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374 Seismological Research Letters Volume 72, Number 2 March/April 2001

ELECTRONIC SEISMOLOGIST

Steve MaloneE-mail: [email protected]

Geophyics, Box 351650University of WashingtonSeattle, WA 98195Telephone: (206) 685-3811Fax: (206) 543-0489

The Electronic Seismologist (ES) has been known to actually

do some research in the field of seismology from time totime. As an operator of a seismic monitoring network theresearch done often is related to the seismicity of the moni-tored region. Detecting changes or trends in seismicity is rel-evant to earthquake and volcano hazards; but are the trendsdetected real or only an artifact of changes in the network operating parameters? Because all seismic networks evolve,change staff, change software and hardware, there is alwaysthe nagging feeling, if not outright knowledge, that interest-ing patterns in the catalog reflect network changes ratherthan changes in the Earth. How can one tell the difference?

The ES is happy to report that there is a handy-dandy software package ideally suited to answering exactly this

question (and many others). ZMAP

, developed by Stefan Wiemer, allows the user to examine an earthquake catalog from many different angles. Not only does it include the tra-ditional map, cross-section, and time sequence parameters,but also several others, such as event size and mechanism.These can be combined in interesting ways to present theuser with different “views” into the data. Considerable seis-mological acumen lies behind the use and presentation of these parameters, which helps the user get the most out of the analyzed catalog. ZMAP

is fairly intuitive to use and pro-duces attractive output. In fact, the ES actually has fun“playing” with it and gets useful results besides. Perhaps oneof the best ways to get a sense of how ZMAP

might be used

is to take a tour of case studies. The following includes many examples, and if they’re not enough there are a slew of refer-ences where one can find more. In his traditional groveling way the ES has prevailed on Stefan Wiemer to write thismonth’s column for him.

A SOFTWARE PACKAGE TO ANALYZESEISMICITY: ZMAP

Stefan Wiemer

Institute of GeophysicsETH HoenggerbergCH-8093, Zurich

SwitzerlandTelephone +41 633 6625

[email protected]

Introduction

Earthquake catalogs are probably the most fundamentalproducts of seismology and remain arguably the most usefulfor tectonic studies. Modern seismograph networks can locateup to 100,000 earthquakes annually, providing a continuousand sometime overwhelming stream of data. ZMAP

is a set of tools driven by a graphical user interface (GUI),

designed tohelp seismologists analyze catalog data. ZMAP

is primarily a research tool suited to the evaluation of catalog quality and to

addressing specific hypotheses; however, it can also be usefulin routine network operations. Roughly 100 scientists world- wide have used the software at least occasionally. About 30peer-reviewed publications have made use of ZMAP

. A com-prehensive listing of ZMAP

features is given in Table 1.

ZMAP

was first published in 1994 and has continued togrow over the past seven years. Concurrent with this article, we are releasing ZMAP

v. 6, which contains numerous bug fixes and a few new features, as well an updated manual.

This paper illustrates some of the various capabilitiesand applications of ZMAP by summarizing a few case studiesthat have been published previously. The examples include(1) catalog quality assessment and data exploration; (2) map-ping b

values beneath a volcano to infer information aboutthe location of magma; (3) estimating seismicity rate changescaused by a large earthquake; (4) stress-tensor inversion on a grid to measure the heterogeneity of a stress field; and (5)mapping the magnitude of complete reporting.

The Philosophy of ZMAP

Matlab-based, open-source code

. ZMAP

is written inMathworks’ (

http://www.mathworks.com

) commercial software language, Matlab

®

, a package widely used among researchers in the natural sciences. Users must purchase a Matlab license to run ZMAP

. Although ZMAP

is written in

Matlab, no knowledge of the Matlab language is neededsince ZMAP

is GUI-driven. The ZMAP

code is, however,open, and users are welcome to modify or supplement asdesired by diving into the guts of the numerous scripts(about 80,000 lines of native code in 600 scripts). ZMAP

should run on all platforms supported by Matlab. We havetested it under Unix, Linux, PC, DEC ALPHA, and Macin-tosh computers (Caveat: Some code, such as stress-tensorinversions, requires the compilation of external FORTRANor C programs).

