text:
alessia at geodynamics.org alessia at geodynamics.org
Thu Mar 19 03:11:33 PDT 2009

Author: alessia
Date: 2009-03-19 03:11:30 -0700 (Thu, 19 Mar 2009)
New Revision: 14389

Removed:
Modified:
Log:
Fixed manual

===================================================================
--- seismo/3D/ADJOINT_TOMO/flexwin_paper/latex/AM-allcitations.bib	2009-03-19 04:46:00 UTC (rev 14388)
+++ seismo/3D/ADJOINT_TOMO/flexwin_paper/latex/AM-allcitations.bib	2009-03-19 10:11:30 UTC (rev 14389)
@@ -4182,12 +4182,14 @@
Volume = 250,
Year = 2006}

- at article{MaggiEtal2008,
+ at article{MaggiEtal2009,
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}
+	Year = 2009,
+	note = {(in press)}
+	}

@article{MJJ99,
Author = {Mahatsente, R. and Jentzsch, G. and Jahr, T.},

===================================================================
--- seismo/3D/ADJOINT_TOMO/flexwin_paper/latex/Makefile	2009-03-19 04:46:00 UTC (rev 14388)
+++ seismo/3D/ADJOINT_TOMO/flexwin_paper/latex/Makefile	2009-03-19 10:11:30 UTC (rev 14389)
@@ -8,13 +8,11 @@
conclusion.tex \
def_base.tex \
discussion.tex \
-figures_manual.tex \
figures_paper.tex \
flexwin_manual.tex \
flexwin_paper.tex \
introduction.tex \
manual_introduction.tex \
-manual_method.tex \
manual_tuning.tex \
manual_technical.tex \
manual_other.tex \

===================================================================
--- seismo/3D/ADJOINT_TOMO/flexwin_paper/latex/acknowledgements.tex	2009-03-19 04:46:00 UTC (rev 14388)
+++ seismo/3D/ADJOINT_TOMO/flexwin_paper/latex/acknowledgements.tex	2009-03-19 10:11:30 UTC (rev 14389)
@@ -8,6 +8,6 @@
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 the U.S.G.S.
-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.
+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. We thank Vala Hjorleifsdottir for her constructive suggestions during the development of the code.
We thank Jeroen Ritsema and an anonymous reviewer for insightful comments that
helped improve the manuscript.

===================================================================
--- seismo/3D/ADJOINT_TOMO/flexwin_paper/latex/figures_manual.tex	2009-03-19 04:46:00 UTC (rev 14388)
+++ seismo/3D/ADJOINT_TOMO/flexwin_paper/latex/figures_manual.tex	2009-03-19 10:11:30 UTC (rev 14389)
@@ -1,300 +0,0 @@
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Table captions
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Tables
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\newpage
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\clearpage
-\begin{table}
-\begin{tabular}{lrrrrrl}
-\hline
-Identifier & Latitude & Longitude & Depth, km & Moment, N m & $M_w$ & Location \\
-\hline
-\multicolumn{7}{c}{Global} \\ \hline
-% CHECK THAT THE MOMENT IS LISTED IN N-M, NOT DYNE-CM
-% CARL HAS FORMULAS TO CONVERT FROM A MOMENT TENSOR TO M0 TO MW
-101895B		& 28.06		& 130.18	& 18.5	& 5.68e19 & 7.1	& Ryukyu Islands \\
-050295B		& -3.77		& -77.07	& 112.8	& 1.27e19 & 6.7	& Northern Peru \\
-060994A		& -13.82	& -67.25	& 647.1	& 2.63e21 & 8.2	& Northern Bolivia \\
-\hline
-\multicolumn{7}{c}{Japan} \\ \hline
-051502B		& 24.66		& 121.66	& 22.4	& 1.91e18 & 6.1	& Taiwan \\
-200511211536A	& 30.97		& 130.31	& 155.0	& 2.13e18 & 6.2	& Kyuhu, Japan \\
-091502B		& 44.77		& 130.04	& 589.4	& 4.24e18 & 6.4	& Northeastern China \\
-\hline
-\multicolumn{7}{c}{Southern California} \\ \hline
-9983429		& 35.01		& -119.14	& 13.5	& 9.19e15 & 4.6	& Wheeler Ridge, California \\
-9818433		& 33.91		& -117.78	& 9.4	& 3.89e15 & 4.3	& Yorba Linda, California \\
-\hline
-\end{tabular}
-\caption{\label{tb:events}
-Example events used in this study.  The identifier refers to the CMT catalog for global events and Japan events, and refers to the Southern California Earthquake Data Center catalog for southern California events.
-}
-\end{table}
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\clearpage
-\begin{table}
-\begin{center}
-\begin{tabular}{lccccc}
-\hline
-		& Global	& \multicolumn{2}{c}{Japan}	& \multicolumn{2}{c}{S. California} \\
-\hline
-$T_{0,1}$	& 50, 150	& 24, 120 	& 6, 30		& 6, 40		& 2, 40		\\
-$r_{P,A}$	& 3.5, 3.0	& 3.5, 3.0	& 3.5, 3.0	& 3.5, 3.0	& 3.5, 2.5	\\
-$r_0$		& 2.5		& 1.5		& 3.0		& 2.5		& 4.0		\\
-$w_E$		& 0.08		& 0.11		& 0.12		& 0.22		& 0.07		\\
-$CC_0$		& 0.85		& 0.70		& 0.70		& 0.74		& 0.85		\\
-$\Delta\tau_0$	& 15		& 12.0		& 3.0		& 3.0		& 2.0		\\
-$\Delta\ln{A}_0$& 1.0 		& 1.0		& 1.0		& 1.5		& 1.0		\\
-\hline
-$c_0$		& 0.7		& 0.7		& 0.7		& 0.7		& 1.0		\\
-$c_1$		& 4.0		& 3.0		& 3.0		& 2.0		& 4.0		\\
-$c_2$		& 0.3		& 0.0		& 1.0		& 0.0		& 0.0		\\
-$c_{3a,b}$	& 1.0, 2.0	& 1.0, 2.0	& 1.0, 2.0	& 3.0, 2.0	& 4.0, 2.5	\\
-$c_{4a,b}$	& 3.0, 10.0	& 3.0, 25.0	& 3.0, 12.0	& 2.5, 12.0	& 2.0, 6.0	\\
-$w_{CC}, w_{\rm len}, w_{\rm nwin}$
-		& 1, 1, 1 	& 1, 1, 1	& 1, 1, 1	& 1, 0, 0	& 1, 0, 0.5	\\
-\hline
-\end{tabular}
-\caption{\label{tb:example_params}
-Values of standard and fine-tuning parameters for the three seismological
-scenarios discussed in this study.
-}
-\end{center}
-\end{table}
-
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Figure captions
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Figures
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\clearpage
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\clearpage
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\clearpage
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\clearpage
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\clearpage
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\clearpage
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\clearpage
-\begin{figure}
-\center \includegraphics[width=6in]{figures/fig/examples_global.pdf}
-\caption{\label{fg:examples}
-(a)~Window selection results for event 101895B from Table~\ref{tb:events} recorded
-at LBTB ($25.01$\degS, $25.60$\degE, $\Delta=113$\deg, radial component).
-Phases contained within selected windows:
-(1)~$SKS$, (2)~$PS+SP$, (3)~$SS$, (4)~fundamental mode Rayleigh wave (5) unidentified late phase.
-(b)~Body wave ray paths corresponding to data windows in (a).
-(c)~Window selection results for event 060994A from Table~\ref{tb:events} recorded at WUS ($41.20$\degN, $79.22$\degE, $\Delta=140$\deg, transverse component).
-Phases contained within selected windows: (1)~$S_{\rm diff}$, (2)~$sS_{\rm diff}$, (3)~$SS$, (4)~$sSS$ followed by $SSS$, (5)~$sS5+S6$, (6)~$sS6+S7$ followed by $sS7$, (7)~major arc $sS4$, (8)~major arc $sS6$.
-(d)~Body wave ray paths corresponding to data windows in (c).
-}
-\end{figure}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\clearpage
-\begin{figure}
-\center \includegraphics[width=6in]{figures/fig/composites_global.pdf}
-\caption{\label{fg:composites}
-(a)-(c)~Summary plots of windowing results for event 101895B in Table~\ref{tb:events}.
-(a)~Global map showing great-circle paths to stations.
-(b)~Histograms of number of windows as a function of normalised cross-correlation $CC$, time-lag $\tau$ and amplitude ratio $\Delta \ln A$; these give information about systematic trends in time shift and amplitude scaling.
-(c)~Record sections of selected windows for the vertical, radial and transverse components.  The filled portions of the each record in the section indicate where windows have been selected by the algorithm.
-(d)-(f)~Summary plots of windowing results for event 060994A in Table~\ref{tb:events}.
-}
-\end{figure}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% JAPAN
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-
-%\clearpage
-%\begin{figure}
-%%\center
-%\includegraphics[width=5.7in]{figures/japan/ERM_II_051502B}
-%\caption{\label{fg:ERM_II_051502B}
-%Window selection results for event 051502B from Table~\ref{tb:events} recorded at station ERM ($42.01$\degN, $143.16$\degE, $\Delta=24.83$\deg).
-%(a)~Event and station map: event is 051502B indicated by the beach ball with the
-%CMT focal mechanism, station ERM is marked as red triangles and all the other stations
-%which recorded this event are marked by grey triangles.
-%(b)~Results for station ERM for the period range \trange{24}{120}.
-%Vertical (Z), radial (R), and transverse (T) records of data (black, left column) and synthetics (red, left column), as well as the STA/LTA records (right column) used to produce the window picks.
-%(c)~Results for station ERM for the period range \trange{6}{30}.
-%}
-%\end{figure}
-%\clearpage
-
-
-\begin{figure}
-%\center
-\includegraphics[width=5.7in]{figures/japan/KIS_BO_091502B}
-\caption{\label{fg:KIS_BO_091502B}
-Window selection results for event 091502B from Table~\ref{tb:events} recorded at station KIS ($33.87$\degN, $135.89$\degE, $\Delta=11.79$\deg).
-(a)~Event and station map: event is 091502B indicated by the beach ball with the
-CMT focal mechanism, station KIS is marked as red triangles and all the other stations
-which recorded this event are marked by grey triangles.
-(b)~Results for station KIS for the period range \trange{24}{120}.
-Vertical (Z), radial (R), and transverse (T) records of data (black, left column) and synthetics (red, left column), as well as the STA/LTA records (right column) used to produce the window picks.
-(c)~Results for station KIS for the period range \trange{6}{30}.
-}
-\end{figure}
-
-\clearpage
-\begin{figure}
-%\center
-\includegraphics[width=5.7in]{figures/japan/SHR_BO_200511211536A}
-\caption{\label{fg:SHR_BO_200511211536A}
-Window selection results for event 20051121536A from Table~\ref{tb:events} recorded at station SHR ($44.06$\degN, $144.99$\degE, $\Delta=17.47$\deg).
-(a)~Event and station map: event 20051121536A is indicated by the beach ball with the
-CMT focal mechanism, station SHR is marked as red triangles and all the other stations
-which recorded this event are marked by grey triangles.
-(b)~Results for station SHR for the period range \trange{24}{120}.
-Vertical (Z), radial (R), and transverse (T) records of data (black, left column) and synthetics (red, left column), as well as the STA/LTA records (right column) used to produce the window picks.
-(c)~Results for station SHR for the period range \trange{6}{30}.
-Note that corresponding low-frequency band-passed filtered version (b) has longer record length (800~s).
-}
-\end{figure}
-
-\clearpage
-\begin{figure}
-%\center
-\includegraphics[width=6in]{figures/japan/200511211536A_T06_rs}
-\caption{\label{fg:200511211536A_T06_rs}
-Summary plots of windowing results for event 200511211536A in Table~\ref{tb:events}, for the period range \trange{6}{30}.
-(a)~Map showing paths to each station with at least one measurement window.
-(b)-(d)~Histograms of number of windows as a function of normalised cross-correlation $CC$, time-lag $\tau$ and amplitude ratio $\Delta \ln A$.
-(e)-(g)~Record sections of selected windows for the vertical, radial and transverse components.
-}
-\end{figure}
-
-\clearpage
-\begin{figure}
-%\center
-\includegraphics[width=6in]{figures/japan/200511211536A_T24_rs}
-\caption{\label{fg:200511211536A_T24_rs}
-Summary plots of windowing results for event 200511211536A in Table~\ref{tb:events}, for the period range \trange{24}{120}.
-}
-\end{figure}
-
-\clearpage
-\begin{figure}
-%\center
-\includegraphics[width=6in]{figures/japan/stats_T06}
-\caption{\label{fg:T06_rs}
-Summary statistics of windowing results for events 051502B, 200511211536A and 091502B in Table~\ref{tb:events}, for the period range \trange{6}{30}.
-}
-\end{figure}
-
-
-%
-%\clearpage
-%\begin{figure}
-%%\center
-%\includegraphics[width=6in]{figures/japan/051502B_T06_rs}
-%\caption{\label{fg:051502B_T06_rs}
-%Summary plots of windowing results for event 051502B in Table~\ref{tb:events}, for the period range \trange{6}{30}.
-%Same as Figure~\ref{fg:200511211536A_T06_rs}.
-%}
-%\end{figure}
-%
-%\clearpage
-%\begin{figure}
-%%\center
-%\includegraphics[width=6in]{figures/japan/091502B_T06_rs}
-%\caption{\label{fg:091502B_T06_rs}
-%Summary plots of windowing results for event 091502B in Table~\ref{tb:events}, for the period range \trange{6}{30}.
-%Same as Figure~\ref{fg:200511211536A_T06_rs}.
-%}
-%\end{figure}
-
-%\clearpage
-%\begin{figure}
-%%\center
-%\includegraphics[width=6in]{figures/japan/091502B_T06_rs}
-%\caption{\label{fg:091502B_T06_rs}
-%Summary plots of windowing results for event 051502B in Table~\ref{tb:events},
-%for the period range \trange{6}{30}. Same as Figure~\ref{fg:200511211536A_T06_rs).
-%}
-%\end{figure}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% SOUTHERN CALIFORNIA
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\clearpage
-\begin{figure}
-%\center
-\includegraphics[width=6in]{figures/socal/9818433_CLC_window.pdf}
-\caption{\label{fg:socal_CLC}
-Window selection results for event 9818433 from Table~\ref{tb:events} recorded at station CLC.
-(a)~Source and station information for event 9818433 and station CLC.
-(b)~Paths to each station with at least one measurement window for the period range \trange{6}{40}.
-There are a total of 341 windows picked within 310 records.
-Triangle denotes station CLC.
-(c)~Paths to each station with at least one measurement window for the period range \trange{2}{40}.
-There are a total of 190 windows picked within 193 records.
-Triangle denotes station CLC.
-(d)~Results for station CLC for the period range \trange{6}{40}.
-Vertical (Z), radial (R), and transverse (T) records of data (black, left column) and synthetics (red, left column), as well as the STA:LTA records (right column) used to produce the window picks.
-(e)~Results for station CLC for the period range \trange{2}{40}.
-Note that corresponding lower-passed filtered versions are shown in (d).
-}
-\end{figure}
-
-\clearpage
-\begin{figure}
-%\center
-\includegraphics[width=6in]{figures/socal/9818433_FMP_window.pdf}
-\caption{\label{fg:socal_FMP}
-Window selection results for event 9818433 from Table~\ref{tb:events} recorded at station FMP.
-Same caption as Figure~\ref{fg:socal_CLC}, only for a different station.
-}
-\end{figure}
-
-\clearpage
-\begin{figure}
-%\center
-\includegraphics[width=6in]{figures/socal/9983429_T06_rs.pdf}
-\caption{\label{fg:socal_rs_T06}
-Summary plots of windowing results for event 9983429 in Table~\ref{tb:events}, for the period range \trange{6}{40}.
-(a)~Map showing paths to each station with at least one measurement window.
-(b)-(d)~Histograms of number of windows as a function of normalised cross-correlation $CC$, time-lag $\tau$ and amplitude ratio $\Delta \ln A$.
-(e)-(g)~Record sections of selected windows for the vertical, radial and transverse components.
-The two branches observed on the vertical and radial components correspond to the body-wave arrivals and the Rayleigh wave arrivals.
-}
-\end{figure}
-
-%\clearpage
-%\begin{figure}
-%%\center
-%\includegraphics[width=7in]{figures/socal/9983429_T02_rs.pdf}
-%\caption{\label{fg:socal_rs_T02}
-%(THIS FIGURE COULD IN THEORY BE CUT OUT, IF SPACE IS SHORT.)
-%Summary plots of windowing results for event 9983429 in Table~\ref{tb:events}, for the period range \trange{2}{40}.
-%Same as Figure~\ref{fg:socal_rs_T06}, only the windowing code has been run using a different set of parameters (Table~\ref{tb:example_params}), so that primarily only the body-wave arrivals are selected.
-%}
-%\end{figure}
-
-
-%\clearpage
-%\begin{figure}
-%%\center
-%Adjoint sources constructed based on the windows picked in Figure~\ref{fg:socal_CLC}d, with the specification of a cross-correlation traveltime measurement. The adjoint sources for this measurement are simply a weighted version of the synthetic velocity traces. The number to the left of each subplot is the $\pm$ height of the $y$-axis. The cross-correlation measurements for traveltime ($\Delta T$) and amplitude ($\Delta \ln A$) are listed above each time window.
-%}
-%\end{figure}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

