$ and $\Delta \ln A_0(t)$ have been configured.

-$r0(t), CC_0(t)$, $\Delta T_0(t)$, $\Delta \ln A_0(t)$ : These parameters ---
-window signal-to-noise ratio, normalised cross-correlation value between
+$r0(t), CC_0(t)$, $\Delta T_0(t)$, $\Delta \ln A_0(t)$ : These parameters --
+window signal-to-noise ratio, normalized cross-correlation value between
observed and synthetic seismograms, cross-correlation time lag, and amplitude
-ratio --- control the degree of well-behavedness of the data within accepted
+ratio -- control the degree of well-behavedness of the data within accepted
windows.  The user first sets constant values for these four parameters, then
adds a time dependence if required.  Considerations that should be taken into
account include the quality of the Earth model used to calculate the synthetic
@@ -67,18 +64,20 @@
(e.g. {\em for t close to the expected arrival for $P_{\rm diff}$, reduce $r_0(t)$}).

-$c{0-4}$ : err... \ldots
+$c_{0-4}$ : These parameters are active in phase B of the algorithm, phase in which the suite of all possible data windows is pared down using criteria on the shape of the STA:LTA $E(t)$ waveform alone.  Detailed descriptions of the behavior of each parameter are available in section~\ref{sec:phaseB} and will not be repeated here.  We suggest the user start by setting these values to those used in our global example (see Table~\ref{tb:example_params}).  Subsequent minimal tuning should be performed by running the algorithm on a subset of the data and closely examining the lists of windows rejected at each stage to make sure the user agrees with the choices made by the algorithm.

-\section{Example user functions\label{ap:user_fn}}
-Functional forms of the time-dependent parameters in Table~\ref{tb:params} used
-for three example scenarios discussed in section~\ref{sec:results}. They vary with
-epicentral distance and earthquake depth.
+The objective of the tuning process summarily described here should be to maximize the selection of windows around desirable features in the seismogram, while minimizing the selection of undesirable features, bearing in mind that the desirability or undesirability of a given feature is subjective, and depends on how the user subsequently intends to use the information contained within he data windows.

-\subsection{Global scenario\label{ap:user_global}}
+\subsection{Examples of user functions\label{ap:user_fn}}

-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.
+As concrete examples of how the time dependence of these tuning parameters can be used, we present here the functional forms of these time dependencies used for the three example tomographic scenarios described in the text (Windowing Examples, section~\ref{sec:results}).

-We use the following parameters:
+
+\subsubsection{Global scenario\label{ap:user_global}}
+
+In the following, $h$ indicates earthquake depth, $t_Q$ indicates the approximate start of the Love wave predicted by a group wave speed of 4.2~\kmps, and $t_R$ indicates the approximate end of the Rayleigh wave predicted by a group wave speed of 3.2~\kmps. In order to reduce the number of windows picked beyond R1, and to ensure that those selected beyond R1 are a very good match to the synthetic waveform, we raise the water level on the STA:LTA waveform and impose stricter criteria on the signal-to-noise ratio and the waveform similarity after the approximate end of the surface wave arrivals.  We allow greater flexibility in cross-correlation time lag $\Delta\tau$ for intermediate depth and deep earthquakes.  We lower the cross-correlation value criterion for surface waves in order to retain windows with a slight mismatch in dispersion characteristics.
+
+We therefore use the following time modulations:
\begin{align}
w_E(t) & =
\begin{cases}
@@ -119,11 +118,9 @@

%--------------------------

-\subsection{Japan scenario\label{ap:user_japan}}
-Below $t_P$ and $t_S$ denote the start of the time windows for P wave and S wave, predicted by 1-D IASPEI91 model \citep{KennettEngdahl1991}.  The finish time for the surface-wave time window is indicated
-by $t_{R1}$.
+\subsubsection{Japan scenario\label{ap:user_japan}}
+In the following, $t_P$ and $t_S$ denote the start of the time windows for $P$- and $S$ waves, as predicted by the 1-D IASPEI91 model \citep{KennettEngdahl1991}, and $t_{R1}$ indicates the end of the surface-wave time window.  For the \trange{24}{120} data, we consider the waveform between start of the $P$ wave to the end of the surface wave.  We therefore modulate $w_E(t)$ as follows:

-For the \trange{24}{120} data, we use
%
\begin{align}
w_E(t) & =
@@ -134,7 +131,7 @@
\end{cases}
\end{align}