S E I S M O L O G I S T

E L E C T R O N I C

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Seismological Research Letters Volume 72, Number 2 March/April 2001 375

TABLE 1Comprehensive Listing of ZMAP

Functions and Relevant References

Tool Objective Comments and References

Histograms Histograms of magnitude, depth, time, hour of the day

Data Import Data import as ASCII, column-separated files, using one of several exist-ing input format filters or a custom-designed one.

Catalog Comparison Identification of identical events in two catalogs spanning the sameregion. Plot of the mean difference in magnitude, depth, location, andtemporal evolution of these differences. Map of hypocenter shifts.

Time Series Analysis Cumulative number of events, time-depth plots, time-magnitude plots,cumulative moment release. Significance of rate changes using z, ß, andtranslation into probability.

Data Subset Selection Select data inside or outside polygons, cut in magnitude, depths, or time.

Maps Maps of seismicity; legend by time, depth, or magnitude. 3D view androtation hypocenters. Cross-sections with one or multiple segments.Link to M_Map toolbox. Importing an plotting topography files(ETOPO5, ETOP2, GTOPO30, USGS 1deg). Importing hierarchical coast-line data.

GENAS Evaluating homogeneity of magnitude reporting with time. Computemagnitude signatures; compare FMS for two periods and model ratechanges.

(Habermann, 1983, 1986, 1987; Zuñiga andWiemer, 1999; Zuñiga and Wyss, 1995)

Declustering Separation of dependent and independent seismicity, identification ofclusters. Based on Reasenberg’s algorithm.

(Reasenberg, 1985)

Mapping Seismicity Rates Map seismicity rates in map view, cross-section, or 3D. Animate maps ofz and ß values as a function of time. Compute alarm cubes, explore 6Dparameter space,

(Maeda and Wiemer, 1999; Wiemer and Wyss,1994; Wyss et al.

, 1996; Wyss et al.

, 1997a;Wyss and Wiemer, 1997, 2000; Wyss and Mar-tyrosian, 1998)

Aftershock Decay Rates Estimate aftershock decay rates based on modified Omori law. Computeprobabilistic aftershock hazard. Compute maps and cross-section of p

values and aftershock probabilities. Link to ASPAR software.

(Kisslinger and Jones, 1991; Reasenberg andJones, 1989, 1990; Wiemer, 2000; Wiemer et

al.

, 2001)

Frequency-magnitude Dis-

tribution

Estimating a

and b

values and uncertainties using maximum likelihood

or weighted least squares as a function of depth, time, and magnitude.Map b

and a

values in map view, cross-section, or 3D. Compute localrecurrence time maps. Differential b

value maps for two periods. Createsynthetic catalog with constant b

.

(Wiemer and Benoit, 1996; Wiemer and

McNutt, 1997; Wiemer and Wyss, 1997; Wysset al.

, 1997b)

Magnitude of Complete-ness

Estimate magnitude of completeness based on the deviation of the FMDfrom a power law. Analyze M

c

as a function of time or depth. Map M

c

inmap view or cross-section.

(Wiemer and Wyss, 2000)

Fractal Dimension Compute the fractal dimension of hypocenters based on the correlationintegral. Create maps and cross-sections of the fractal dimension.

(Sammis et al.

, 2001)

Quarry Maps Compute and map out the daytime to nighttime ratio of events in order toidentify explosion. Dequarry catalogs by removing daytime events at sig-nificantly anomalous nodes.

(Wiemer and Baer, 2000)

Time to Failure Estimate the time to failure based on accelerated moment release orBenioff strain.

(Bufe et al.

, 1994; Bufe and Varnes, 1996;Jaume and Sykes, 1999; Varnes, 1989)

Stress Tensor Inversion for the best fitting stress tensor using Michael’s or Gephart’sapproach. Uncertainty estimation. Maps/cross-sections of stress orien-tation and variance/heterogeneity of the stress field. Maps of the tempo-ral change in the stress field.

External call, requires compilation of FORTRANand C code. (Gephart, 1990a; Michael, 1984;Wiemer et al.

, 2001)

Cumulative Misfit Compute the cumulative misfit to a predefined stress tensor. Cumulativemisfit as a function of time, depth, magnitude, lat, lon, or in map view orcross-section.

