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Computers & Geosciences 34 (2008) 967–977

www.elsevier.com/locate/cageo

ISOLA a Fortran code and a Matlab GUI to performmultiple-point source inversion of seismic data$

Efthimios N. Sokosa,�, Jiri Zahradnikb

aLaboratory of Seismology, Geology Department, University of Patras, Rio 26504, GreecebFaculty of Mathematics and Physics, Charles University in Prague, Czech Republic

Received 22 December 2006; received in revised form 3 May 2007; accepted 27 July 2007

Abstract

In this paper, a software package for multiple- or single-point source inversion is presented. The package consists of

ISOLA-GUI, a user-friendly MATLAB-based interface, and the ISOLA Fortran code, which is the computational core of

the application. The methodology used is similar to iterative deconvolution technique, often used in teleseismic studies, but

here adjusted for regional and local distances. The advantage of the software is the graphical interface that provides the

user with an easy to use environment, rich in graphics and data handling routines, while at the same time the speed of

Fortran code is retained. Besides that, the software allows the results to be exported to popular software packages, like

Generic Mapping Tools, while at the same time utilizing them for quality plots of the results. The modular design of

ISOLA-GUI can be used by users for the addition of supplementary routines in all the stages of processing. An example of

the method’s ability to obtain a quick insight into the complexity of an earthquake is presented, using records from a

moderate size event.

r 2008 Elsevier Ltd. All rights reserved.

Keywords: Seismology; Moment tensor determination; Iterative deconvolution; Extended source; Graphical user interface

1. Introduction

Precise knowledge of seismic source parameters isa prerequisite for understanding physical processeson faults during earthquakes. Although importantinformation can be extracted even from the first fewseconds of the seismic record (such as earthquakelocation, its fault-plane solution, etc.), detailed

e front matter r 2008 Elsevier Ltd. All rights reserved

geo.2007.07.005

ilable from server at http://www.iamg.org/

x.htm or http://seismo.geology.upatras.gr/isola/.

ing author. Tel.: +302610 997556;

90639.

esses: esokos@upatras.gr (E.N. Sokos),

ff.cuni.cz (J. Zahradnik).

studies have to include complete seismograms.These kinds of studies can provide further con-straints on the hypocentral depth and earthquakemoment, providing valuable information on aregion’s deformation style. Therefore, modernseismological networks can provide, in an auto-mated way, the moment tensor of the event inaddition to the hypocentre and magnitude. On theother hand, a variety of methods to invert wave-forms into spatio-temporal evolution of the ruptureprocess and resulting slip distribution have beendeveloped. While the growing amount of global,regional and local data, and increasing facility toretrieve them in near-real time through the Internet,

.

ARTICLE IN PRESSE.N. Sokos, J. Zahradnik / Computers & Geosciences 34 (2008) 967–977968

are challenging enough to steadily update themodelling methods.

Several codes are available to invert the tele-seismic data into point- or multiple-point sourcemoment-tensor models, including the slip distribu-tion models (Dreger and Helmberger, 1993; Kikuchiand Kanamori, 1991; McCaffrey et al., 1991).Regional data can be inverted by, for example, thecodes of Dreger and Helmberger (1993), Ammon(2001).1 Complexity of regional and local studies,compared to the teleseismic ones, is obvious: atdistances of the order of 100–103 km seismic signalsare not solely composed of a few simple phases, highfrequencies are abundant, interference waves (suchas, for example, Lg) may predominate on records,and near-field effects can be significant. Raymethods, applicable at teleseismic distances, haveto be replaced by full-wave methods, representingcomplete wavefields. Several frequency–wavenum-ber methods can be used, such as, for example, thediscrete wavenumber method (Bouchon, 1981). As arule, these demand far more computer power thanthe ray methods. The other reason for computerspeed is due to the fact that the waveform inversionhas to include grid search. Indeed, although seismicmoment tensor is related to records via linearrelations, optimization of the source position andtiming (not precisely known from standard location)makes the inversion non-linear. All these factors callfor the use of a fast computer language, e.g. Fortran.However, other factors call for tools with extendedprocessing and plotting capabilities, like Matlab. It isbecause source retrieval is a complex process, consist-ing of a series of related stages, requiring an interactiveapproach and great deal of graphical representation.Typically, to avoid the need for detailed (unknown)structural models, relatively low frequencies should beextracted from the data, but, long-period signals mayfall below the (natural or instrumental) noise level.Thus selection of usable records and their carefulprocessing is crucial, and, together with the selectionof a suitable frequency band, requires extensiveinterpretational experience. Matching records withsynthetics, while simultaneously solving problems ofnon-uniqueness of the inversion (e.g. recognizing poorresolution of some of the parameters), is anotherreason, for an interactive graphical mode.

