Automated procedure for point and kinematic source inversion at regional distances

Transcription

1 Click Here for Full Article JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115,, doi: /2009jb006450, 2010 Automated procedure for point and kinematic source inversion at regional distances Simone Cesca, 1,2 Sebastian Heimann, 1,2 Klaus Stammler, 2 and Torsten Dahm 1 Received 11 March 2009; revised 1 September 2009; accepted 13 November 2009; published 8 June [1] The development of fast, automatic routines for the retrieval of point source parameters of medium to large earthquakes was convincingly established in the last years and decades, providing an increasing number of focal mechanism solutions. Original applications at teleseismic distances have been successively accompanied by specific routines for regional data sets. The majority of these methods are based on the fit of low passed time traces. We present here a new technique for the automatic retrieval of point source parameters and highly parameterized kinematic rupture models at regional distances, assuming the recently proposed eikonal model to describe the extended source. In our approach we use a larger set of information to better constrain the source parameters, including the fit of amplitude spectra and displacements at different phases and frequency ranges. The time consumption of the inversion process is significantly improved, thanks to the implementation of Green s functions databases. We adopt a multistep inversion approach, finally providing the focal mechanism, magnitude, and centroid location of the point source. For events with magnitude higher than a threshold of Mw 5.5, source geometry, rupture extension, and average slip may be additionally retrieved. We discuss the methodology and the inversion stability, showing applications to significant earthquakes in two case areas. We focus on Germany and Greece, and their neighboring areas, considering major shallow earthquakes in the last 5 years. The proposed method is currently implemented for automatic data processing at the Seismological Observatory of the Federal Institute for Geosciences and Natural Resources in Germany. Citation: Cesca, S., S. Heimann, K. Stammler, and T. Dahm (2010), Automated procedure for point and kinematic source inversion at regional distances, J. Geophys. Res., 115,, doi: /2009jb Introduction [2] The development of automated routines for data analyses at teleseismic distances has brought to the recompilation of moment tensor catalogs for large earthquakes at teleseismic distances, for example, by the Global CMT [Dziewonski et al., 1981; Dziewonski and Woodhouse, 1983], the United States Geological Survey National Earthquake Information Center, USGS NEIC [Sipkin, 1982, 1986] and the Earthquake Research Institute (ERI) of the University of Tokyo [Kawakatsu, 1995]. These inversion routines utilize long period body waves (USGS, ERI) or body and mantle waves (Global CMT) to derive the moment tensor (USGS) or the centroid moment tensor (Global CMT, ERI). The major limit of these applications resides in the magnitude of the studied events (Mw > 5.5). Owing to intrinsic limit for source depth estimation, source depths shallower than a threshold of km cannot be resolved. 1 Institute of Geophysics, University of Hamburg, Hamburg, Germany. 2 Federal Institute for Geosciences and Natural Resources, Hanover, Germany. Copyright 2010 by the American Geophysical Union /10/2009JB [3] Regional moment tensor catalogs have been provided by different institutions, since early works by Nakanishi et al. [1992], Ritsema and Lay [1993], and Giardini et al. [1993]. Limiting to the European Mediterranean region, the INGV European Mediterranean RCMT Catalog [Pondrelli et al., 2002], the Swiss Federal Institute of Technology in Zürich (ETHZ) [Bernardi et al., 2004], the Institute de Physique du Globe de Paris (IPGP), the Instituto Andaluz de Geofisica (IAG) [Stich et al., 2003], the Instituto Geográfico Nacional (IGN) [Rueda and Mezcua, 2005], the National Observatory of Athens (NOA) [Melis and Konstantinou, 2006], the Aristotle University of Tessaloniki (AUTH) [Roumelioti et al., 2007], the University of Patras (USPL) [Sokos and Zahradnik, 2008] and the Kandilli Observatory, Bogazici University (KOERI) provide catalogs of moment tensor solutions. Regional applications have focused on smaller magnitudes events, using seismic data at regional distances. As a consequence, it has been possible to obtain moment tensor solutions for earthquakes with magnitude down to Mw 3.5 and to improve source depth estimation in case of shallow events. Regional applications are based on the fit of low passed seismograms, using either the whole waveform (e.g., ETHZ, IAG, IGN, NOA, AUTH, UPSL) or only surface waves (INGV RCMT). At least for shallow earthquakes, this 1of24