External call, requires compilation of FORTRANand C code. (Lu et al.

, 1997; Wyss and Lu,1995)

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Interactive data exploration

. ZMAP

combines many stan-dard and advanced seismological analysis tools, aspiring tomake data exploration easier and more efficient. The usercan quickly select subsets in space, time, and magnitude,plot histograms, compute b

or p

values, compare the fre-quency-magnitude distributions of different time periodsand locations, compare daytime versus nighttime activity,compute the fractal dimension of hypocenters, create cross-sections, overlay topography, compute stress-tensor inver-sions, and much more (Table 1). The ability to apply and

combine these analysis tools within one software platformhelps users explore or mine their data in detail. A typicalsnapshot of some ZMAP

windows is shown in Figure 1.

Mapping seismicity parameters

. Identifying and evaluating spatial and temporal variations in seismicity is one of the pri-mary research objectives of ZMAP

. By creating dense spatialgrids and sampling overlapping volumes of circular (2D) orspherical shape (3D), users can map such parameters as seis-micity rate changes, b

values, p

values, stress-tensor orienta-

tions, and the magnitude of completeness. In any map, theuser can interactively view the source of the parameter underinvestigation (

e.g.

, a frequency-magnitude plot) and com-pare neighboring volumes.

Maps are computed on an interactively defined grid thatgenerally excludes low-seismicity areas (Figure 2B). There aretwo methods programmed into ZMAP

to map seismicity:using either constant radii or a constant number of samples.The first method produces maps with a continuous spatialresolution but varying sample sizes. Consequently, uncer-

tainties can vary significantly in space. A constant samplesize, on the other hand, results in more homogeneous uncer-tainties, but the resolution, which is inversely proportionalto the density of earthquakes, will vary across the region of interest. This is demonstrated in Figure 2B, where we plot a cross-sectional view of the hypocenters beneath Mt. St.Helens. Circles plotted at selected nodes indicate the vol-umes sampled around each particular node. The grid spacing is generally chosen such that the volumes overlap signifi-cantly, providing a natural smoothing of the results.

Figure 1.

Snapshots of some ZMAP

windows. The upper left frame shows the cumulative number of events (0 < M<1.2; thick line) for the creeping

section of the San Andreas Fault north of Parkfield. The thin line is the z

value, which measures the significance of a seismicity rate change. Note the

decrease in rate around 1995. The lower left shows catalog completeness, M

c

, as a function of time, computed for overlapping windows each containing

1,000 earthquakes. The upper right shows the annual rate of earthquakes as a function of magnitude. Rates are computed based on the periods 1990–1995

(“o”) and 1995–2000 (“x”). Note the decrease in the detection ability for M

< 1.2 after 1995. The top frame is the cumulative, the middle frame the noncu-

mulative form. The bottom frame shows the magnitude signature. The lower right window plots a histogram of hypocentral depth.

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Sample Applications

The sample applications shown below are intended to illus-trate some of the capabilities of ZMAP

. The images shown

were all created with ZMAP

, edited manually using the Mat-lab edit capabilities, and then imported as JPEG files or Windows metafiles into PowerPoint to be arranged on a page. The online help (http://www.seismo.ethz.ch/staff/ste-fan/) discusses in detail how each analysis was performed.Each case study is taken from published work that discussesthe science and interpretation in detail.

Assessing Catalog Homogeneity and Interactive DataExploration ZMAP

can be used to investigate or monitor the reporting history and health of a seismic network. The user can addressquestions such as: Did the detection threshold change in a particular area at a certain time? Did the meaning of magni-tude change? A long list of man-made changes in earthquakecatalogs has by now been documented (Habermann, 1983,1986, 1987, 1991; Wyss and Toya, 2000; Zuñiga and Wiemer, 1999; Zuñiga and Wyss, 1995). These changes inthe reporting rate can be introduced by modifications to thenetwork and can either mask or mimic natural changes inthe seismicity. Using GENAS (investigation of rate changesas a function of magnitude threshold), magnitude signa-

tures, b

-value curves, and maps of rate changes one canattempt to unravel the reporting history of earthquake cata-logs as a function of space and time.