Therefore, in this paper, we present a newsoftware package, that is based on an extension of

1Web address: http://eqseis.geosc.psu.edu/�cammon/HTML/

MTinvDocs/mtinv01.html.

the Kikuchi and Kanamori method to regional andlocal distances, which efficiently combines theFortran and Matlab skills. Fortran for the powerand speed for compute-intensive wave propagationmodelling and source inversion (Green’s functions)and Matlab for quick and user-friendly datahandling, control of the inversion process andplotting of the results. The name of the package isISOLA, since the retrieved point-source momenttensors (called subevents) represent isolated aspe-rities, or slip patches of the fault. The package hasbeen developed since 2003 and although somepreliminary versions of the Fortran part werereleased on the Internet (Zahradnik et al., 2005),2

this is the first presentation in a journal. Thepackage depends on Matlab for the GUI display,data pre-processing and plotting. The Fortran codesexist as standalone executable files, which are calledby the ISOLA-GUI, in order to perform tasks likeGreen’s function calculation and inversion. Usersmay decide to use just the Fortran codes but the useof the Matlab-based ISOLA-GUI simplifies andaccelerates the whole procedure, substantially. Be-sides Matlab graphics, GMT (Wessel and Smith,1991) is used in all the stages of the procedure, inorder to produce publication-quality figures of theretrieved moment tensors. The M_map softwarepackage3 is also used mainly for plotting mapswithin the Matlab environment.

ISOLA-GUI offers access to all the inversionprocedures through modules that perform specifictasks, e.g. data import, filter, inversion, plotting, etc.Modules can run in parallel and most of them‘‘remember’’ user’s response or try to suggestsuitable values of the parameters, in order to speedup the processing. Although most of the inputparameters are self-explanatory, ‘‘tooltips’’ havebeen added for some of them. However these arenot a substitute of the program’s manual, whichcontains an extensive description of the methodwith examples. The user is urged to study themanual prior to the application of the inversion.

The objective of this paper is to inform theresearch community about the package and itsbroad variety of options. Specific details of thesoftware use are presented in the manual accom-panying the program package. Earthquake physicsin this paper is reduced to a necessary minimum andthe reader is referred to the paper describing

2Web address: http://seis30.karlov.mff.cuni.cz/.3Web address: http://www.eos.ubc.ca/�rich/map.html.

ARTICLE IN PRESSE.N. Sokos, J. Zahradnik / Computers & Geosciences 34 (2008) 967–977 969

previous applications of the code to the 2003Lefkada, Greece, earthquake of magnitude Mw6.3(Zahradnik et al., 2005). The code has proved usefulalso for other M5+ earthquakes at distances up to400 km (Adamova et al., 2006; Tselentis et al.,2006), but also for weaker M3+ and M4 events atlocal distances (e.g. see the moment tensor solutionsroutinely provided by the University of PatrasSeismological Laboratory to the European Medi-terranean Seismological Centre (EMSC)4).

2. Program description

ISOLA-GUI presented here was created using theguide tool of Matlab and its purpose is to allow easyinteraction with the Fortran codes (mainly input filepreparation and output file display) as well as fastdata pre-processing, Green’s function calculationsand graphic output of the results. The software isrich in graphics and the various plots are createdusing a combination of Matlab’s graphic capabil-ities as well as GMT software (Wessel and Smith,1991; Wessel and Smith, 1998). A lot of care hasbeen taken to produce a software package that willbe easy to handle, will help the user judge theaccuracy of the inversion results, and will producefast and comprehensive output, accurate results andpublication ready plots. The program has beencreated with Matlab 6.5 under Windows operatingsystem but has been tested with newer Matlabversions (Matlab 7.0) as well as with other operatingsystems (Linux) and can work after minor mod-ifications, mainly in the system call commands andin the text file structure.