2 approach results highly weighted on the fit of surface waves, which amplitudes dominate the seismograms. The inversion is typically realized in the time domain (e.g., INGV RCMT, IAG, IGN, NOA, AUTH, UPSL) or equivalently by fitting the full spectra (ETHZ, IPGP). Different institutions adopted different algorithms. INGV RCMT uses an iterative CMT least square inversion [Pondrelli et al., 2004] modified after Ekström et al. [1998] and Arvidsson and Ekström [1998]; ETHZ moment tensor solutions [Bernardi et al., 2004] are based on the algorithm originally described in the work of Giardini [1992]; IAG [Stich et al., 2003] uses a linear moment tensor inversion [Langston et al., 1982] assuming a range of possible source depths; time domain moment tensor inversion following Dreger and Helmberger [1993], Pasyanos et al. [1996], and Dreger [2003] have been implemented at AUTH [Roumelioti et al., 2007] and at IGN [Rueda and Mezcua, 2005]; NOA moment tensor solutions [Melis and Konstantinou, 2006] use the linear time domain inversion method described in the work of Randall et al. [1995]; UPSL uses the ISOLA code [Sokos and Zahradnik, 2008], an iterative deconvolution method based on Kikuchi and Kanamori [1991]. In both linear and nonlinear inversion approaches, source depth is retrieved by testing a set of values and comparing misfits; in some cases constraints are adopted for very shallow depths (e.g., INGV RCMT imposes a fixed depth between 10 and 15 km for events shallower than 15 km [Pondrelli et al., 2007]), in other cases the source depth is originally fixed to check data quality (e.g., ETHZ, using a starting depth of 18 km) and improved only at a later stage. Centroid moment tensor solutions are provided by INGV RCMT, IPGP and UPSL, while other institutions assume fixed the original epicentral location. Given the comparison in the time domain, data and synthetics may need to be aligned before or during the inversion; different approaches are used, including the prior alignment of theoretical and observed first arrivals (IAG, NOA), the alignment of synthetic seismograms associated to specific representative sources (IGN), or the estimation of time corrections for each trace after the inversion of the moment tensor (ETHZ). The inclusion of higher frequencies, as discussed before, is limited again by the approximate knowledge of the crustal structure and, in case of larger earthquakes, by the fact that high frequency radiation is related to the finiteness of the focal region, and thus not possible to be studied under a point source approximation. The mentioned regional applications use a variety of bandpass filters ranging from 12 to 20 s (NOA) to s (ETHZ), the most common bandpass being s. A common approach (e.g., IAG, IGN, AUTH, UPSL) is to have different bandpass filters, depending on the event magnitude. [4] In what refers to the modeling of extended sources, different trials have been realized in the past, using broadband seismic, accelerometers, and deformation data. Limiting to pure seismological applications, several works based on slip map determination have followed the original studies by Olson and Apsel [1982] and Hartzell and Helmberger [1982]. As shown by Beresnev [2003] for the case of the Mw 7.6 Kocaeli (Izmit, Turkey) earthquake of 1999, attempts to derive detailed slip maps inverting for a large number of unknown parameters resulted in a wide sets of solutions, all well fitting the data, but inconsistent between themselves. Similar inconsistencies have been shown also for preliminary application to synthetic data sets provided within the SPICE project benchmark [Mai et al., 2007], questioning the reliability of these inversion approaches. A significant contribution, both in terms of the simplification of the rupture models and of the automation of kinematic inversion, is the work of Vallée and Bouchon [2004] using the slip patches method. Previous studies have provided several solutions for kinematic parameters, but source models are not always consistent between themselves. [5] We assume here a simplified but realistic description of the rupturing process. The model is further referred as the eikonal source model, since the rupture front propagates on the base of an eikonal solver. The flexibility of this model and the reduced number of parameters required to describe the rupture process make it a preferable choice for the implementation of automatic inversion routine. The inclusion of such routines within standard earthquake processing will allow the retrieval of main kinematic parameters of the earthquake source, and would finally lead to a significant improvement of seismic source catalogs. We adopt a new multistep approach for the estimation of earthquake source parameters at regional distances, which is based on a combined fit of time traces and amplitude spectra at different frequency ranges. In this manuscript, the method is applied to a significant number of earthquakes in Europe focusing on two regions and data sets: Greece (earthquakes with Mw > 5.0, using regional data) and Germany (Ml > 4.0, using local data). Automated application at the Seismological Observatory of the Federal Institute for Geosciences and Natural Resources (BGR) will provide a new point source catalog for central Europe, based on a frequency domain inversion approach, as well as solutions for highly parameterized kinematic source models, retrieving source parameters such as the fault orientation (distinguishing between fault plane and auxiliary plane), the rupture area, the rupture direction and its duration. This represents a challenging automatic approach to the retrieval of kinematic source parameters at regional distances, assuming the eikonal source model, and it is entirely based on the fit of seismic observations. 2. Methodology: A Multistep Approach [6] We adopt here a multistep inversion approach, with the specific aim of defining a robust inversion method, suitable for the automated inversion of the extended source parameters. The source parameters are retrieved at different successively inversion steps, each time adopting the most proper range of frequency, norm definition and inversion method Inversion Strategy and the Eikonal Source Model [7] In order to afford the problem of nonunique solutions, we have decided to implement a highly parameterized source model. This model (Figure 1) allows the representation of the extended source by a reduced number of parameters (13 parameters, here stated in brackets). The fault plane is oriented by the three angles strike, dip and rake (, d, l). The rupture surface along the fault plane is defined from a given point (centroid with coordinates latitude Q, longitude F, depth z, origin time t 0 ) and extending for a maximum distance defined by the parameter radius R. Additionally, this surface is limited by constraining surface (generalized planes), which are natural boundaries for the rupture process. These 2of24

3 Figure 1. Scheme of the inversion strategy. The inversion is realized in two major steps: point source (focal mechanism and centroid location) and kinematic model inversion. At different steps, different data, minimization techniques, and inversion approaches are used. boundaries are the free surface, above, and the base of the crust, below (we limit our applications here to the case of crustal sources). The crustal thickness is dependent on the epicentral location and based on CRUST2.0 model [Bassin et al., 2000]. Parameters nucleation coordinate x and y (n x,n y ) identify the nucleation point (epicenter) within the rupture surface. From the nucleation point rupture propagates with a variable rupture velocity, v r (x, y, z). In order to reduce the number of some parameters, we define v r as a percentage of the shear wave velocity v s (x, y, z). This will typically result in a faster propagation of the rupture at depth, toward the base of the crust, and slower at the free surface. The approach is either more realistic than assuming a constant v r and allows the description of the rupture propagation with a unique parameter. The risetime t r defines the time required for the slip to occur at each point; if the source spatial extension is null, and a point source is modeled, t r will describe the length of its source time function. [8] The 13 parameters describing the eikonal model (Figure 1) can be grouped into two main categories: 8 parameters are required for the description of a point source, whereas the remaining 5 are strictly related to the finite rupture. Point source parameters can be divided into two subgroups: strike, dip, rake and scalar moment affect the radiation pattern, while latitude, longitude, depth and origin time locate the source in space and time. Low frequency seismograms, below the corner frequency, contain enough information to retrieve point source parameters. The remaining 5 parameters, related to the finite rupture, can be inverted only if higher frequency seismograms are reproduced. The proposed parameters classification suggests that source parameters should be inverted subsequentially at different frequencies. We propose a two step inversion process (Figure 1): (1) initially, we focus on the point source, first deriving the focal mechanism and then locating the centroid, (2) during the second inversion step, the extended source parameters are retrieved. The uncertainty of model parameters as well as the inference of specific receiver configurations (e.g., strongly uneven azimuthal coverage) may be discussed on the base of a bootstrap approach, by iteratively repeating the inversion 3of24