A simple example of network quality assessment isshown in Figure 1. The cumulative number of events along the creeping section of the San Andreas Fault north of Park-field (0 < M

< 1.2) indicates a decrease in the rate of smallearthquakes around 1995. The cumulative and noncumula-tive number of events as a function of magnitude is com-pared for two periods (1990–1995 and 1995–2000). Thisplot reveals that the number of events with M

< 1.2 droppedby about 65% in the latter period, whereas no change isobserved for larger earthquakes. The simplest explanation of this pattern is that there was a change in the network config-uration or processing strategy which decreased the detectionability of the CALNET network in the creeping section after1995.

The b Value beneath Mount St. Helens ZMAP

is frequently used to facilitate spatial mapping of the

b

value in various seismotectonic regimes. The b

value,defined as log

10

N

= a – bM

, where N

is the cumulative num-ber of earthquakes, and a

and b

are constants related to theactivity and earthquake size distribution, respectively (Gutenberg and Richter, 1944; Ishimoto and Iida, 1939),

Figure 2.

(A) The b

value as a function of depth at Mount St. Helens. The seismicity for the period 1987–1995 with M

> 0.3 was analyzed, using a

sliding window of 100 earthquakes. Vertical bars indicate the uncertainty in b

, horizontal bars the depth range sampled. (B) Cross-sectional view (north-

south) through Mount St. Helens. Crosses mark the locations of nodes of an interactively

selected grid (spaced at 0.2 ×

0.2 km) used to compute the b

-

value image shown in (C). For selected nodes, the circles mark the volumes sampled, each containing N

= 100 earthquakes. (C) Image of the b

-value dis-

tribution underneath Mount St. Helens, computed using the grid shown in (B). Dark colors indicate low b

values.

0

1

2

3

4

5

6

7

8

90.5 1 1.5

b-value

D e p t h [ k m ]

2 3 4

A B C

Distance [km]

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has been shown to vary spatially on scales of hundreds of meters to tens of kilometers (

e.g.

, Wiemer and Benoit, 1996; Wiemer and Katsumata, 1999; Wiemer and McNutt, 1997; Wiemer et al.

, 1998; Wiemer and Wyss, 1997; Wyss et al.

,2000). These variations are related to differences in stress,pore pressure, and material heterogeneity and therefore cangive important constraints when analyzing the seismotecton-ics and hazard potential of a region. High b

values are often

correlated with the presence of magma in volcanic regions(Jolly and McNutt, 1999; Murru et al.

, 1999; Power et al.

,1995; Wiemer and McNutt, 1997; Wiemer et al.

, 1998; Wyss et al.

, 1997b). We present as an example data fromMount St. Helens (Wiemer and McNutt, 1997), using earthquakes of magnitude 0.4 and greater recorded by thelocal network during the period of 1988–1995, a total of about 2,000 events.

Using ZMAP

, we can investigate spatial variations in b

value in one, two, and three dimensions. Looking at b

valuesas a function of depth (Figure 2A), we find high values of b(b > 1.1) at around 2.5 km and deeper than 6 km below sea level. For this analysis, a constant number of events per sam-ple (100) is used, incremented downward by 25 events foreach step. The two-dimensional gridding along a 2-km- wide, north-south-trending cross-section (Figure 2B) showsthat indeed the b value exhibits its strongest variations as a function of depth. The orientations of the cross-section andthe hypocenters are shown in Plate 1A. Finally, a three-dimensional gridding is applied and a perspective view of thetopography of Mt. St. Helens added (Plate 1A). For this par-ticular case study, the 3D view contributes little to the scien-tific analysis of the data, since the seismicity distribution islargely one-dimensional. Creating an artistic image such asPlate 1A often requires some effort using the editing options

in Matlab in order to get the perspective and the light prop-erties right; however, the outcome may be worth the effort.To verify that the mapped differences in b value are indeedsignificant, we plot in Figure 3A comparisons of b values forthe shallowest earthquakes (b = 0.77) and the depth range 2–3 km (b = 1.82). The difference in the frequency-magnitudedistributions is clear to the eye and highly statistically signif-icant, which is established using a statistical test proposed by Utsu (1992).

