ZMap A Software Package to analyze seismicity.pdf

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A SOFTWARE PACKAGE TO ANALYZE SEISMICITY: ZMAP  Stefan Wiemer

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ELECTRONIC SEISMOLOGIST 

Institute of Geophysics ETH Hoenggerberg CH-8093, Zurich Switzerland Telephone +41 633 6625 [email protected]

Steve Malone E-mail: [email protected] Geophyics, Box 351650 University of Washington Seattle, WA 98195 Telephone: Telephone: (206) 685-3811 Fax: (206) 543-0489

The Electronic Seismologist (ES) has been known to actually  do some research in the field of seismology from time to time. As an operator of a seismic monitoring network the research done often is related to the seismicity of the monitored region. Detecting changes or trends in seismicity is relevant to earthquake and volcano hazards; but are the trends detected 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 always the nagging feeling, if not outright knowledge, that interesting patterns in the catalog reflect network changes rather than 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,  Wiemer, allows the user to examine an earthquake catalog  from many different angles. Not only does it include the traditional 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 the user with different “views” into the data. Considerable seismological 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 produces attractive output. In fact, the ES actually has fun “playing” “playing” with it and gets useful results besides. Perhaps one of 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 they’re not enough there are a slew of references where one can find more. In his traditional groveling   way the ES has prevailed on Stefan Wiemer to write this month’s column for him.

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Introduction Earthquake catalogs are probably the most fundamental products of seismology and remain arguably the most useful for tectonic studies. Modern seismograph networks net works can locate up to 100,000 earthquakes annually, providing a continuous and sometime overwhelming stream of data. ZMAP is a set of  tools driven by a graphical user interface (GUI), designed to help 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 useful in routine network operations. Roughly 100 scientists world wide have used the software software at least occasionally. occasionally. About 30 peer-reviewed publications have made use of  ZMAP . A comprehensive listing of ZMAP features is given in Table 1.  ZMAP  was  was first published in 1994 and has continued to grow 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 capabilities and applications of ZMAP by summarizing a few case studies that have been published previously. The examples include (1) catalog quality assessment and data exploration; (2) mapping b values beneath a volcano to infer information about the location of magma; (3) estimating seismicity rate changes caused 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. code.  ZMAP  is written in Mathworks’ (http://www.mathworks.com ) commercial soft ware 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 needed since  ZMAP  is GUI-driven. The  ZMAP  code is, however, open, and users are welcome to modify or supplement as desired 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 have tested it under Unix, Linux, PC, DEC ALPHA, and Macintosh computers (Caveat: Some code, such as stress-tensor inversions, requires the compilation of external FORTRAN or C programs).

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TABLE 1 Comprehensive 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 existing input format filters or a custom-designed one.

Catalog Comparison

Identification of identical events in two catalogs spanning the same region. Plot of the mean difference in magnitude, depth, location, and temporal 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, and translation 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 and rotation 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 coastline data.

GENAS

Evaluating homogeneity of magnitude reporting with time. Compute magnitude signatures; compare FMS for two periods and model rate changes.

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

Declustering

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

(Reasenberg, 1985)

Mapping Seismicity Rates

Map seismicity rates in map view, cross-section, or 3D. Animate maps of (Maeda and Wiemer, 1999; Wiemer and Wyss, z and ß values as a function of time. Compute alarm cubes, explore 6D 1994; Wyss et al., 1996; Wyss et al., 1997a; parameter space, Wyss and Wiemer, 1997, 2000; Wyss and Martyrosian, 1998)

Aftershock Decay Rates

Estimate aftershock decay rates based on modified Omori law. Compute probabilistic aftershock hazard. Compute maps and cross-section of p  values and aftershock probabilities. Link to ASPAR software.

(Kisslinger and Jones, 1991; Reasenberg and Jones, 1989, 1990; Wiemer, 2000; Wiemer et al., 2001)

Frequency-magnitude Dis- Estimating a and b values and uncertainties using maximum likelihood tribution 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 local recurrence time maps. Differential b value maps for two periods. Create synthetic catalog with constant b .

(Wiemer and Benoit, 1996; Wiemer and McNutt, 1997; Wiemer and Wyss, 1997; Wyss et al., 1997b)

Magnitude of Completeness

Estimate magnitude of completeness based on the deviation of the FMD (Wiemer and Wyss, 2000) from a power law. Analyze M c  as a function of time or depth. Map M c  in map view or cross-section.