===================================================================
(Binary files differ)

===================================================================
--- seismo/3D/ADJOINT_TOMO/flexwin_paper/latex/flexwin_manual.tex	2009-03-19 04:46:00 UTC (rev 14388)
+++ seismo/3D/ADJOINT_TOMO/flexwin_paper/latex/flexwin_manual.tex	2009-03-19 10:11:30 UTC (rev 14389)
@@ -6,6 +6,7 @@
\usepackage{setspace}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
+\usepackage{url}
\usepackage{natbib}
\usepackage[noend]{algorithmic}
@@ -17,7 +18,7 @@

\input{def_base}
\begin{document}
-\title{FLEXWIN: An automated time-window selection algorithm for seismic tomography}
+\title{FLEXWIN User Manual}
\author{Alessia Maggi}
\date{}
\maketitle

===================================================================
(Binary files differ)

===================================================================
--- seismo/3D/ADJOINT_TOMO/flexwin_paper/latex/manual_introduction.tex	2009-03-19 04:46:00 UTC (rev 14388)
+++ seismo/3D/ADJOINT_TOMO/flexwin_paper/latex/manual_introduction.tex	2009-03-19 10:11:30 UTC (rev 14389)
@@ -24,6 +24,6 @@
the algorithm was designed for use in 3D-3D adjoint tomography, its inherent
flexibility should make it useful in many data-selection applications.

-For a detailed introduction to FLEXWIN as applied to seismic tomography, please consult \cite{MaggiEtal2008} ({\tt flexwin/latex/flexwin\_paper.pdf}).  If you use FLEXWIN for your own research, please cite \cite{MaggiEtal2008}.
+For a detailed introduction to FLEXWIN as applied to seismic tomography, please consult \cite{MaggiEtal2009}.  If you use FLEXWIN for your own research, please cite \cite{MaggiEtal2009}.