The scientific interpretation of these results, of course,still depends on the ingenuity of the analyst. Based on theanalysis of the b-value at Mt. St. Helens and nine other vol-canoes (Jolly and McNutt, 1999; Murru et al., 1999; Poweret al., 1998; Wiemer and McNutt, 1997; Wiemer et al.,1998; Wyss et al., 1997b; Wyss et al., 2000), we have pro-posed that (1) the b value underneath volcanoes is not gener-ally higher, but pockets of high b exist in otherwise quite

normal crust. (2) These pockets of high b may signal thepresence of magma, since in the vicinity of a substantial body of magma, high pore pressure, high temperature gradients,and high b values all favor high b values. The absence of highb values, on the other hand, should be taken as a strong indi-cation that no substantial magma body is present near thisvolume.

Mapping Seismicity Rate Changes Measuring changes in the seismicity rate is a tricky business.It is important, because rate changes are believed to bedirectly related to changes in stress or pore pressure (Dieter-ich, 1994; Dieterich and Okubo, 1996). Applicationsinclude constraining stress changes caused by Coulomb fail-ure (Harris, 1998; Stein et al., 1992) or precursory ratechanges (Katsumata and Kasahara, 1996; Maeda and Wiemer, 1999; Wiemer and Wyss, 1994; Wyss and Haber-mann, 1988; Wyss and Martyrosian, 1998; Wyss and Wiemer, 1997). Measuring rate changes is difficult because(1) artificially introduced rate changes are common in seis-micity rates, (2) aftershocks and other clustered eventsshould be excluded before measuring background rates, and(3) defining the significance of an observed rate change is notsimple.

ZMAP helps in various ways to deal with each of these

obstacles. As an example, we investigate the change in theseismicity rates in southern California associated with the1992 M 7.3 Landers earthquake. For details, please refer to Wyss and Wiemer (2000). The first task is preparing a homogeneous input data set. We spatially map the magni-tude of complete reporting, M c , for different periods. Areas with higher M c , such as the offshore region and south of theMexican border, can thus be excluded based on an objectivecriterion. We next test for the presence of explosions in the

Plate 1. (A) Left: Cross-section view through Mount St. Helens, overlain by topography. The orientation of the cross-section is shown in the inset at

lower left. Hypocenters are color-coded by depth; symbol size indicates magnitude. Right: Three-dimensional image of the b values beneath Mount St.

Helens, based on the seismicity from 1987–1995. Red colors indicate high b values. Horizontal planes are drawn at 8 and 3 km depths. (B) Perspective

view of southern California, centered on the Landers region. Colors map the change in the seismicity rate between the periods 1985–1992.48 and 1992.5–1999.7. Red colors, or negative z values, indicate an increase in the seismicity rate in the latter periods and vice versa. Triangles mark the epicenters of

the Landers, Big Bear, and Hector Mine main shocks. (C) Map of southern California, centered on the Landers region. Bars indicate the orientation of the

stress field obtained by inverting the 100 focal mechanisms nearest to each node of a grid spaced 2 × 2 km. The period investigated is 1992–2000. Stars

mark the hypocenters of the 1992 Landers and 1999 Hector Mine main shocks. The variance of the individual stress tensor inversions is color-coded, with

blue to purple colors indicating high variance, hence a heterogeneous stress field. The two insets show individual stress-tensor inversions and their

uncertainties, obtained using a bootstrap method (yellow: σ1; red: σ2; blue: σ3). (D) Map of the western U.S.; the magnitude of complete reporting, M c,

computed by measuring the deviation from an assumed power law, is color-coed. The inset shows the frequency-magnitude plots for two subvolumes

marked A and B.

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Z - v al ue

Landers

Hector Mine

Big BearN

Ratedecrease

Rateincrease

(A) Mt. St. Helens b -values

(B) Landers Rate Changes

(C) Stress Tensor Orientation (D) Magnitude of Completeness

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stress field). The two inserts show the individual inversionresults and their uncertainties, obtained using a bootstrap-ping approach (Michael, 1987a).

The overall stress directions obtained agree reasonably well with a more detailed study by Hauksson (1994). Resultssuggest that areas that experience a high slip during the mainshock show a more heterogeneous stress field which cannotbe fit by a single stress tensor, whereas areas outside the main

rupture show a low variance, hence a more homogeneousstress field (Wiemer et al., 2001).