The program starts by running the ISOLA m-file,which generates the main user interface (Fig. 1).From this main GUI, the following functions areavailable (a) data format conversion, (b) datainspection, filtering, shifting, (c) crustal modeldefinition, (d) data pre-processing and sourcedefinition, and (e) Green’s function calculation,inversion, and plotting of results. These functionsare described in detail in the following sections.

2.1. Data (format conversion—inspection) (utilities

I, II)

Although ISOLA’s native format is quite simple(4 column ascii files, i.e., time, NS, EW, Z

4Web address: http://www.emsc-csem.org/index.php?page=

current&sub=qmt.

component) an option for format conversion fromSAC5 and Guralp Compressed Format to ISOLAnative format, is provided. The conversion isaccomplished using Matlab codes (m-files) freelyavailable on the Web6 (Thorne, 2005).7 These m-files and the accompanying GUI codes can be usedas a guide for any user who wishes to implement hisspecific data format conversion. Alternatively, thedata format conversion can be done using anexternal program. Besides the format conversion,a few options are provided for data qualityassessment prior to moment tensor inversion. Theuser can test various filters, perform instrumentcorrection, integrate or shift the data, etc. Thesetasks are of major importance since in many casesthe data contain various spurious signals, e.g.trends, that can affect the inversion, while at thesame time these are not easily recognizable in thetime series data (Zahradnik and Plesinger, 2005). Itis therefore recommended that these tests areapplied prior to any inversion attempt.

2.2. Crustal model

The crustal model to be used in all the subsequentsteps of the analysis (like Green’s function calcula-tion, polarity checking, etc) is defined just onceduring the ISOLA-GUI execution, using the crust-

mod tool. The P and S velocities (Vp, Vs), density,and P and S quality factors (Qp, Qs) are typed intext boxes or read from text files, while the Matlabcode takes care of the proper formatting, that isimportant for the ISOLA Fortran codes. A fewfacilities are available for creation of plots of Vp, Vsvelocities with depth and calculation of Vs ordensity values using empirical relations. The codeas it stands supports a single crustal model for allthe stations but future versions will support multiplecrustal models.

2.3. Data pre-processing—source definition

The data pre-processing part (instrument correc-tion, alignment, integration, decimation, etc.) mustbe carried out carefully, since any error introducedat this stage can cause significant errors in theinversion step. Using ISOLA-GUI, the user canapply all the above corrections on the data and at

5Web address: http://www.llnl.gov/sac/.6Web address: http://www.guralp.net/.7Web address: http://gcc.asu.edu/mthorne/saclab.

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Fig. 1. Main ISOLA Matlab GUI.

Fig. 2. ISOLA-GUI tool for data pre-processing.

E.N. Sokos, J. Zahradnik / Computers & Geosciences 34 (2008) 967–977970

the same time have a visual control of the results.The user is guided by the program in performing allthe tasks in the proper order, while the GUI keepstrack of user’s last response and stores files inproper folders. In this way the process is fast andwell controlled (Fig. 2). If there is a need for somespecial correction or data processing, a new modulecan be easily added in the procedure with minimumMatlab programming.

Definition of trial source positions for the eventsource is done through a GUI code, namedsourcepre, which has been specially designed toautomate and simplify this task. Two options (the‘‘point’’ or ‘‘extended’’ source) are available to theuser. By point we mean trial sources that are located

under the epicentre, while with the extended sourceoption, sources on a horizontal line or on a planewith arbitrary orientation can be defined. The‘‘point’’ source option is used for a first approxima-tion of the inversion problem and depends on thequality of the given epicentre. Using this type ofinversion can indicate the inversion’s preferreddepth for the event, but if the epicentre is wrongthe results could be misleading. Thus in many casesit may be desirable to rerun the inversion around theepicentre, using trial positions on a plane, or on afew horizontal planes at different depths. In thisway the inversion will find the optimum position ofthe event in space. The option of an arbitrary trialplane may be useful when studying the fine structure

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of the source in the nodal planes. The ISOLA-GUIcreates all the necessary files for the Green’sfunction calculations—inversion, along with plotsof the source distribution (in geographical andCartesian coordinates) for user inspection. Underthe Matlab environment the plots are producedusing the M_Map tool, but GMT format files arecreated too, thus the user can produce customizedmaps latter.