===================================================================
--- seismo/3D/ADJOINT_TOMO/flexwin_paper/latex/manual_method.tex	2009-03-19 04:46:00 UTC (rev 14388)
+++ seismo/3D/ADJOINT_TOMO/flexwin_paper/latex/manual_method.tex	2009-03-19 10:11:30 UTC (rev 14389)
@@ -1,521 +0,0 @@
-\chapter{FLEXWIN, the algorithm\label{sec:algorithm}}
-
-FLEXWIN
-operates on pairs of
-observed and synthetic single component seismograms.  There is no restriction
-on the type of simulation used to generate the synthetics, though realistic
-Earth models and more complete propagation theories yield waveforms that are more similar to the observed
-seismograms, and thereby allow the definition of measurement windows
-covering more of the available data.  The input seismograms can be measures of
-displacement, velocity or acceleration, indifferently.  There is no requirement
-for horizontal signals to be rotated into radial and transverse directions.
-
-The window selection process has five phases, each of which is discussed individually
-below: {\em phase 0:} pre-processing; {\em phase A:} definition of preliminary
-measurement windows; {\em phase B:} rejection of preliminary windows based on
-the content of the synthetic seismogram alone; {\em phase C:} rejection of
-preliminary windows based on the differences between observed and synthetic
-seismograms; {\em phase D:} resolution of preliminary window overlaps.  The parameters that permit tuning of the
-window selection towards a specific tomographic scenario are all contained in a
-simple parameter file (see Table~\ref{tb:params}).  More complexity and finer
-tuning can be obtained by rendering some of these parameters time dependent, via user defined functions that can depend on the source parameters (e.g. event location or depth).
-
-\begin{table}
-\begin{tabular}{lp{0.8\linewidth}}
-\hline
-\multicolumn{2}{l}{Standard tuning parameters:} \\[5pt]
-$T_{0,1}$     & band-pass filter corner periods \\
-$r_{P,A}$     & signal to noise ratios for whole waveform \\
-$r_0(t)$      & signal to noise ratios single windows \\
-$w_E(t)$      & water level on short-term:long-term ratio \\
-$CC_0(t)$          & acceptance level for normalized cross-correlation\\
-$\Delta\tau_0(t)$  & acceptance level for time lag \\
-$\Delta\ln{A}_0(t)$   & acceptance level for amplitude ratio \\
-\hline
-\multicolumn{2}{l}{Fine tuning parameters:} \\ [5pt]
-$c_0$ & for rejection of internal minima \\
-$c_1$ & for rejection of short windows \\
-$c_2$ & for rejection of un-prominent windows \\
-$c_{3a,b}$  & for rejection of multiple distinct arrivals \\
-$c_{4a,b}$  & for curtailing of windows with emergent starts and/or codas \\
-$w_{CC}\quad w_{\rm len}\quad w_{\rm nwin}$ & for selection of best non-overlapping window combination \\
-\hline
-\end{tabular}
-\caption{\label{tb:params}
-Overview of standard tuning parameters, and of fine
-tuning parameters.  Values are defined in a parameter file, and the
-time dependence of those that depend on time is described by user-defined functions.
-}
-\end{table}
-
-
-%----------------------
-
-\pagebreak
-\section{Phase 0 -- Pre-processing \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: band-pass filtering with a non-causal Butterworth
-filter, whose
-short and long period corners we denote as $T_0$ and $T_1$ respectively.
-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.
-All further references to seismograms'' in this paper will refer to these filtered waveforms.
-
-%----------------------
-
-%\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
-\begin{align}
-P_{\rm signal} & = \frac{1}{t_E-t_A} \int_{t_A}^{t_E}d^2(t)dt, \\
-P_{\rm noise}  & = \frac{1}{t_A-t_0} \int_{t_0}^{t_A}d^2(t)dt, \label{eq:noise}
-\end{align}
-where $d(t)$ denotes the observed seismogram, $t_0$ is its start time, $t_A$ is
-set to be slightly before the time of the first arrival, and $t_E$ is the end
-of the main signal (a good choice for $t_E$ is the end of the dispersed surface
-wave).  The amplitude signal-to-noise ratio is defined analogously as
-${\rm SNR}_A = A_{\rm signal}/A_{\rm noise}$,
-where $A_{\rm signal}$ and $A_{\rm noise}$ are the maximum values of $|d(t)|$
-in the signal and noise time-spans respectively.  The limits for these two
-signal-to-noise ratios are given by the parameters $r_P$ and $r_A$ in Table~\ref{tb:params}.  We reject any record for which
-${\rm SNR}_P < r_P$ or ${\rm SNR}_A < r_A$.
-
-%----------------------
-
-%\subsubsection{Construction of STA:LTA timeseries}
-
-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.
-If we denote the Hilbert transform of the synthetic seismogram by
-$\mathcal{H}[s(t)]$, its envelope $e(t)$ is given by:
-$$-e(t) = | s(t) + i \mathcal{H}[s(t)] |. -$$
-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,
-\begin{align}
-S(t_i) & = C_S \; S(t_{i-1}) + e(t_i) \\
-L(t_i) & = C_L \; L(t_{i-1}) + e(t_i) ,
-\end{align}
-and obtain their ratio:
-$E(t_i) = S(t_i)/L(t_i)$.
-The constants $C_S$ and $C_L$ determine the decay of the relative
-weighting of earlier parts of the signal in the calculation of the current
-average.  This decay is necessarily longer for the long term average than
-for the short term average, implying that $C_S < C_L < 1$.  The choice of these
-constants determines the sensitivity of the STA:LTA timeseries.
-\citet{BaiKennett2001} used a similar timeseries to
-analyse the character of broad-band waveforms, and allowed the constants
-$C_S$ and $C_L$ to depend on the dominant period of the waveform under
-analysis.  We have followed their lead in setting
-$$-C_S = 10^{- \delta t / T_0} \qquad {\rm and} \qquad C_L = 10^{-\delta t / 12 T_0}, -$$
-where the use of $T_0$, the low-pass corner period of our band-pass filter,
-substitutes that of the dominant period.
-
-An example of a synthetic seismogram and its corresponding envelope and STA:LTA timeseries $E(t)$ is
-shown in Figure~\ref{fg:stalta}.  Before the first arrivals on the synthetic
-seismogram, the $E(t)$ timeseries warms up and rises to a plateau.  At each
-successive seismic arrival on the synthetic, $E(t)$ rises to a
-local maximum.  We can see from Figure~\ref{fg:stalta} that these local maxima
-correspond both in position and in width to the seismic phases in the
-synthetic, and that the local minima in $E(t)$ correspond to the
-transitions between one phase and the next.  In the following sections we shall
-explain how we use these correspondences to define time windows.
-
-\begin{figure}
-\center \includegraphics[width=6in]{figures/050295B.050-150/ABKT_II_LHZ_seis_nowin.pdf}
-\caption{\label{fg:stalta}
-Synthetic seismogram and its corresponding envelope and STA:LTA timeseries.
-The seismogram was calculated using SPECFEM3D and the
-Earth model S20RTS \citep{RitsemaEtal2004} for the CMT catalog event
-050295B, whose details can be found in Table~\ref{tb:events}.  The
-station, ABKT, is at an epicentral distance of 14100~km and at an azimuth of 44
-degrees from the event.  The top panel shows the vertical component synthetic
-seismogram, filtered between periods of 50 and 150 seconds. The center panel shows its envelope, and the bottom panel
-shows the corresponding STA:LTA waveform.  The dashed line overlaid on
-the STA:LTA waveform is the water level $w_E(t)$.
-}
-
-\end{figure}
-%
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\clearpage
-\pagebreak
-\section{Phase A -- Preliminary measurement windows \label{sec:phaseA}}
-%{\em Parameters used: $w_E(t)$}.
-
-The correspondence between local maxima in the STA:LTA waveform $E(t)$ and the
-position of the seismic phases in the synthetic seismogram suggests that we
-should center time windows around these local maxima.  The
-correspondence between the local minima in $E(t)$ and the transition between
-successive phases suggests the time windows should start and end at these local
-minima.  In the case of complex phases, there may be several local maxima and
-minima within a short time-span.  In order to correctly window these complex
-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
-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
-Figure~\ref{fg:stalta} corresponds to $w_E=0.08$ for the duration of the main
-seismic signal.  Typical values for $w_E$ vary between $0.05$ and $0.25$ depending on the seismological scenario and
-the desired sensitivity.  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. The functional forms of the time-dependent parameters are defined by the user, can depend on
-remain unchanged once the system has been tuned (see Appendix~\ref{ap:user_fn}).
-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.
-
-We take each acceptable local maximum in turn as a seed maximum, and create all
-possible candidate windows that contain it, as illustrated by
-Figure~\ref{fg:win_composite}a.  Each candidate window is defined by three times: its
-start time $t_S$, its end time $t_E$ and the time of its seed maximum $t_M$.
-The start and end times correspond to local minima in $E(t)$.  It is important
-to note that in many of the window rejection algorithms, $t_M$ will be significant.  For $N$ local maxima that lie above $w_E(t)$, the number of preliminary candidate windows defined in this manner is
-$$-N_{\rm win} = \sum_{n=1}^N \left[nN - (n-1)^2\right] \sim O(N^3). -$$
-
-\begin{figure}
-\center \includegraphics[width=6in]{figures/fig/window_composite.pdf}
-\caption{\label{fg:win_composite}
-(a)~Window creation process.  The thick black line represents the STA:LTA
-waveform $E(t)$, and the thick horizontal dashed line its water level $w_E(t)$.
-Local maxima are indicated by alternating red and blue dots, windows are
-indicated by two-headed horizontal arrows.  The time of the local maximum used
-as the window seed $t_M$ is denoted by the position of the dot. Only windows for the fourth local maximum are shown.  (b)~Rejection of candidate windows based on the amplitude of the local minima.  The two deep
-local minima indicated by the grey arrows form virtual barriers. All candidate
-windows that cross these barriers are rejected.
-(c)~Rejection of candidate
-windows based on the prominence of the seed maximum.  The local maxima
-indicated by the grey arrows are too low compared to the local minima
-adjacent to them.  All windows that have these local maxima as their seed are
-rejected (black crosses over the window segments below the time series).
-(d)~Shortening of long coda windows.  The grey bar indicates the maximum coda
-duration $c_{4b} T_0$.  Note that after the rejection based on prominence represented in (c) and before shortening of long coda windows represented in (d), the algorithm rejects candidate windows based on the separation of distinct phases, a process that is illustrated in Figure~\ref{fg:separation}.
-}
-\end{figure}
-%
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\clearpage
-\pagebreak
-\section{Phase B -- Rejection based on the synthetic \label{sec:phaseB}}
-%{\em Parameters used: $T_0$, $w_E(t)$, $c_{0-4}$.}
-
-After having created a complete suite of candidate time windows in the manner
-described above, we start the rejection process.  We reject windows based on
-two sets of criteria concerning respectively the shape of the STA:LTA waveform $E(t)$,
-and the similarity of the observed and synthetic waveforms
-$d(t)$ and $s(t)$ within each window.   Here we describe the first set of
-criteria; the second set is described in the following section.
-
-The aim of shape-based window rejection is to retain the set of candidate
-time windows within which the synthetic waveform $s(t)$ contains well-developed seismic phases or groups of phases. The
-four rejection criteria described here are parameterized by the constants
-$c_{0-3}$ in Table~\ref{tb:params}, and are scaled in time by $T_0$ and in
-amplitude by $w_E(t)$.  We apply these criteria sequentially.
-
-Firstly, we reject all windows that contain internal local minima of $E(t)$
-whose amplitude is less than $c_0 w_E(t)$.  We have seen above that local
-minima of $E(t)$ tend to lie on the transitions between seismic phases.  By
-rejecting windows that span deep local minima, we are in fact forcing partition
-of unequivocally distinct seismic phases into separate time windows (see Figure~\ref{fg:win_composite}b).