Mapping Minimum Magnitude of Completeness (M c )The quality of all regional and local earthquake catalogsdecreases with distance from the center of the network.Obvious boundaries of deterioration are coastlines, interna-tional borders, and seams between networks. To avoid prob-lems that could be introduced in seismicity studies by heterogeneity of M c , ZMAP allows the user to map M c todefine the spatial extent of the high-quality part of the cata-log (e.g., Wiemer and Wyss, 2000). The technique used mostfrequently to assess M

c

is based on estimating it from theFMD itself. This is often done in seismicity studies by visualexamination of the cumulative or noncumulative FMD;however, we prefer to apply a quantitative criterion, where we measure the goodness of fit to an assumed power law (Wiemer and Wyss, 2000). An example of a map of M c forthe western U.S., based on the CNSS catalog for the period1995–2000, is shown in Plate 1D. M c ranges from > 2.5 off-shore Mendocino to < 1 in central California.

OBTAINING ZMAP , DOCUMENTATION, ANDSUPPORT

ZMAP is freely available on the Internet. Please refer tohttp://www.seismo.ifg.ethz/staff/stefan to download the cur-rent version of ZMAP (version 6). The compressed files areabout 5 Mb and should run under Matlab 5.x and 6.0.Other resources on the ZMAP home page include a list of papers published using ZMAP , a collection of sample data files, and a collection of presentations made using the ZMAP software. If your Internet connection does not allow down-loading via the Internet, we can send you a CD-ROM ver-sion of ZMAP . Please contact [email protected].

The only support currently available beyond the onlinedocumentation is contacting me via e-mail. Help requests will be addressed as quickly as possible, but as they increase

in volume this may become unmanageable. A ZMAP help e-mail list is being considered.

KNOWN PROBLEMS

From the responses from the 100+ scientists using ZMAP , itis clear that, although designed to work on any Matlab-sup-ported platform, some users experience problems while run-ning various functions. Others become frustrated with thevariable robustness of certain features of ZMAP and the

occurrence of errors. Although the source code is open, it isnot trivial to find the appropriate script and variable in orderto extend or improve ZMAP .

As with any software, the garbage in-garbage out princi-ple applies to ZMAP . If you try, for example, to estimate spa-tial and temporal variations of b values and your catalog contains only 200 events, you may get colorful maps buttheir meaning is questionable at best.

THE FUTURE OF ZMAP

The future of ZMAP is somewhat unclear. There will likely be occasional future updates of ZMAP , largely driven by research interests. New features that have been partially implemented or are being considered are:

• Probabilistic hazard mapping, both in a Poissonian(Frankel, 1995) (Bender and Perkins, 1987) or time-dependent fashion. We are developing a module basedon ZMAP that will compute probabilistic aftershock and foreshock hazard maps (Wiemer, 2000) in near-realtime and display the results on the Internet.

• Implementation of the M8 algorithm for earthquakeprediction (Kossobokov et al., 1997).

• A different declustering algorithm based on the ETASmodel (Ogata et al., 1995, 1996).

• A real-time module to monitor the quality of seismicity data and search for artifacts in reporting.

• Computing Coulomb stress changes with uncertaintiesand comparison with observed rate changes.

Suggestions for future developments and criticisms of theexisting package are highly encouraged!

ACKNOWLEDGMENTS

The author would like to thank Matt Gerstenberger, SteveMalone, Charlotte Rowe, and Max Wyss for comments andsuggestions that greatly helped to improve the manuscript. Iam deeply indebted to all those who helped through theirprogramming to make ZMAP a better tool: Alexander All-man, Denise Bachmann, Matt Gerstenberger, Zhong Lu,Francesco Pacchiani, Yuzo Toda, and Ramon Zuñiga. Specialthanks to Max Wyss, whose relentless support and creativeideas over the past eight years has made ZMAP possible. Thesupport from an IASPEI PC software development grant has

been a great motivation. I am thankful to the University of Alaska Fairbanks, the Science and Technology Agency of Japan, and ETH Zurich for supporting the development of ZMAP .

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SRL encourages guest columnists to contribute to the “Elec-tronic Seismologist.” Please contact Steve Malone with yourideas. His e-mail address is [email protected].

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