Fractal Dimension

Compute the fractal dimension of hypocenters based on the correlation integral. Create maps and cross-sections of the fractal dimension.

Quarry Maps

Compute and map out the daytime to nighttime ratio of events in order to (Wiemer and Baer, 2000) identify explosion. Dequarry catalogs by removing daytime events at significantly anomalous nodes.

Time to Failure

Estimate the time to failure based on accelerated moment release or Benioff strain.

Stress Tensor

Inversion for the best fitting stress tensor using Michael’s or Gephart’s External call, requires compilation of FORTRAN approach. Uncertainty estimation. Maps/cross-sections of stress orien- and C code. (Gephart, 1990a; Michael, 1984; tation and variance/heterogeneity of the stress field. Maps of the tempo- Wiemer et al., 2001) ral change in the stress field.

Cumulative Misfit

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

(Sammis et al., 2001)

(Bufe et al., 1994; Bufe and Varnes, 1996; Jaume and Sykes, 1999; Varnes, 1989)

External call, requires compilation of FORTRAN and C code. (Lu et al., 1997; Wyss and Lu, 1995)

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Figure 1. Snapshots of some ZMAP windows. The upper left frame shows the cumulative number of events (0 < 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 (northsouth) 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 distribution underneath Mount St. Helens, computed using the grid shown in (B). Dark colors indicate low b values. 

Sample Applications The sample applications shown below are intended to illustrate some of the capabilities of  ZMAP . The images shown  were all created with ZMAP , edited manually using the Matlab 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/stefan/) discusses in detail how each analysis was performed. Each case study is taken from published work that discusses the science and interpretation in detail.

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

tures, b-value curves, and maps of rate changes one can attempt to unravel the reporting history of earthquake catalogs as a function of space and time.  A simple example of network quality assessment is shown in Figure 1. The cumulative number of events along  the creeping section of the San Andreas Fault north of Parkfield (0 <  M  < 1.2) indicates a decrease in the rate of small earthquakes around 1995. The cumulative and noncumulative number of events as a function of magnitude is compared for two periods (1990–1995 and 1995–2000). This plot reveals that the number of events with M < 1.2 dropped by about 65% in the latter period, whereas no change is observed for larger earthquakes. The simplest explanation of  this pattern is that there was a change in the network configuration or processing strategy which decreased the detection ability of the CALNET network in the creeping section after 1995.

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 10N = a – bM , where N is the cumulative number of earthquakes, and a  and b are constants related to the activity and earthquake size distribution, respectively  (Gutenberg and Richter, 1944; Ishimoto and Iida, 1939),

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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 can give important constraints when analyzing the seismotectonics 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 from Mount St. Helens (Wiemer and McNutt, 1997), using  earthquakes of magnitude 0.4 and greater recorded by the local 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 values as 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 sample (100) is used, incremented downward by 25 events for each step. The two-dimensional gridding along a 2-km wide, north-south-trending cross-section (Figure 2B) shows that indeed the b value exhibits its strongest variations as a  function of depth. The orientations of the cross-section and the hypocenters are shown in Plate 1A. Finally, a threedimensional gridding is applied and a perspective view of the topography of Mt. St. Helens added (Plate 1A). For this particular case study, the 3D view contributes little to the scientific analysis of the data, since the seismicity distribution is largely one-dimensional. Creating an artistic image such as Plate 1A often requires some effort using the editing options in Matlab in order to get the perspective and the light properties right; however, the outcome may be worth the effort. To verify that the mapped differences in b value are indeed significant, we plot in Figure 3A comparisons of b values for the shallowest earthquakes ( b = 0.77) and the depth range 2– 3 km (b = 1.82). The difference in the frequency-magnitude distributions is clear to the eye and highly statistically significant, 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 the analysis of the b-value at Mt. St. Helens and nine other volcanoes (Jolly and McNutt, 1999; Murru et al., 1999; Power et al., 1998; Wiemer and McNutt, 1997; Wiemer et al., 1998; Wyss et al., 1997b; Wyss et al., 2000), we have proposed that (1) the b value underneath volcanoes is not generally higher, but pockets of high b  exist in otherwise quite normal crust. (2) These pockets of high b  may signal the presence 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 high b values, on the other hand, should be taken as a strong indication that no substantial magma body is present near this volume.