2.4. Green’s function computation—inversion

The Green’s function calculation is performedusing the frequency wavenumber method (Bouchon,1981). The code is written in Fortran but the usercontrols its use through the ISOLA-GUI, using thegreenpre tool. We have tried to limit the number ofinput parameters as much as possible, thus the userhas to specify only the maximum frequency of theGreen’s function computation. Then the codeautomatically generates the Green’s functions andthe corresponding elementary seismogram files,while at the same time it stores everything in theproper folders.

The inversion is the core of the procedure and isperformed using another ISOLA-GUI tool calledinvert, presented in Fig. 3. The user can select thetype of inversion (full, deviatoric, double couple(DC), fixed), the frequency band of the inversion,

Fig. 3. ISOLA GUI used for

the number of subevents, and the time span of theiroccurrence. Various helpful features are included,like a special option for automatic calculation ofstation weights, based on the maximum amplitudeof the displacement record, and a tool for plottingcorrelation and focal mechanism vs source positionand its time shift (Fig. 4). Besides the correlation,the double couple percentage of the solution (DC%)can also be plotted, since in many cases it canprovide indication about problematic inversionresults. The correlation plot is quite important anda major advantage of the software is that the usercan have visual control of the inversion results,while the inversion progresses, and actually drivethe inversion procedure based on this diagram andrelevant constraints, e.g. polarity measurements,rupture velocity, the assumed tectonic style in thearea, etc. The application of constraints may bedesirable depending on the resolution of theinversion parameters. For example, for the case oflow resolution the constrained (fixed) focal mechan-ism may prevent ‘‘wild jumping’’ of subevents inspace and time. In this sense, a requirement for userto select his preferred choice of the subeventposition and time is quite common and definitelyimproves the results compared to the fully auto-matic run, which is based only on the absolute valueof the correlation. In any case both user’s andautomatic selection of subevents are possible duringthe inversion procedure.

inversion calculations.

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Fig. 4. Plot of correlation vs time shift, source position and focal mechanism for single source inversion. Largest correlation was obtained

for source 2 (6 km depth) and 3.16 s time shift. Focal mechanism shading changes according to double couple percentage, while for

diagram clarity, we only plot solutions having double couple percentage larger that 70%. Preferred solution is depicted by a larger

beachball.

8Web address: http://www.itsak.gr/Zakynthos_2006SMR.pdf.

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2.5. Plotting of results

The last step is the plotting of the inversionresults, in particular the moment tensor solutionand the best fit between data and synthetics (Fig. 5).Again, a special tool was designed, named plotres,which uses Matlab and GMT graphic capabilities toprepare quality plots of the results. The variancereduction per tested source and the correspondingfocal mechanism can be plotted together on a graphin order to inspect the inversion convergencethrough the whole computation. An option forcomparing the computed focal mechanism solutionwith the available first motion polarities is alsoavailable. The plotting tool was designed primarilyfor users with limited knowledge of usage of GMTor Matlab graphics. Nevertheless our intention wasnot to prepare a GMT front-end but help usersproduce nice maps quickly. Experienced users caneasily produce custom plots using the output textfiles with the inversion results. Additionally, Matlabprogrammers can easily add their own specialfeatures to the plotres tool, such as creation of atext file with the moment tensor solution, suitablefor email notification.