4 Table 1. Summary of Bandpass Filters and Range of Epicentral Distances Used Within This Study Inversion Step 1 Inversion Step 2 Bandpass (Hz) Epicentral Distance (km) Bandpass (Hz) Epicentral Distance (km) Greece, Mw Greece, Mw < Germany, Ml Germany, Ml < using different stations configurations, based on the available data sets Point Source and Amplitude Spectra Inversion [9] At the beginning of step 1, we start from a rough location and magnitude estimation (e.g., provided by a seismological observatory, and invert strike, dip and rake) and further improve the source depth and the scalar moment (Figure 1, inversion step 1a). We use the entire waveforms and apply a bandpass filter to seismic data (see Table 1), in order to fit the flat part of the seismogram spectra and stabilize the inversion process. We prefer a frequency domain inversion approach, fitting amplitude spectra, instead of the classical one in the time domain. Advantages of amplitude spectra moment tensor inversion methods have been described in the past, for example by Romanowicz [1982], Dahm et al. [1999], and Cesca et al. [2006]. The method is less sensitive to a precise trace alignment and to phase shifting owing to mismodeling of the crustal structure, allowing thus more stable solutions also at slightly higher frequencies (e.g., up to 0.1 Hz for magnitude Mw 4.0 events). This approach is helpful toward a more precise source depth estimation. Since only amplitude spectra are fitted, an intrinsic ambiguity affects the retrieved solution, as compression and dilatation quadrants of the focal sphere cannot be distinguished. Given the nonlinearity of the inversion approach and the possible nonuniqueness of solutions, we run the inversion several times, using a set of different starting configurations. [10] We use unrotated displacement seismograms (north, east, vertical components), so that also single traces can be used, when any of the components are damaged or unavailable. Data are filtered using a bandpass, which frequency corners are chosen on the basis of the magnitude of the studied earthquake (Table 1). A distance dependent taper is applied, on the basis of the arrival of theoretical P phases for the chosen velocity model and empirical estimation of the length of surface wave trains, in order to select the whole waveform, but reducing as much as possible the length of the seismograms: this way, we avoid the inclusion of time windows only affected by noise. From each of the starting configurations, synthetic seismograms and amplitude spectra are calculated and then inverted to found the best point source parameters. The inversion routine is based on a Levenberg Marquardt approach and the fitting procedure minimizes the difference of amplitude spectra. The L2 norm is better suited using the Levenberg Marquardt approach. Misfits are normalized against zero traces. After the first inversion step (Figure 1), strike, dip, rake, scalar moment and centroid depths are estimated. Since compression and dilatation quadrants cannot be distinguished, focal mechanisms with both polarities are possible. The risetime is fixed (two samples, 1 s) during this inversion step. Nevertheless, once the point source parameters are retrieved, this parameter can be inverted to get some additional information about the rupture process duration, or the length of the point source time function Point Source and Time Domain Inversion [11] During the inversion step 1b, we intend to improve the centroid source location, by keeping fixed the radiation pattern parameters and the source depth. The discrepancy between centroid and hypocentral locations may rise in case of large earthquakes, where the rupture extension can reach values of hundreds of kilometers and the rupture duration may last several seconds. Additionally, we aim to solve the polarity ambiguity of the point source focal mechanism solution. A time domain approach including phase polarity information is better suited to reach both these goals. We apply here the same bandpass as for inversion step 1a. We now concentrate on body waves arrivals, choosing S waves time windows as these present larger amplitudes. Note that this is clearly different to other automated point source moment tensor inversion at regional distances, which fit full waveforms or surface waves [e.g., Stich et al., 2003; Pondrelli et al., 2004; Bernardi et al., 2004]. The polarity ambiguity, or discrimination between compression and dilatation quadrants, is solved at first by calculating synthetic seismograms for the two possible solutions, shifting them to best correlate with observations, and evaluating the L2 norm misfits. At this point, we search for the best centroid location, by testing a range of spatial and temporal shifts around the starting configuration defined by latitude Q, longitude F and origin time t 0. After inversion step 1b, the entire group of eight point source parameters are provided (Figure 2). Location parameters refer now to the centroid, and strike, dip and rake refer to the radiation pattern of the point source; that is, represent either the fault plane or the auxiliary plane (FAULT AUX ambiguity) Kinematic Model and Amplitude Spectra Inversion Including High Frequencies [12] Once the point source model has been derived, we fix the fault orientation (considering both the two possible fault planes), the centroid location (center of the extended source model) and the magnitude, and focus on the remaining parameters of the eikonal source model. The advantage of the choice of this model appear now clear, since we afford the inversion problem to derive only 5 parameters. Although our source model could significantly simplify the real rupture process, we believe this approach allows a much more robust estimation of important kinematic parameters, such as the fault plane orientation, the rupture area, the rupture velocity, and directivity effects. 4of24