-Secondly, we reject windows whose length is less than $c_1 T_0$.  By
-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
-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:
-$$-%h/h_M > f(\frac{\Delta T}{T_0}; c_{3a},c_{3b}), -h/h_M > f(\Delta T/T_0; c_{3a},c_{3b}), -$$
-where $h_M$ is the height of the seed maximum $E(t_M)$ above the deepest
-minimum between itself and another maximum, $h$ is the height of this other
-maximum above the same minimum, and $f$ is a function of the time
-separation $\Delta T$ between the two maxima (see Figure~\ref{fg:separation}).
-The function $f(\Delta T)$ has the following form:
-$$-f(\Delta T) = -\begin{cases} -c_{3a} & \text{ \Delta T/T_0 \leq c_{3b}} \\ -c_{3a}\exp{[-(\Delta T/T_0-c_{3b})^2/c_{3b}^2]} & \text{ \Delta T/T_0 > c_{3b}.} -\end{cases} -\label{eq:sep} -$$
-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 also 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.
-
-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
-be evaluated in terms of the similarity between observed and synthetic
-waveforms within the window limits.  Special precautions may have to be taken,
-however, in the case of windows that contain long coda waves: the
-details of codas are often poorly matched by synthetic seismogram calculations,
-as they are essentially caused by multiple scattering processes.   In order to
-avoid rejecting a nicely fitting phase because of a poorly fitting coda or a
-poorly fitting emergent start, we introduce the $c_4$ tuning parameters, which
-permit shortening of windows starting with monotonically increasing $E(t)$
-or ending with monotonically decreasing $E(t)$.
-These windows are shortened on the left if they start earlier than $c_{4a} T_0$
-before their first local maximum, and on the right if they end later than
-$c_{4b} T_0$ after their last local maximum (see Figure~\ref{fg:win_composite}d).
-
-Figures~\ref{fg:win_composite} and~\ref{fg:separation} illustrate the shape based
-rejection procedure (Phase B) on a schematic $E(t)$ time series.  Each
-successive criterion reduces the number of acceptable candidate windows.  A
-similar reduction occurs when this procedure is applied to real $E(t)$ time series, as shown
-by the upper portion of Figure~\ref{fg:win_rej_data}.
-
-\begin{figure}
-\center \includegraphics[width=5in]{figures/fig/window_rejection_separation.pdf}
-\caption{\label{fg:separation}
-Rejection of candidate windows based on the separation of distinct phases.
-(a)~Heights of pairs of local maxima above their intervening minimum.
-(b)~The black line represents $f(\Delta T/T_0)$ from
-equation~(\ref{eq:sep}) with $c_{3a}=c_{3b}=1$.  Vertical bars represent
-$h/h_M$ for each pair of maxima.  Their position along the horizontal axis is
-given by the time separation $\Delta T$ between the maxima of each pair.  The
-color of the bar is given by the color of the seed maximum corresponding to $h_M$.  Bars whose height
-exceeds the $f(\Delta T/T_0)$ line represent windows to be rejected.
-(c)~The windows that have been rejected by this criterion are indicated by black
-crosses.
-}
-\end{figure}
-
-\begin{figure}
-\center \includegraphics[width=6in]{figures/fig/window_rejection_global_data.pdf}
-\caption{\label{fg:win_rej_data}
-Window rejection applied to real data.
-Top panel: observed (black) and synthetic (red) seismograms for the 050295B event
-recorded at ABKT (see Figure~\ref{fg:stalta}).
-Subsequent panels: candidate windows at different stages, separated into Phase B (shape based rejection) and
-Phase C (fit based rejection).  Each candidate window is indicated by a black
-segment.  The number of windows at each stage is shown to the left of the
-panel.
-}
-\end{figure}
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\clearpage
-\pagebreak
-\section{Phase C -- Rejection based on seismogram differences \label{sec:phaseC}}
-%{\bf User parameters: $CC_0(t)$, $\Delta\tau_0(t)$, $\Delta\ln{A}_0(t)$}
-
-After having greatly reduced the number of candidate windows by rejection based
-on the shape of the STA:LTA time series $E(t)$, we are now left with a set of
-windows that contain well-developed seismic phases or
-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.
-
-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
-observed and synthetic seismograms $CC$,
-cross-correlation time lag $\Delta \tau$, and amplitude ratio $\Delta \ln -A$.  The signal to noise ratio for single windows is defined as an amplitude
-ratio, ${\rm SNR}_W=A_{\rm window}/A_{\rm noise}$, where $A_{\rm window}$ and
-$A_{\rm noise}$ are the maximum absolute values of the observed seismogram $|d(t)|$ in the window
-and in the noise time-span respectively (see equation~\ref{eq:noise}).  The cross-correlation value $CC$ is defined as the maximum value of the
-cross-correlation function ${\rm CC}={\rm max}[\Gamma(t^\prime)]$, where
-$$-\Gamma(t^\prime) = \int s(t-t^\prime)d(t)dt, -$$
-and
-quantifies the similarity in shape between the $s(t)$ and $d(t)$
-waveforms.  The time lag $\Delta \tau$ is defined as the value of $t^\prime$
-at which $\Gamma$ is maximal, and quantifies the delay in time between a
-synthetic and observed phase arrival. The amplitude ratio $\Delta \ln A$ is
-defined as the amplitude ratio between observed and synthetic
-seismograms \citep{DahlenBaig2002}
-$$-\Delta\ln{A} = \left[ \frac{\int d(t)^2 dt}{\int s(t)^2 dt} \right]^{1/2} - 1. \label{eq:dlnA_def} -$$
-The limits that trigger rejection of windows based on the values of these four
-quantities are the time dependent parameters $r_0(t)$, $CC_0(t)$, $\Delta -\tau_0(t)$ 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.
-Figure~\ref{fg:criteria} shows the time
-dependence of $CC_0$ , $\Delta \tau_0$ and $\Delta \ln A_0$ for an example seismogram.
-
-We only accept candidate windows that satisfy all of the following:
-\begin{align}
-{\rm SNR}_W & \geq r_0(t_M), \label{eq:snr_win} \\
-{\rm CC} & \geq {\rm CC}_0(t_M), \label{eq:cc} \\
-|\Delta\tau| & \leq \Delta\tau_0(t_M), \label{eq:tau} \\
-|\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
-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
-windows (see lower portion of Figure~\ref{fg:win_rej_data}).  They are
-essential, however, in eliminating problems due secondary events (natural or
-man-made), diffuse noise sources, or instrumental glitches.
-
-
-\begin{figure}
-\center \includegraphics[width=6in]{figures/050295B.050-150/ABKT_II_LHZ_criteria.pdf}
-\caption{\label{fg:criteria}
-Time dependent fit based criteria
-for the 050295B event recorded at ABKT. The time-dependence of these criteria
-is given by the formulae in Appendix~\ref{ap:user_global}. The lower limit on
-acceptable cross-correlation value, $CC_0$ (solid line), is
-0.85 for most of the duration of the seismogram; it is lowered to 0.75 during
-the approximate surface wave window  defined by the group velocities 4.2\kmps\
-and 3.2\kmps, and is raised to 0.95 thereafter.  The upper limit on time lag,
-$\tau_0$ (dotted line), is 21~s for the whole seismogram.  The upper limit on amplitude
-ratio, $\Delta \ln A_0$ (dashed line), is 1.0 for most of the seismogram; it is reduced to
-1/3 of this value after the end of the surface waves.
-}
-\end{figure}
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\clearpage
-\pagebreak
-\section{Phase D -- Overlap resolution \label{sec:phaseD}}
-%{\em User parameters: $w_{CC}$, $w_{\rm len}$.}
-
-After having rejected candidate data windows that fail any of the shape or
-similarity based criteria described above, we are left with a small number of
-windows, each of which taken singly would be an acceptable time window for
-measurement.  As can be seen from Figure~\ref{fg:win_composite}d and the last
-panel of Figure~\ref{fg:win_rej_data}, the remaining windows may
-overlap partially or totally with their neighbours.  Such overlaps are
-problematic for automated measurement schemes, as they lead to multiple
-measurements of those features in the seismogram that lie within the overlapping
-portions.  Resolving this overlap problem is the last step in the
-windowing process.
-
-Overlap resolution can be seen as a set of choices leading to
-the determination of an optimal set of time windows.  What do we mean by
-optimal?  For our purposes, an optimal set of time windows contains only windows that
-have passed all previous tests, that do not overlap with other windows in the set,
-and that cover as much of the seismogram as possible.  When choosing between
-candidate windows, we favour those within which the
-observed and synthetic seismograms are most similar (high values of $CC$).
-Furthermore, should we have the choice between two short windows and a longer,
-equally well-fitting one covering the same time-span, we may wish to favour
-the longer window as this poses a stronger constraint on the tomographic inversion.
-
-The condition that optimal windows should have passed all previous tests
-removes the straightforward solution of merging overlapping windows.  Indeed, given any two
-overlapping windows, we know that the window defined by their merger
-existed in the complete list of candidate windows obtained at the end of
-Phase~A, and that its absence from the current list means it was rejected
-either because of the shape of its $E(t)$ time-series (Phase~B), or because of
-an inadequate similarity between observed and synthetic waveforms (Phase~C).
-It would therefore be meaningless to re-instate such a window at this stage.
-Any modification of current candidate windows would be disallowed by similar
-considerations.  We must therefore choose between overlapping
-candidates.
-
-We make this choice by constructing all possible non-overlapping subsets of
-candidate windows, and scoring each subset on three criteria: length of
-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 $CC$ 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
-$w_{CC}$, $w_{\rm len}$ 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
-with any other group.  The selection of the optimal subsets can then be
-performed independently within each group.  We score each non-overlapping
-subset of windows within a group using the following three metrics:
-\begin{align}
-S_{CC} &= \sum_i^{N_{\rm set}} CC_i / N_{\rm set},\\
-S_{\rm len} &= [\sum_i^{N_{\rm set}} t^e_i - t^s_i]/[t^e_g - t^s_g], \\
-S_{\rm nwin} & = 1 - N_{\rm set}/N_{\rm group},
-\end{align}
-where $CC_i$ is the cross-correlation value of the $i$th window in
-the subset, $N_{\rm set}$ is the number of windows in the subset, $N_{\rm -group}$ is the number of windows in the group, and $t^s_i$, $t^e_i$, $t^s_g$
-and $t^e_g$ are respectively the start and end times of the $i$th candidate
-window in the set, and of the group itself.  The three scores
-are combined into one using the weighting parameters:
-$$-S = \frac{w_{CC}S_{CC}+w_{\rm len}S_{\rm len}+w_{\rm nwin}S_{\rm nwin}}{w_{CC}+w_{\rm len}+w_{\rm nwin}}. -\label{eq:score} -$$
-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
-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.
-
-\begin{figure}
-\center \includegraphics[width=5in]{figures/fig/window_overlap.pdf}
-\caption{\label{fg:phaseD}
-The selection of the best non-overlapping window
-combinations.  Each grey box represents a distinct group of windows.
-Non-overlapping subsets of windows are shown on separate lines.  Only one
-line from within each group will be chosen, the one corresponding to the
-highest score obtained in equation~(\ref{eq:score}).  The resulting optimal set
-of data windows is shown by thick arrows.}
-\end{figure}
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{figure}
-\center \includegraphics[width=6in]{figures/fig/window_results.pdf}
-\caption{\label{fg:res_abkt}
-Window selection results for event 050295B
-from Table~\ref{tb:events} recorded at ABKT ($37.93$\degN,
-$58.11$\degE, $\Delta=127$\deg, vertical
-component).
-(a)~Top: observed and synthetic seismograms (black and red
-traces); bottom: STA:LTA timeseries $E(t)$.  Windows chosen by the algorithm
-are shown using light blue shading.  The phases contained these windows are:
-(1) $PP$, (2) $PS+SP$, (3) $SS$, (4) $SSS$, (5) $S5$, (6) $S6$, (7) fundamental
-mode Rayleigh wave.
-(b)~Ray paths corresponding to the body wave phases present in the data windows.
-}
-\end{figure}
-%