3. Case study, Zakynthos 2006 seismic sequence

To demonstrate the use of the software, wepresent the moment tensor analysis for a strongearthquake that occurred on April 11, 2006 at17:29UTC, offshore of Zakynthos island in westernGreece, (EMSC location Lat:37.71N, Lon:20.91E,Mw ¼ 5.6). The event was recorded by three broadband instruments of PSLNET, a new satellitetelemetry network, starting operation in 2006 andbelonging to the Seismological Laboratory of theUniversity of Patras (Tselentis et al., 2006). Thisevent was the strongest from a series of medium sizeearthquakes (more than five events of Mw44.5)that affected the island of Zakynthos for a period of2 months causing moderate damage to the island’sstructures.8 The records of this event, as SAC files,are included with the program distribution to serveas an example. The same event will be used here todemonstrate the analysis using ISOLA-GUI.

Initially, the data are converted to ISOLA nativeformat using the specially designed SACimport tool.Then the quality of the records and the signal to

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Fig. 5. (a) Waveform comparison for single source inversion. (b) Moment tensor solution results, output by ISOLA-GUI for single source

inversion.

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noise ratio at various frequency bands are checkedusing the datafilt tool in order to define the properfrequency band for the inversion. The next step is toprepare the crustal model that will be used in theanalysis, in this case it is the model previouslyproposed by Haslinger et al. (1999) during localearthquake tomography studies in western Greece.The model is converted to the proper format usingthe crustmod tool. Next steps involve input of eventinformation, selection of stations to be used in theinversion, and raw data pre-processing, which aredone using the eventinfo, stationselect, and datain

tools (Fig. 1). At this point, we can decide on singleor multiple point source inversion and prepare thenecessary trial source position and Green’s functionfiles using the sourcepre and greenpre tools, respec-tively. We will present both single and multiplesource inversion for this event, starting with the firstone.

3.1. Single source inversion

We select deviatoric point source inversion for aseries of trial source positions lying at variousdepths below the epicentre position determined byEMSC. The total trial sources tested were 10, with a3 km vertical separation, spanning depths from 3 to30 km. This type of inversion will indicate thepreferred centroid depth, and it is a logical first stepduring the moment tensor study. Using the invert

tool, inversion parameters such as the frequencyband for the inversion, and parameters of the timesearch can be set. For this single source inversionrun, we used frequencies extending from 0.037 to0.062Hz with cosine tapering applied to both ends(Fig. 5a). Using the same tool, during the inversionrun, a plot of correlation and focal mechanism vssource position and its time shift is constructed.Such a plot is presented in Fig. 4 where it isclear, from correlation maximum, that the preferredsolution is at a depth of 6 km (source number 2corresponds to this depth) for a time shift of3.16 s. The results of the inversion are plotted laterusing the specially designed plotres tool (Fig. 5a, b).What is interesting from the single source results isthat the DC% is really low for this event, indicatingthat the possible effect of the source complexitycan be ‘mapped’ into a large but only apparentCLVD value. Of course this is just one explanationfor the large CLVD value but it motivates us todisplay the use of ISOLA, for multiple sourceinversion.

3.2. Multiple source inversion

Multiple source inversion is another key point ofthe ISOLA method. Usually this type of inversion isperformed for large earthquakes using data atteleseismic distances, but with ISOLA it is possibleto perform the same type of inversion using local orregional data. In this way more details of the seismicsource can be revealed.

In order to run a multiple source inversion, a setof possible source positions has to be defined; this isaccomplished with the sourcepre tool. In Fig. 8, amap of the trial source positions for the studiedevent is displayed. In this multiple source inversionrun, we use source positions located on a horizontalplane at a depth of 6 km (the depth preferred in thesingle source inversion) having a spacing of 12 km;we use a grid of 25 trial source positions. Using thisset of sources and the appropriate Green’s func-tions, we start running the inversion and subse-quently searching for two elementary sources, usingthe invert tool. The selected frequency band for theinversion is extended to higher frequencies(0.02–0.13Hz, with cosine tapering) in order toobtain detailed information about the sourcerupture process. During the inversion ISOLApauses and asks the user to accept the automaticallydetected optimum source position and time, or topropose a different solution for the first subevent.Creating a plot of all the possible solutions assiststhe user to decide if the proposed automaticsolution is acceptable. We need to note here thatISOLA automatically proposes a solution based onthe maximum correlation. This solution can differgreatly in the DC% when compared with another‘‘nearby’’ solution with a slightly smaller correlationvalue. Having a tool that displays this in an efficientgraphical way allows the user to explore all theconcurrent solutions and choose one, based onvarious assumptions. Such a plot for the firstsubevent is presented in Fig. 6. The automaticsolution is marked with a larger beachball, while anoption for plotting results for a single source is alsoavailable (Fig. 7).