 Mapping Seismicity Rate Changes  Measuring changes in the seismicity rate is a tricky business. It is important, because rate changes are believed to be directly related to changes in stress or pore pressure (Dieterich, 1994; Dieterich and Okubo, 1996). Applications include constraining stress changes caused by Coulomb failure (Harris, 1998; Stein et al., 1992) or precursory rate changes (Katsumata and Kasahara, 1996; Maeda and  Wiemer, 1999; Wiemer and Wyss, 1994; Wyss and Habermann, 1988; Wyss and Martyrosian, 1998; Wyss and  Wiemer, 1997). Measuring rate changes is difficult because (1) artificially introduced rate changes are common in seismicity rates, (2) aftershocks and other clustered events should be excluded before measuring background rates, and (3) defining the significance of an observed rate change is not simple.  ZMAP  helps in various ways to deal with each of these obstacles. As an example, we investigate the change in the seismicity rates in southern California associated with the 1992 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 magnitude of complete reporting,  M c , for different periods. Areas  with higher M c , such as the offshore region and south of the Mexican border, can thus be excluded based on an objective criterion. 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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(A) Mt. St. Helens b -values

(B) Landers Rate Changes

Hector Mine Big Bear

N Rate decrease

Landers Z - va   l ue  Rate increase

(C) Stress Tensor Orientation

(D) Magnitude of Completeness

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Figure 3. Comparison of the cumulative frequency-magnitude distribution for shallow earthquakes at Mount St. Helens (filled circles) and for the depth range 2–3 km (open squares). The probability that the two samples come from the same population is about 1.4–10, based on Utsu’s (1992) test.

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study region by spatially mapping the daytime to nighttime ratio of events. A significantly enhanced ratio is indicative of  quarry blast contamination that often remains in the data  regardless of the network operator’s efforts (Wiemer and Baer, 2000). We identify a number of explosion-prone regions, which we exclude. By studying the homogeneity of  reporting as a function of time and magnitude, we search for artificial rate changes in the data and the suitable overall  M c  cut-off. Finally we settle for a data set for the period 1985– 1999.8 (before the Hector Mine earthquake) with an overall  M c  of 1.7. This data set is then declustered using Reasenberg´s (1985) approach.  We spatially map the remaining seismicity rate changes, comparing the periods 1985–1992.48 and 1992.6–1999.8, using constant sample volumes of 20 km radius and a grid spacing of 5 km. Two different statistical functions have been implemented in  ZMAP   to measure the significance of rate change: z   values (Habermann, 1981, 1988) and  ß   values (Matthews and Reasenberg, 1988; Reasenberg and Simpson, 1992). A map of rate changes measured by z   is shown in Plate 1B. Red colors signify rate increases, blue colors rate decreases. The map is wrapped on top of the GTOPO30 topography; this is possible in ZMAP  only when the Matlab mapping toolbox is available. We can interactively select circular or polygonal volumes from the map and view the cumulative number of events as a function of time and the z  values that measure rate changes (Figure 4). The pattern of rate change mapped by this technique is quite remarkable, since it reveals long-range (> 100 km) and long-duration (> 7 years) rate changes associated with the 1992 Landers main shock. The pattern of increased and

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Time in years  Figure 4. Cumulative number of earthquakes above M  1.7 south of the

Hector Mine hypocenter. In this volume, the seismicity rate dropped drastically after the 1992 Landers earthquake. The thin line indicates the significance of rate changes, measured using the z  value.

decreased seismicity matches qualitatively the predicted rate changes caused by the combined static and dynamic stress changes predicted for the Landers rupture (Stein et al., 1992). In order to establish a significant rate decrease, it is generally necessary to compare observations for several years.