===================================================================
--- seismo/3D/ADJOINT_TOMO/flexwin_paper/latex/manual_other.tex	2009-03-19 04:46:00 UTC (rev 14388)
+++ seismo/3D/ADJOINT_TOMO/flexwin_paper/latex/manual_other.tex	2009-03-19 10:11:30 UTC (rev 14389)
@@ -3,12 +3,16 @@
To report bugs or suggest improvements to the code, please send an email to the CIG Computational Seismology Mailing List (cig-seismo at geodynamics.org) or Alessia Maggi (alessia at sismo.u-strasbg.fr), and/or use our online bug tracking system Roundup (www.geodynamics.org/roundup).

\section{Notes and Acknowledgments}
-[FIXME]  The filtering routines used in {\tt seismo\_subs.f90} are based on the SacLib libraries constructed by Brian Savage from the original source code of SAC (developed at Lawrence Livermore).  What about SAC licences??
+The main developers of the FLEXWIN source code are Alessia Maggi and Carl Tape.  The following individuals (listed in alphabetical order) have also contributed to the development of the source code: Daniel Chao, Min Chen, Vala Hjorleifsdottir, Qinya Liu, Jeroen Tromp.  The following individuals (listed in alphabetical order) contributed to this manual: Sue Kientz, Alessia Maggi, Carl Tape.

-The main developers of the FLEXWIN source code are Alessia Maggi and Carl Tape.  The following individuals (listed in alphabetical order) have also contributed to the development of the source code: Daniel Chao, Min Chen, Jeroen Tromp.  The following individuals (listed in alphabetical order) contributed to this manual: Sue Kientz, Alessia Maggi, Carl Tape \ldots
+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.

+We acknowledge support by the National Science Foundation under grant EAR-0711177.
+
+

Any commercial use must be negotiated with the Office of Technology Transfer at
the California Institute of Technology.  This software may be subject to U.S.

===================================================================
--- seismo/3D/ADJOINT_TOMO/flexwin_paper/latex/manual_technical.tex	2009-03-19 04:46:00 UTC (rev 14388)
+++ seismo/3D/ADJOINT_TOMO/flexwin_paper/latex/manual_technical.tex	2009-03-19 10:11:30 UTC (rev 14389)
@@ -12,75 +12,29 @@
\end{itemize}

FLEXWIN requires the following libraries external to the package in order to
-compile and run: libsacio.a and libSacLib.a.  Eventually, both libraries
-will be distributed by IRIS as part of the SAC package (at the moment only
-libsacio is distributed this way).  For the time being, you should compile
-libSacLib.a using the source code in the SacLib directory that accompanies
-flexwin.
+compile and run: {\tt libsacio.a} and {\tt libsac.a}. Both libraries
+are distributed by IRIS as part of the SAC package (version 101.2 and above).
+\url{http://www.iris.edu/software/sac/sac.request.htm}.
+(To check your version, type sac.)

-{\bf Important note}: The SacLib directory is a temporary fix.  The SAC source code
-from which the SacLib library is compiled is proprietary and should not be
-distributed by anyone other than IRIS.  Brian Savage - the author of SacLib -
-is currently working on a new version of the library that will be distributed
-with future versions of SAC.  The official release of flexwin will require

\section{Obtaining the code}

-[TODO] Write this better once structure of code (and packages that will be
-delivered) is finalised.
+The code is available as a gzipped tarball from CIG (Computational Infrastructure for Geodynamics, \url{http://www.geodynamics.org}). The tarball is unpacked by typing {\tt tar xvzf flexwin.tgz}.

-The code is available as a gzipped tarball from CIG (Computational Infrastructure for Geodynamics, {\tt http://www.geodynamics.org}). The tarball is unpacked by typing {\tt tar xvzf flexwin.tgz}.
-
The package contains the flexwin code and documentation, as well as a set of
test data, examples of user files for different scenarios, and a set of utility
scripts that may be useful for running flexwin on large datasets.

-The contents of the flexwin directory are as follows:
-{\small
-\begin{verbatim}
-flexwin
-|-- Makefile.in
-|-- PAR_FILE
-|-- TODOs
-|-- configure
-|-- configure.ac
-|-- distaz.f
-|-- flexwin.f90
-|-- io_subs.f90
-|-- latex
-|-- make_gfortran
-|-- make_intel
-|-- make_intel_caltech
-|-- maxima.f90
-|-- measure_windows_xcorr.f90
-|-- measurement_module.f90
-|-- scripts
-|-- seismo_subs.f90
-|-- select_windows_stalta2.f90
-|-- test_data
-|-- travel_times.f90
-|-- ttimes_mod
-|-- user_files
-|-- user_functions.f90
-|-- user_parameters.f90
--- xcorr-measure.f90
-\end{verbatim}
-}

-
\section{Compilation}

-[TODO] - Rewrite this for the official release.
-
-{\bf Note}: Do NOT use the configure script for beta test compilation.  It will not
-work.
-
If your compiler of choice is gfortran, then you should be able to use the
{\tt make\_gfortran} makefiles with only minor modifications (notably you may need to
change the search path for the {\tt libsacio.a} library).  If you prefer another
-compiler, you should modify the OPT and FC lines in the makefiles accordingly.
+compiler, you should modify the OPT and FC lines in the makefiles accordingly. We tested the code using gfortran version 4.1.2
+(To check your version, type{\tt gfortran --version}.)

{\bf Important note}: All the code is compiled with the -m32 option, which makes
32bit binaries.  This option is currently required to enable compatibility with
@@ -89,19 +43,11 @@