-For the \trange{6}{30} data, we avoid selecting surface-wave arrivals, and therefore we make the modifications
+For the \trange{6}{30} data, the fit between the synthetic and observed surface waves is expected to be poor, as the 3D model used to calculate the synthetics cannot produce the required complexity. We therefore want concentrate on body wave arrivals only, and avoid surface wave windows altogether by modulate $w_E(t)$ as follows:
%
\begin{align}
w_E(t) & =
@@ -145,7 +142,8 @@
\end{cases}
\end{align}

-For data in both period ranges, we use
+We use constant values of $r_0(t)=r_0$, $\mathrm{CC}_0(t)=\mathrm{CC}_0$ and $\Delta \ln A_0(t)=\Delta \ln A_0$ for both period ranges.  In order to allow greater flexibility in cross-correlation time lag $\Delta\tau$ for intermediate depth and deep earthquakes we use:
+
\begin{align}
\Delta\tau_0(t) & =
\begin{cases}
@@ -156,11 +154,11 @@
\end{align}
%--------------------------

-\subsection{Southern California scenario\label{ap:user_socal}}
+\subsubsection{Southern California scenario\label{ap:user_socal}}

-Below $t_P$ and $t_S$ denote the start of the time windows for the crustal P wave and the crustal S wave, computed from a 1D layered model \citep{Wald95}.  The start and finish times for the surface-wave time window, $t_{R0}$ and $t_{R1}$, as well as the criteria for the time shifts $\Delta\tau_0(t)$, are computed from the formulas in \cite{KomatitschEtal2004}. The source-receiver distance (in km) is denoted by $\Delta$.
+In the following, $t_P$ and $t_S$ denote the start of the time windows for the crustal P wave and the crustal S wave, computed from a 1D layered model appropriate to Southern California \citep{Wald95}.  The start and end times for the surface-wave time window, $t_{R0}$ and $t_{R1}$, as well as the criteria for the time shifts $\Delta\tau_0(t)$, are derived from formulas in \cite{KomatitschEtal2004}. The source-receiver distance (in km) is denoted by $\Delta$.

-For the \trange{6}{40} data, we use
+For the \trange{6}{40} data, we exclude any arrivals before the $P$ wave and reduce the number of windows picked beyond R1 by modulating $w_E(t)$.  We use constant values of $r_0(t)=r_0$, $\mathrm{CC}_0(t)=\mathrm{CC}_0$ and $\Delta \ln A_0(t)=\Delta \ln A_0$, but modulate the cross-correlation time lag criterion so that it is less strict at larger epicentral distances and for surface waves.  We therefore use:
%
\begin{align}
w_E(t) & =
@@ -170,20 +168,15 @@
2 w_E & \text{$t > t_{R1}$},
\end{cases}
\\
-r_0(t) & = r_0,
-\\
-\mathrm{CC}_0(t) & = \mathrm{CC}_0,
-\\
\Delta\tau_0(t) & =
\begin{cases}
3.0 + \Delta/80.0 & \text{$t \le t_{R0}$}, \\
3.0 + \Delta/50.0 & \text{$t > t_{R0}$},
\end{cases}
-\\
-\Delta \ln A_0(t) & = \Delta \ln A_0 .
\end{align}

-For the \trange{2}{40} data, we avoid selecting surface-wave arrivals, and therefore we make the modifications
+For the \trange{2}{40} data, we avoid selecting surface-wave arrivals as the 3D model used to calculate the synthetics cannot produce the required complexity.  We remove the distance dependence on $\Delta\tau_0(t)$, as higher frequency body waves are well behaved in this model, and keep all other criteria the same.  The parameter modulation for these data becomes:
+
%
\begin{align}
w_E(t) & =
@@ -196,4 +189,5 @@
\Delta\tau_0(t) & = \Delta\tau_0.
\end{align}

-%--------------------------
+}
+%-----------------------

===================================================================
--- seismo/3D/ADJOINT_TOMO/flexwin/latex/discussion.tex	2008-11-04 09:49:03 UTC (rev 13252)
+++ seismo/3D/ADJOINT_TOMO/flexwin/latex/discussion.tex	2008-11-04 16:36:23 UTC (rev 13253)
@@ -1,9 +1,22 @@
+{\bf
+\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.
+
+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.
+
+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.
+
+
+
+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.
+}

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.

@@ -13,8 +26,7 @@

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.
-%noise in the observed seismograms is described well, which is rare.
-Without an adequate description of the noise, it is prudent to resort to the selection of time windows even for waveform difference measurements.
+Without an adequate description of the noise, it is more prudent to resort to the selection of time windows even when tomographic inversion is performed on waveform difference measurements.

%------------------------------