Stress Tensor Inversions  In addition to hypocenter information,  ZMAP   can be used to analyze focal mechanism data either by analyzing the cumulative misfit of a set of focal mechanisms to a given stress tensor (Lu and Wyss, 1996; Lu et al., 1997; Wyss and Lu, 1995), or by computing inversions for the best-fitting  stress tensor. Two inversion programs are called from ZMAP , Michael’s (Michael, 1984, 1987a, 1987b, 1991; Michael et  al.) and Gephart’s (Gephart and Forsyth, 1984; Gephart, 1990a; Gephart, 1990b).  ZMAP  allows the computation of  individual stress-tensor inversions, stress tensor as a function of time and depth, and inversions on a grid in either map view of cross-section (using Michael’s method only).  An example application, again for southern California, is shown in Plate 1C. We use the relocated set of focal mechanisms from 1992.48–2000.5 by Hauksson (2000), with a  solution misfit < 0.1. First we create a grid with a 2 × 2 km spacing, excluding areas of low seismicity. The nearest 100 earthquakes to each node are sampled and their focal mechanisms inverted using Michael’s approach. The resulting  directions of the principal stress axes, σ 1, are plotted as lines on a map underlain by topography. We further color-code the variance of the resulting inversion at each node. Blue to purple colors indicate a high variance ( i.e., heterogeneous

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stress field). The two inserts show the individual inversion results and their uncertainties, obtained using a bootstrapping approach (Michael, 1987a). The overall stress directions obtained agree reasonably   well with a more detailed study by Hauksson (1994). Results suggest that areas that experience a high slip during the main shock show a more heterogeneous stress field which cannot be fit by a single stress tensor, whereas areas outside the main rupture show a low variance, hence a more homogeneous stress field (Wiemer et al., 2001).

occurrence of errors. Although the source code is open, it is not trivial to find the appropriate script and variable in order to extend or improve ZMAP .  As with any software, the garbage in-garbage out principle applies to ZMAP . If you try, for example, to estimate spatial and temporal variations of b  values and your catalog  contains only 200 events, you may get colorful maps but their meaning is questionable at best.

 Mapping Minimum Magnitude of Completeness (M  ) c  The quality of all regional and local earthquake catalogs decreases with distance from the center of the network. Obvious boundaries of deterioration are coastlines, international borders, and seams between networks. To avoid problems that could be introduced in seismicity studies by  heterogeneity of  M c ,  ZMAP   allows the user to map  M c  to define the spatial extent of the high-quality part of the catalog (e.g., Wiemer and Wyss, 2000). The technique used most frequently to assess  M c   is based on estimating it from the FMD itself. This is often done in seismicity studies by visual examination 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  for the western U.S., based on the CNSS catalog for the period 1995–2000, is shown in Plate 1D. M c  ranges from > 2.5 offshore Mendocino to < 1 in central California.

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:

OBTAINING ZMAP , DOCUMENTATION, AND SUPPORT

THE FUTURE OF ZMAP 

• Probabilistic hazard mapping, both in a Poissonian (Frankel, 1995) (Bender and Perkins, 1987) or timedependent fashion. We are developing a module based on  ZMAP   that will compute probabilistic aftershock  and foreshock hazard maps (Wiemer, 2000) in near-real time and display the results on the Internet. • Implementation of the M8 algorithm for earthquake prediction (Kossobokov et al., 1997). • A different declustering algorithm based on the ETAS model (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 uncertainties and comparison with observed rate changes. Suggestions for future developments and criticisms of the existing package are highly encouraged!

 ZMAP   is freely available on the Internet. Please refer to http://www.seismo.ifg.ethz/staff/stefan to download the current version of  ZMAP  (version 6). The compressed files are about 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 downloading via the Internet, we can send you a CD-ROM version of ZMAP . Please contact [email protected]. The only support currently available beyond the online documentation 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 email list is being considered.

KNOWN PROBLEMS From the responses from the 100+ scientists using  ZMAP , it is clear that, although designed to work on any Matlab-supported platform, some users experience problems while running various functions. Others become frustrated with the variable robustness of certain features of  ZMAP   and the

ACKNOWLEDGMENTS The author would like to thank Matt Gerstenberger, Steve Malone, Charlotte Rowe, and Max Wyss for comments and suggestions that greatly helped to improve the manuscript. I am deeply indebted to all those who helped through their programming to make  ZMAP   a better tool: Alexander Allman, Denise Bachmann, Matt Gerstenberger, Zhong Lu, Francesco Pacchiani, Yuzo Toda, and Ramon Zuñiga. Special thanks to Max Wyss, whose relentless support and creative ideas over the past eight years has made ZMAP  possible. The support 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 .

REFERENCES Bender, B. and D. M. Perkins (1987). SEISRISK III: A computer program for seismic hazard estimation, U.S. Geological Survey Bulletin 1772, 20 pp.

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

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