Steps to compile the flexwin package:
\begin{enumerate}
-\item Compile {\tt libSacLib.a}.  In the {\tt SacLib} directory (which is outside the {\tt flexwin}
-directory) type: {\tt make -f make\_gfortran}.
-\item Compile {\tt libtau.a} and create {\tt iasp91.hed} and {\tt iasp91.tbl}.  In the
-{\tt flexwin/ttimes\_mod} directory type: {\tt make -f make\_gfortran}.  This will compile
-{\tt libtau.a}, and two programs, {\tt remodl} and {\tt setbrn}.  The makefile will also run
-{\tt remodl} and {\tt setbrn} to create the {\tt iasp91.hed} and {\tt iasp91.tbl} files.  You should
-then type {\tt make -f make\_gfortran install} to install the iasp91 files.
-\item Compile {\tt flexwin}.  Edit the {\tt make\_gfortran} file in the root directory to ensure the {\tt SACLIBDIR} variable points to the location of your SAC libraries (by default {\tt /opt/sac/lib}).  Then type {\tt make -f make\_gfortran}.
+\item Compile {\tt libtau.a} and create {\tt iasp91.hed} and {\tt iasp91.tbl}.  In the {\tt flexwin/ttimes\_mod} directory type: {\tt make -f make\_gfortran}.  This will compile {\tt libtau.a}, and two programs, {\tt remodl} and {\tt setbrn}.  The makefile will also run {\tt remodl} and {\tt setbrn} to create the {\tt iasp91.hed}and {\tt iasp91.tbl} files.  You should then type {\tt make -f make\_gfortran install} to install the iasp91 files.
+\item Compile flexwin.  Edit the {\tt make\_gfortran} file in the flexwin root directory to ensure the {\tt SACLIBDIR} environment variable points to the location of your SAC libraries (by default {\tt \$SACHOME/lib}). Then type {\tt make -f make\_gfortran}. \end{enumerate} -You should end up with the {\tt flexwin} executable. The program requires the iasp91 -files (or links to them) to be present in the directory from which the code is -launched. +You should end up with the {\tt flexwin} executable. The program requires the {\tt iasp91.hed} and {\tt iasp91.tbl} files (or symbolic links to them) to be present in the directory from which the code is launched. \section{Running the Test case} @@ -118,7 +64,7 @@ file. Your result should be identical to that shown in Figure~\ref{fg:test_data}. \begin{figure} -\center \includegraphics[width=4in]{../test_data/MEASURE.orig/ABKT_II_LHZ_seis.pdf} +\center \includegraphics[width=4in]{manual_figures/ABKT_II_LHZ_seis.pdf} \caption{\label{fg:test_data} Windowing results for the test data set, plotted using the {\tt ./plot\_seismos\_gmt.sh} script. } @@ -171,10 +117,8 @@ subroutines in {\tt io\_subs.f90}. \section{Scripts} -Several plotting routines ({\tt plot\_*.sh}) are provided as examples for -plotting seismograms, measurements and adjoint sources. All plotting is -done in gmt. These scripts will need to be modified to suit your -particular plotting needs. +Several plotting routines ({\tt plot\_*.sh}) are provided in the {\tt scripts} subdirectory as examples for plotting seismograms, measurements and adjoint sources. All plotting is +done using GMT (Generic Mapping Tools). These scripts will need to be modified to suit your particular plotting needs. The script {\tt extract\_event\_windowing\_stats.sh} extracts statistical information on the window selection process, on the measurements. Again, Modified: seismo/3D/ADJOINT_TOMO/flexwin_paper/latex/manual_tuning.tex =================================================================== --- seismo/3D/ADJOINT_TOMO/flexwin_paper/latex/manual_tuning.tex 2009-03-19 04:46:00 UTC (rev 14388) +++ seismo/3D/ADJOINT_TOMO/flexwin_paper/latex/manual_tuning.tex 2009-03-19 10:11:30 UTC (rev 14389) @@ -2,19 +2,21 @@ FLEXWIN is adapted to your specific problem by modifying the values of the parameters in Table~\ref{tb:params}, and the functional form of those parameters that are time-dependent. We consider the algorithm to be correctly adapted when false positives (windows around undesirable features of the seismogram) are minimized, and true positives (window around desirable features) are maximized. 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. -The base values of the various parameters are set in the {\tt PAR\_FILE}, which is read at run time. The functional forms of the time dependent parameters may be adjusted by modifying {\tt user\_parameters.f90}, and re-compiling the code. +The base values of the various parameters are set in the {\tt PAR\_FILE}, which is read at run time. Examples of base parameter values for the three tomographic scenarios discussed by \cite{MaggiEtal2009} can be found in Table~\ref{tb:example_params}. The functional forms of the time dependent parameters may be adjusted by modifying {\tt user\_parameters.f90} (see next section), and re-compiling the code. \begin{table} \begin{tabular}{lp{0.8\linewidth}} \hline \multicolumn{2}{l}{Standard tuning parameters:} \\[5pt] -$T_{0,1}$& band-pass filter corner periods \\ +$T_{0,1}$& bandpass filter corner periods \\$r_{P,A}$& signal to noise ratios for whole waveform \\$r_0(t)$& signal to noise ratios single windows \\$w_E(t)$& water level on short-term:long-term ratio \\ -$CC_0(t)$& acceptance level for normalized cross-correlation\\ +$\mathrm{CC}_0(t)$& acceptance level for normalized cross-correlation\\$\Delta\tau_0(t)$& acceptance level for time lag \\$\Delta\ln{A}_0(t)$& acceptance level for amplitude ratio \\ +$\Delta\tau_{\rm ref}$& reference time lag \\ +$\Delta\ln{A}_{\rm ref}$& reference amplitude ratio \\ \hline \multicolumn{2}{l}{Fine tuning parameters:} \\ [5pt]$c_0$& for rejection of internal minima \\ @@ -22,7 +24,7 @@$c_2$& for rejection of un-prominent windows \\$c_{3a,b}$& for rejection of multiple distinct arrivals \\$c_{4a,b}$& for curtailing of windows with emergent starts and/or codas \\ -$w_{CC}\quad w_{\rm len}\quad w_{\rm nwin}$& for selection of best non-overlapping window combination \\ +$w_{\mathrm{CC}}\quad w_{\rm len}\quad w_{\rm nwin}$& for selection of best non-overlapping window combination \\ \hline \end{tabular} \caption{\label{tb:params} @@ -32,18 +34,20 @@ } \end{table} -\section{User modifiable parameters} -The main user-modifiable parameters in the {\tt PAR\_FILE} are: +\section{User parameters} +The main user parameters in the {\tt PAR\_FILE} are: \begin{description} \item[{\tt WIN\_MIN\_PERIOD}]Corresponds to$T_0$in Table~\ref{tb:params}, and is the short wavelength cut-off for the band-pass filter applied to the raw synthetic and observed seismograms. \item[{\tt WIN\_MAX\_PERIOD}]Corresponds to$T_1$in Table~\ref{tb:params}, and is the long wavelength cut-off for the band-pass filter applied to the raw synthetic and observed seismograms. \item[{\tt SNR\_INTEGRATE\_BASE}]Corresponds to$r_P$in Table~\ref{tb:params}, and is the minimum signal to noise ratio on the power of the observed seismogram for windowing to continue. \item[{\tt SNR\_MAX\_BASE}]Corresponds to$r_A$in Table~\ref{tb:params}, and is the minimum signal to noise ratio on the modulus of the observed seismogram for windowing to continue. -\item[{\tt WINDOW\_AMP\_BASE}]Corresponds to$r_0$in Table~\ref{tb:params}, and is the minimum signal to noise ratio for a window on the observed seismogram to be acceptable. +\item[{\tt WINDOW\_S2N\_BASE}]Corresponds to$r_0$in Table~\ref{tb:params}, and is the minimum signal to noise ratio for a window on the observed seismogram to be acceptable. \item[{\tt STALTA\_BASE}]Corresponds to$w_E$in Table~\ref{tb:params}, and is the water level to be applied to the synthetic short-term/long-term average waveform in order to generate candidate time windows. See Figure~\ref{fg:win_composite}a. \item[{\tt CC\_BASE}]Corresponds to$CC_0$in Table~\ref{tb:params}, and is the minimum normalized cross-correlation value between synthetic and observed seismogram for a window to be acceptable. \item[{\tt TSHIFT\_BASE}]Corresponds to$\Delta\tau_0$in Table~\ref{tb:params}, and is the maximum cross-correlation lag (in seconds) between synthetic and observed seismogram for a window to be acceptable. \item[{\tt DLNA\_BASE}]Corresponds to$\Delta\ln{A}_0$in Table~\ref{tb:params}, and is the maximum amplitude ratio ($\Delta\ln{A}$or$\Delta A/A$) between synthetic and observed seismogram for a window to be acceptable. +\item[{\tt TSHIFT\_REFERENCE}]Corresponds to$\Delta\tau_{\rm ref}$in Table~\ref{tb:params}, and allows for a systematic traveltime bias in the synthetics. +\item[{\tt TSHIFT\_REFERENCE}]Corresponds to$\Delta\ln{A}_{\rm ref}$in Table~\ref{tb:params}, and allows for a systematic amplitude bias in the synthetics. \item[{\tt C\_0}]Corresponds to$C_0$in Table~\ref{tb:params}, and is expressed as a multiple of$w_E$. No window may contain a local minimum in its STA:LTA waveform that falls below the local value of$C_0 w_E$. See Figure~\ref{fg:win_composite}b. \item[{\tt C\_1}]Corresponds to$C_1$in Table~\ref{tb:params}, and is expressed as a multiple of$T_0$. No window may be shorter than$C_1 T_0$. \item[{\tt C\_2}]Corresponds to$C_2$in Table~\ref{tb:params}, and is expressed as a multiple of$w_E$. A window whose seed maximum on the STA:LTA waveform rises less than$C_2 w_E$above either of its adjacent minima is rejected. See Figure~\ref{fg:win_composite}c. @@ -56,6 +60,38 @@ \item[{\tt WEIGHT\_N\_WINDOWS}]Corresponds to$w_{\rm nwin}$in Table~\ref{tb:params}, and is the weight given to the total number of windows in the process of resolving window overlaps. \end{description} +\begin{table} +\begin{center} +\begin{tabular}{lcccccc} +\hline + & Global & \multicolumn{2}{c}{Japan} & \multicolumn{3}{c}{S. California} \\ +\hline +$T_{0,1}$& 50, 150 & 24, 120 & 6, 30 & 6, 30 & 3, 30 & 2, 30 \\ +$r_{P,A}$& 3.5, 3.0 & 3.5, 3.0 & 3.5, 3.0 & 3.0, 2.5 & 2.5, 3.5 & 2.5, 3.5 \\ +$r_0$& 2.5 & 1.5 & 3.0 & 3.0 & 4.0 & 4.0 \\ +$w_E$& 0.08 & 0.11 & 0.12 & 0.18 & 0.11 & 0.07 \\ +$\mathrm{CC}_0$& 0.85 & 0.70 & 0.73 & 0.71 & 0.80 & 0.85 \\ +$\Delta\tau_0$& 15 & 12.0 & 3.0 & 8.0 & 4.0 & 3.0 \\ +$\Delta\ln{A}_0$& 1.0 & 1.0 & 1.5 & 1.5 & 1.0 & 1.0 \\ +$\Delta\tau_{\rm ref}$& 0.0 & 0.0 & 0.0 & 4.0 & 2.0 & 1.0 \\ +$\Delta\ln{A}_{\rm ref}$& 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\ +\hline +$c_0$& 0.7 & 0.7 & 0.7 & 0.7 & 1.3 & 1.0 \\ +$c_1$& 4.0 & 3.0 & 3.0 & 2.0 & 4.0 & 5.0 \\ +$c_2$& 0.3 & 0.0 & 0.6 & 0.0 & 0.0 & 0.0 \\ +$c_{3a,b}$& 1.0, 2.0 & 1.0, 2.0 & 1.0, 2.0 & 3.0, 2.0 & 4.0, 2.5 & 4.0, 2.5 \\ +$c_{4a,b}$& 3.0, 10.0 & 3.0, 25.0 & 3.0, 12.0 & 2.5, 12.0 & 2.0, 6.0 & 2.0, 6.0 \\ +$w_{\mathrm{CC}}, w_{\rm len}, w_{\rm nwin}$+ & 1, 1, 1 & 1, 1, 1 & 1, 1, 1 & 0.5,1.0,0.7 & 0.70,0.25,0.05 & 1,1,1 \\ +\hline +\end{tabular} +\caption{\label{tb:example_params} +Values of standard and fine-tuning parameters for the three seismological +scenarios discussed \cite{MaggiEtal2009}. This table is identical to Table~3 of that study. +} +\end{center} +\end{table} + \begin{figure} \center \includegraphics[width=6in]{figures/fig/window_composite.pdf} \caption{\label{fg:win_composite} @@ -105,7 +141,7 @@ \section{Time dependence of user parameters} A subset of the FLEXWIN parameters from Table~\ref{tb:params} are time-dependent (where time is measured along the seismogram). This feature enables the user to exercise fine control of the windowing algorithm. The user can modulate the time-dependence of these parameters by editing the {\tt set\_up\_criteria\_arrays} subroutine in the {\tt user\_functions.f90} file. This subroutine is called after the seismograms have been read in, and the following variables have been set: \begin{description} -\item[{\tt npts, dt, b, npts}] Number of points, time step, time of first point with respect to the reference time of both seismograms. The observed and synthetic seismograms should have identical values of these three quantities. +\item[{\tt npts, dt, b}] Number of points, time step, time of first point with respect to the reference time of both seismograms. The observed and synthetic seismograms should have identical values of these three quantities. \item[{\tt evla, evlo, evdp, stla, stlo}] Event latitude, event longitude, event depth (km), station latitude, station longitude, read from the observed seismogram. \item[{\tt azimuth, backazimuth, dist\_deg, dist\_km}] Calculated from the event and station locations above. \item[{\tt kstnm, knetwk, kcmpnm}] Station name, network name, component name, read from the observed seismogram. @@ -181,3 +217,204 @@ The above examples illustrate the power of the {\tt user\_functions.f90} file. The user can choose to include/exclude any portion of the seismogram, and to make the rejection criteria for windows more or less stringent on any other portion of the seismogram. All the seismogram-dependent variables whose values are known when the {\tt set\_up\_criteria\_arrays} subroutine is executed may be used to inform these choices, leading to an infinite number of windowing possibilities. The careful user will use knowledge of the properties of the observed data set, the limitations of the synthetic waveforms, and the final use to which the selected windows will be put in order to tailor the subroutine to the needs of each study. For a given set of data and synthetics, the {\tt PAR\_FILE} and {\tt user\_functions.f90} files uniquely determine the windowing results. + +\subsection{Examples of user functions\label{ap:user_fn}} + +As concrete examples of how the time dependence of the tuning parameters can be exploited, we present here the functional forms of the time dependencies used for the three example tomographic scenarios (global, Japan and southern California) described in \cite{MaggiEtal2009}. In each example we use predicted arrival times derived from 1D Earth models to help modulate certain parameters. Note, however, that the actual selection of individual windows is based on the details of the waveforms, and not on information from 1D Earth models. + +\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\taufor 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} + w_E \text{t \leq t_R$} ,\\ + 2 w_E \text{$t > t_R$}, + \end{cases} +\\ +r_0(t) & = + \begin{cases} + r_0 & \text{$t \leq t_R$}, \\ + 10r_0 & \text{$t > t_R$} , + \end{cases} +\\ +\mathrm{CC}_0(t) & = + \begin{cases} + \mathrm{CC}_0 & \text{$t \leq t_R$}, \\ + 0.9 \mathrm{CC}_0 & \text{$t_Q < t \leq t_R$}, \\ + 0.95 & \text{$t > t_R$} , + \end{cases} +\\ +\Delta\tau_0(t) & = + \begin{cases} + \begin{cases} + \tau_0 & \text{$t \leq t_R$}, \\ + \tau_0/3 & \text{$t > t_R$} , + \end{cases} + & \text{$h \leq$70~km} \\ + 1.4\tau_0 & \text{70~km$< h <$300~km}, \\ + 1.7\tau_0 & \text{$h \geq$300~km}, + \end{cases} + \\ +\Delta \ln A_0(t) & = + \begin{cases} + \Delta \ln A_0 & \text{$t \leq t_R$}, \\ + \Delta \ln A_0/3 & \text{$t > t_R} . + \end{cases} +\end{align} + +%-------------------------- + +\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}$indicates the end of the surface-wave time window. For the \trange{24}{120} data, we consider the waveform between the start of the$P$wave to the end of the surface-wave. We therefore modulate$w_E(t)as follows: + +% +\begin{align} +w_E(t) & = + \begin{cases} + 10 w_E & \text{t < t_P$}, \\ + w_E & \text{$t_P \le t \leq t_{R1}$}, \\ + 10 w_E & \text{$t > t_{R1}}. + \end{cases} +\end{align} + +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 to concentrate on body-wave arrivals only, and avoid surface-wave windows altogether by modulatingw_E(t)as follows: +% +\begin{align} +w_E(t) & = + \begin{cases} + 10 w_E & \text{t < t_P$}, \\ + w_E & \text{$t_P \le t \leq t_S$}, \\ + 10 w_E & \text{$t > t_S}. + \end{cases} +\end{align} + +We use constant values ofr_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\taufor intermediate depth and deep earthquakes we use: + +\begin{align} +\Delta\tau_0(t) & = + \begin{cases} + 0.08 \text{t_P$} & \text{$h \leq$70~km}, \\ + \max(0.05 \text{$t_P$}, 1.4\tau_0) & \text{70~km$< h <$300~km}, \\ + \max(0.05 \text{$t_P$}, 1.7\tau_0) & \text{$h \geq300~km}. + \end{cases} +\end{align} +%-------------------------- + +\subsubsection{Southern California scenario\label{ap:user_socal}} + +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$. + +%CHT modified + +For the \trange{6}{40} and \trange{3}{40} data, we use constant values of$r_0(t)=r_0$,$\mathrm{CC}_0(t)=\mathrm{CC}_0$,$\Delta\tau_0(t)=\Delta\tau_0$, and$\Delta \ln A_0(t)=\Delta \ln A_0$. We exclude any arrivals before the$P$wave and after the Rayleigh wave. This is achieved by the box-car function for$w_E(t): +% +\begin{align} +w_E(t) & = + \begin{cases} + 10 w_E & \text{t < t_P$}, \\ + w_E & \text{$t_P \le t \leq t_{R1}$}, \\ + 10 w_E & \text{$t > t_{R1}}, + \end{cases} +\end{align} +%For the \trange{6}{40} data, we exclude any arrivals before theP$wave and reduce the number of windows picked beyond R1 by modulating$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) & = +% \begin{cases} +% 10 w_E & \text{t < t_P$}, \\ +% w_E & \text{$t_P \le t \leq t_{R1}$}, \\ +% 2 w_E & \text{$t > t_{R1}$}, +% \end{cases} +%\\ +%\Delta\tau_0(t) & = +% \begin{cases} +% 3.0 + \Delta/80.0 & \text{$t \le t_{R0}$}, \\ +% 3.0 + \Delta/50.0 & \text{$t > t_{R0}}, +% \end{cases} +%\end{align} + +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. The water-level criteria then becomes: + +\begin{align} +w_E(t) & = + \begin{cases} + 10 w_E & \text{t < t_P$}, \\ + w_E & \text{$t_P \le t \leq t_S$}, \\ + 10 w_E & \text{$t > t_S}. + \end{cases} +%\\ +%\Delta\tau_0(t) & = \Delta\tau_0. +\end{align} + + +%----------------------- + + +\section{Tuning considerations} +FLEXWIN is not a black-box application, and as such cannot be applied blindly +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 the algorithm for the given problem. Here we +shall discuss general considerations the user should bear in mind during +the tuning process. + +We suggest the following as a practical starting sequence for tuning the algorithm +(the process may 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}$: In setting the corner periods of the bandpass filter, the +user is deciding on the frequency content of the information to be used in the +tomographic problem. Values of these corner periods should reflect the +information content of the data, the quality of the Earth model and the +accuracy of the simulation used to generate the synthetic seismogram. The +frequency content in the data depends on the spectral characteristics of the +source, on the instrument responses, and on the attenuation +characteristics of the medium. As$T_{0,1}$depend on the source and station +characteristics, which may be heterogeneous in any given data-set, these filter +periods can be modified dynamically by constructing an appropriate user +function (e.g. {\em if station is in list of stations with instrument X then +reset T0 and T1 to new values}). + +$r_{P,A}$: In setting the signal-to-noise ratios for the entire seismogram the +user is applying a simple quality control on the data. Note that these criteria +are applied after filtering. No windows will be defined on data that fail this +quality control. + +$w_E(t)$: The short-term average long-term average ratio$E(t)$of a constant signal +converges to a constant value when +the length of the time-series is greater than the effective averaging length of +the long-term average. This value is 0.08 for the short-term average long-term average ratio used in FLEXWIN (it has a small dependence on$T_0$, which can be ignored in most applications). We suggest the user start with a constant +level for$w_E(t)$equal to this convergence value. The time dependence of +$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$}). +We suggest finer adjustments to$w_E(t)$be made after$r0(t)$, +$CC_0(t)$,$\Delta T_0(t)$and$\Delta \ln A_0(t)$have been configured. + +$r_0(t)$,$\mathrm{CC}_0(t)$,$\Delta \tau_{\rm ref}$,$\Delta
+\tau_0(t)$,$\Delta \ln A_{\rm ref}$and$\Delta \ln A_0(t)$: These parameters --- +window signal-to-noise ratio, normalized cross-correlation value between +observed and synthetic seismograms, cross-correlation time lag, and amplitude +ratio --- control the degree of well-behavedness of the data within accepted +windows. The user first sets constant values for these four parameters, then +adds a time dependence if required. Considerations that should be taken into +account include the quality of the Earth model used to calculate the synthetic +seismograms, the frequency range, the dispersed nature of certain arrivals (e.g. +{\em for t corresponding to the group velocities of surface-waves, reduce +$CC_0(t)$}), and {\em a priori} preferences for picking certain small-amplitude seismic phases +(e.g. {\em for t close to the expected arrival for$P_{\rm diff}$, reduce$r_0(t)$}). +$\Delta \tau_{\rm ref}$and$\Delta \ln A_{\rm ref}$should be set to zero at first, and only +reset if the synthetics contain a systematic bias in traveltimes or amplitudes. + + +$c_{0-4}$: These parameters control the process by which the suite of all possible data windows is pared down using criteria on the shape of the STA:LTA$E(t)$waveform alone. We suggest the user start by setting these values to those used in our global example (see Table~\ref{tb:example_params}). Subsequent minimal tuning should be performed by running the algorithm on a subset of the data and closely examining the lists of windows rejected at each stage to make sure the user agrees with the choices made by the algorithm. + +$w_{\mathrm{CC}}$,$w_{\rm len}$and$w_{\rm nwin}$: These parameters control the overlap resolution stage of the algorithm. Values of$w_{\mathrm{CC}}= w_{\rm len} = w_{\rm nwin} = 1\$ should be reasonable for most applications.
+
+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.
+