After a detailed check and a combined use of theabove diagrams, one can easily identify otherpossible solutions that have slightly smaller correla-tion and thus have not been automatically proposedby the program. For example, source 8 at time shift0.6 s, or source 13 at time shift 4.6 s, has similarcorrelation and focal mechanism, but differ sig-nificantly from the automatically chosen solution in

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Fig. 6. Correlation diagram for first sub-event during multiple source inversion. Horizontal axis is time shift, vertical axis is trial source

number, and contours are correlation values. Focal mechanism shading changes according to double couple percentage. Only solutions

having double couple percentage larger that 70% are plotted. Preferred solution is depicted by a larger beachball.

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proposed by the program is depicted by an arrow.

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their source position and DC%. At this point, basedon what has been described already, we select sourceposition 13 and time shift of 4.6 s as our preferred

solution instead of the automatically proposed 4 s.The focal mechanism is the same for both solutions,but the DC% increases from 60% to 95%, with just

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a 3% difference in correlation. Such a choice isperhaps better compatible with the tectonic regimein Zakynthos, since it explains the first sub-event asa pure shear source. Following the same procedurefor the second sub-event, we end up with anexplanation of the waveforms as being due torupture of two pure-shear sources (Fig. 8). Thefocal mechanism of the second subevent is differentfrom the first one, suggesting a complicated rupture,and possibly explaining the large CLVD part for thesingle source solution. Nevertheless, final conclu-sions concerning the rupture history of this eventwould need special care (Zahradnik et al., 2007),and a full physical justification of the DC% wouldrequire more efforts, well beyond the scope of thepresent paper.

4. Conclusions

The moment tensor analysis of local and regionalevents is a standard procedure applied to broad-band seismic networks worldwide, in many caseseven as an automatic procedure. In all suchapplications the inversion is performed for asingle-point source. The programs ISOLA and

Fig. 8. Plot of 25 trial source positions, along wit

ISOLA-GUI presented in this paper allow an easyapplication of the iterative deconvolution method ofKikuchi and Kanamori (1991), for local andregional events, thus the method can be used forboth single and multiple source geometry. TheMatlab-based GUI facilitates easy data handling,while at the same time providing complete usercontrol during all the processing steps and easygraphical display of the results, using both Matlaband GMT capabilities. The waveform inversion isdone using the Fortran ISOLA code, in order totake advantage of language speed, while userinteraction even during the inversion is within theMatlab environment. Various tools are available forthe user to explore the data quality, adjust thecomputational parameters, correct the data, anddisplay inversion results in a publication-readyform. The modular design of the GUI allows theeasy upgrade as well as the inclusion of user-createdadditional modules, using elementary skills in theMatlab programming language. The software, themanual, and examples files are available for down-load at http://seismo.geology.upatras.gr/isola/, forthe Windows operating system, while a Unix/Linuxversion will be available soon.

h final results for multiple source inversion.

ARTICLE IN PRESSE.N. Sokos, J. Zahradnik / Computers & Geosciences 34 (2008) 967–977 977

Acknowledgments

The authors would like to thank Petra Adamovafor extensive testing of the software. Some parts ofthe Matlab GUI use functions freely available onthe Web, like the rsac and coral distribution. In theFortran section, several subroutines written byother authors were also used: M. Bouchon, O.Coutant, J. Sileny, J. Jansky and O. Novotny, J.A.Snoke, P. Reasenberg and D. Oppenheimer. Codesfrom Fortran Numerical Recipes were also em-ployed. This work was supported by the EC project3HAZ-Corinth and the following research projectsin Czech Republic: GAUK 279/2006/BGEO/MFF,GACR 205/07/0502, MSM0021620860.

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