`


text:
A cylinder is similar to a rectangular solid except that the base is a circle instead of a rectangle. The volume of a cylinder is the area of its circular base times its height. The amount of space occupied by the cylinder is called its volume. It unit of measurement is cubic units.
The volume of a cylinder whose base has radius 'r' and whose height is 'h' is V = $\pi r^2$ h.

## What is the Volume of a Cylinder

Volume of a cylinder is the product of area of the cylinder and its height. The formula for volume is depends on the area of the cylinder and its height. The volume of a cylinder is represented by cubic units.

The area of a cylinder can be written as, A = $\pi$ * r2.

=> Volume of cylinder = $\pi$ r2 h

Here, $\pi$ is the constant variable, r is the radius of the cylinder and h is the height of the cylinder.
The constant variable $\pi$ is equal to $\frac{22}{ 7}$ or 3.14

## Volume of a Cylinder Formula

Volume of a cylinder is the number of units used to fill a cylinder. Volume of a cylinder is a measurement of the occupied units of a cylinder. The volume is represented by cubic units like cubic centimeter, cubic millimeter and so on. Volume of a cylinder is the product of area of base of the cylinder and its height.

Formula:

The Volume of the Cylinder can be written as,

V = $\pi r^2$h

where,
V = Volume of a cylinder
r = Radius of a cylinder
h = Height of a cylinder.

## How to Find the Volume of a Cylinder

To find the volume of the cylinder, we have to multiply the height of the cylinder to its area. Firstly find the area of the cylinder (using formula A = $\pi$ * r2) and then multiply with the height of the cylinder. The volume of a cylinder is represented by cubic units.

Steps for Finding the Volume of the Cylinder:

Step 1: Find the area of the cylinder.

Step 2: Multiply the area of the cylinder and height of the cylinder.

Step 3
: Write answer in the proper square unit of measurement.

Example 1:

Find the volume of the cylinder having radius 4 cm and height 6 cm.

Solution:

Step 1:

Radius of the cylinder (r) = 4 cm
Height of the cylinder (h) = 6 cm

Step 2:

Volume of a cylinder (V) = $\pi$ r2 h

= $\frac{22}{7}$ * 42 * 6

= $\frac{22}{7}$ * 4 * 4 * 6

= 301.71

Hence the volume of a cylinder is 301.71 cm3 .

Example 2:
If the height of a cylinder is increased by 20% but radius of its base remains the same, then its volume will be increased by how many percent.

Solution:

Let the initial height and radius of the cylinder be 'h' and 'r' respectively

Step 1:

Initial volume of the cylinder = $\pi r^2$ h

and increased height = $\frac{100 + 20}{100}$ h

= $\frac{12}{10}$ h

Step 2:

Volume of the resulting cylinder = $\frac{\pi r^2 * 12 h}{10}$

Increased volume of the cylinder = $\frac{12\pi r^2 h}{10}$ - $\pi r^2$ h

= $\frac{2\pi r^2 h}{10}$

Therefore % increase in volume = $\frac{2\pi r^2 h}{10}$ x $\frac{100}{\pi r^2 h}$

= 20 %

Hence the volume of the cylinder will be increased by 20%.

format: plain


text: I think you can have such a subspace. Let $f : X \to R R$ be a discontinous linear functional (such a functional exists assuming Axiom of Choice, see wikipedia). The claim is that its kernel $K = ker(f) \ker f$ is a proper non-meager subspace. It is definitely proper. Assume it would be meager. Then it is contatined contained in the countable union of closed subsets Ai. $A_i$. Since K=ker(f) $K=\ker f$ it has codimesnion codimension 1, so there is $z \in X X$ such that every $x \in X X$ can be written as $x = k + azaz$, for some number a $a$ and some $k \in KK$. Let Bi $B_i$ be the set of elemets Ai elements $A_i + [-i,i]z -i,i]z$ (that is the set of $x \in X X$ for whcih which $x = k+az we have k k+az$ where $k$ is in Ai $A_i$ and a $a$ in [-i,i]). $[-i,i]$). Then, I think, Bi $B_i$ are closed and they have to have empty enteriorinterior. Indeed, if there is a small ball around $k + az az$ in Bi $B_i$ then f $f$ will be continuous at k+az, $k+az$, and then (since f $f$ is linear) continuous everywhere, contradicting the choice of f. $f$. Thus Bi $B_i$ are closed and nowhere dense, but their union is then the whole space X, $X$, which contradicts Baire's theorem.


text:
Problem: Vanadium forms four different oxides in which the percent by mass of vanadium is respectively 76 % , 68 % , 61 % , and 56 % .Find the formula of the first oxide.

FREE Expert Solution

Step 1 Assuming 100 g, V is 76 g and O is 24 g

= 1.49 mol V

= 1.5 mol O

Step 2 Divide each mol by the least moles

= 1 V

= 1 O

Problem Details

Vanadium forms four different oxides in which the percent by mass of vanadium is respectively 76 % , 68 % , 61 % , and 56 % .

Find the formula of the first oxide.


text:
# understanding of a proof of the invariance of 3-D laplacian?

I learned the proof of the fact that 3-D laplacian is invariant under all rigid motions in space in Strauss's Partial Differential Equations:

Any rotation in three dimensions is given by $${\bf x'}=B{\bf x},$$ where $B$ is an orthogonal matrix. The laplacian is $$\Delta u=\sum_{i=1}^3 u_{ii}=\sum_{i,j=1}^3\delta_{ij}u_{ij}$$ where the subscripts on $u$ denote partial derivatives. Therefore, $$\Delta u=\sum_{k,l}\Big(\sum_{i,j}b_{ki}\delta_{ij}b_{lj}\Big)u_{k'l'} =\sum_{k,l}\delta_{kl}u_{k'l'} =\sum_{k}u_{k'k'}.$$

Added: I believe the chain rule is needs here, but I don't see how it is applied here.

Here is my question:

How can I get the first equality, i.e. $$\Delta u=\sum_{k,l}\Big(\sum_{i,j}b_{ki}\delta_{ij}b_{lj}\Big)u_{k'l'}?$$

-
The factor $\sum_{i,j} b_{ki} \delta_{ij} b_{lj}$ is just the (k,l)th entry of the matrix $BIB^{-1}$ (because $B^{-1} = B^T$ when B is orthogonal), i.e. $I$, and so is $\delta_{kl}$, though I don't quite understand what k' and l' mean that's different to k and l, so maybe that doesn't answer your question... – Billy Aug 1 '11 at 17:14
The first equality is the chain rule. (If this is not obvious, perhaps the notation needs to be improved.) – Zhen Lin Aug 1 '11 at 17:15
I would think the whole thing could be written in matrix notation, without these sums and indices. – Michael Hardy Aug 1 '11 at 17:33
It looks to me that you are trying to show something like $B^{-1} \triangle ~ B = \triangle$. – Alice Aug 1 '11 at 17:35

I strongly dislike the use of undecorated subscripts for partial derivatives, so I will write $\partial_j$ for the partial differentiation operator $\partial / \partial x_j$. For convenience I will use the summation convention for repeated indices.
Firstly, we have the change-of-coordinates equation $\tilde{x}_{i'} = B_{i' j} x_j$. The chain rule states $$\frac{\partial}{\partial x_j} = \frac{\partial \tilde{x}_{i'}}{\partial x_j} \frac{\partial}{\partial \tilde{x}_{i'}}$$ so, writing $\tilde{\partial}_{i'}$ for the operator $\partial / \partial \tilde{x}_{i'}$, putting these together, we have $\partial_j = B_{i' j} \tilde{\partial}_{i'}$. The Laplacian is defined by $\nabla^2 = \delta_{i j} \partial_i \partial_j$, so substituting the previous equation in we obtain $\nabla^2 = \delta_{i j} B_{i k'} B_{j l'} \tilde{\partial}_{k'} \tilde{\partial}_{l'}$. By orthogonality, $\delta_{i j} B_{i k'} B_{j l'} = B_{j k'} B_{j l'} = \delta_{k' l'}$, so we are done.


text:
# Pros and Cons of Elasticity of Demand Represented as an Absolute Value

I've been reading quite a bit about elasticity of demand. There seems to be an argument among texts as to whether elasticity of demand should be represented as negative or as an absolute value. The argument for one method over the other depends on the text, but generally boils down to "because this is how we do it." I'm looking for a more meaningful discussion about this topic.

What are the pros and cons of using the negative? Of the absolute value?

• Can you please point to some sources about this argument? It is somewhat surprising to hear of it, as functional elasticity is a mathematical concept and I would think one cannot change the sign merely because one does not like it. Of course linguisticually it is usually easier to talk about the absolute value of the price elasticity of demand. But perhaps you would like to retain some difference between the sign of price elasticity of demand and income elasticity of demand? Apr 18 '17 at 21:31
• @denesp I don't have my books on hand, but here is an example from some lecture notes that I just found online; it touches on my question: "Textbooks differ on whether to take the absolute value or not. If you don't take the absolute value, you'll get a negative elasticity, which means that the demand curve is downward sloping. But to keep things positive, we'll always take the absolute value." Apr 19 '17 at 12:41
• There seems to be no argument there, merely an explanation about the difference. Apr 19 '17 at 14:30
• What I'm gathering is that when reporting elasticity results, the decision use negative or absolute value is a matter of discression. Since there are instances in which elasticity results are actually positive, I assume that the person reporting such results would indicate that the presentation is a positive number and not just a matter of convention. Essentially, any time elasticity of demand is reported as a positive number, assume it's the absolute value unless otherwise noted. Does this sound correct? Apr 19 '17 at 15:16
• I guess, people use absolute value because they are accustomed to positive numbers. AFAIK, negative numbers appear later then positive numbers and even fractions in history. Apr 20 '17 at 18:08

Elasticity of demand is almost always assumed to be negative. It is assumed that there is an inverse relationship between price and quantity demanded. If you want to buy 2 hamburgers for $5 each you aren't suddenly going to want to buy 3 hamburgers if they now cost $10 each. If this isn't the case it means that consumers aren't rational which blows up 99% of the models economics has to offer.


text:
# The Muon g-2 Experiment Overview and Status as of June 2016

@inproceedings{Holzbauer2016TheMG,
title={The Muon g-2 Experiment Overview and Status as of June 2016},
author={Jenny Holzbauer},
year={2016}
}
The Muon g-2 Experiment at Fermilab will measure the anomalous magnetic moment of the muon to a precision of 140 parts per billion, which is a factor of four improvement over the previous E821 measurement at Brookhaven. The experiment will also extend the search for the electric dipole moment (EDM) of the muon by approximately two orders of magnitude, with a sensitivity down to 10-21 e.cm. Both of these measurements are made by combining a precise measurement of the 1.45T storage ring magnetic… Expand
7 Citations

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Reevaluation of the hadronic contributions to the muon g−2 and to $\alpha (M^{2}_{Z})$
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The Hadronic Light-by-Light Scattering Contribution to the Muon and Electron Anomalous Magnetic Moments
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text:
# Marissa Mayer’s had a year at Yahoo, and I’ll give her a B

After a year at Yahoo, I have to give Marissa Mayer at least a B. She’s managed to keep investors happy — partly by a fairly aggressive stock buy back, using funds from sales of Alilbaba stock — but also because her fast clip of acquisitions and strong morale of Yahoo staff look like she’s actually building something in the formerly inert web company.

Let’s revisit that acquisition spree. In just the last few months, Yahoo made nine acquisitions: Summly, Astrid, Milewise, Loki Studios, Go Poll Go, PlayerScale, Rondee, Ghostbird Software and Tumblr. Some of these are acqui-hires, but Tumblr is potentially a huge deal, if Yahoo can figure out how to make money there.

Actually, I think making money on ads should be straightforward on Tumblr, since the company curates so-called ‘topics’ (more or less tags), like ‘design’ and ‘tech’. It would be fairly simple to rent ad space on those topics (and all the others) to brands wanting to be there. And they probably get good traffic, and could get more if Tumblr made the pages public, so visitors wouldn’t have to login to get there.

But money is exactly the point, because Mayer apparently is spending a lot, and ad and search revenues are falling. Ad revenue fell 12% to $472 million from$535 million a year earlier. Search is a mixed bag, but revenues are down 9% since the year before, but Yahoo’s deal with Microsoft means that Microsoft will make up for poor search revenues.

All told, Yahoo has spent $1.2 billion since the start of the year, even after selling$846 million of Alibaba stock back. Yahoo still has an estimated $10 billion in Alibaba stock, and$4.8 billion in the bank, but \$1.2 billion in six months is worrisome.

However, Yahoo’s market perception is falling, down from an index of 38 in July 2012 to around 25 today, as measured by YouGov. That was much higher than competitors, but now the difference is negligible.

So, the bottom line: can Mayer build a new social media centered leviathan quickly enough to satisfy the market and her shareholders? I think the jury is out, but she is making the moves that would be the first steps of a future winner. She’s made some fast cosmetic fixes to existing properties (although I think the Flickr ‘upgrade’ just moved the ugly around), and the acquisition of Tumblr could be the start of something gigantic, if she can get David Karp to open up the topics to Tumblr non-users.

We’ll see if she can pull together some other monster product from the tiny start-ups she’s fond of buying. She’d better, or it will just look like expensive hiring.

And finally: the ‘no remote work’ policy is a step backward for worker rights. Yes, Mayer believes that it is necessary to create the kind of culture at Yahoo that she believes is the foundation for being a better company. So if it is a short-term, ‘let’s act like a startup’ sprint, maybe we could all just hold our noses for a year. But the proof is in the pudding, even in that case. If she does get that culture to ferment, then she’ll have to relax the rules, or it’s simply building a stress factory that will drive away anyone who wants a life, or children, or needs to care for aging parents. So, we’ll have to see what sort of culture emerges, and what it produces. I’d give her a B+ if she’d figured out that a great corporate culture can support remote work, even when trying to turn it around.

So, she’s bought herself time, but the clock is ticking.