5 Figure 2. Location (dots) and main parameters, according to reference catalogs, of the selected earthquake data sets; stations used for Greece (triangles) and Germany (inverted triangles) applications are shown. Velocity models are plotted at the bottom right corner, showing Vp (solid lines), Vs (dashed lines), and density (dotted lines) profiles. 5of24

6 [13] To properly choose the best strategy, several tests have been realized to check the main effects of kinematic parameters on seismograms characterization and the response of different inversion approaches. A first consideration refers to the risetime. Applications to synthetics and to real cases have shown that a bias between risetime and rupture time, within two extreme cases. On one side, we may choose a long risetime in the range of the source duration as estimated during inversion step 1. This leads to unrealistic small extension of the rupture plane during inversion step 2, consistent with the previous point source one. On the other side, if the risetime is fixed to its minimum duration, the duration of the rupture process will require a large spatial extension of the rupture plane. Within the range of applications here presented, mostly dealing with magnitudes from Mw 4 to Mw 6.5, a reliable representation is to assume a fixed ratio between the risetime and a rupture time. A fixed ratio between risetime and rupture duration is also indicated by scaling relations of earthquake rupture dynamic [e.g., Stein and Wysession, 2003]. Since the duration of the rupture process is already known after the step 1a of the inversion, the risetime can be then fixed to 1/3 of this value, valid for a circular fault. This choice, which may not be appropriate for larger earthquakes, additionally benefits the inversion process, as the number of unknown decreases to 4. [14] Effects of kinematic parameters on synthetic seismograms have been analyzed for the remaining parameters. Changes in the parameter values describing the extended fault mainly affect the synthetic spectra above the corner frequency of the source spectra. Such a consideration is well known, and is the base of the successful estimation of point source parameters when the inversion is constrained to the range below the source corner frequency. We therefore include higher frequencies at this inversion step. Considering one of the two possible fault planes, the position of the nucleation point within the plane, the size of the rupture surface and the rupture velocity all map into the shape of the waveforms, and the directivity effects can be well evaluated in the frequency domain, by comparing amplitude spectra. For example, the waveform show shorter higher amplitude pulses at stations with azimuths closer to the direction of the rupture front, and broader low amplitude pulses at stations located in the opposite direction. Such effects are consequence of a seismic Doppler effect and are observed both for body and surface waves. The combination of the source radius and the rupture velocity will map into the representation of the extended source by means of the superposition of point sources, affecting their number, distribution, origin time and the duration of their seismic radiation. These effects are seen again in the waveform shapes. According to first studies on the rupturing of shear cracks [Burridge, 1973; Andrews, 1976; Das and Aki, 1977], the rupture front may either propagate at sub Rayleigh or supershear velocity. Although the majority of the modeling of extended faults has indicated that rupture velocities pertain to the first group, supershear velocities have been possibly observed for some different events [e.g., Archuleta, 1984; Bouchon et al., 2001; Bouchon and Vallée, 2003]. The relative rupture velocities derived by the results proposed after Vallée and Bouchon [2004] for a significant set of earthquakes all lie in the range between 0.3 v s and 0.9 v s. Our synthetic tests have indicated that the relative rupture velocity is a difficult parameter to derive. A variation of this parameter within a realistic range has often a minor effect on the seismogram fit. Additionally, a trade off may exist between rupture velocity, risetime, rupture time and finite source length. According to the difficulty in a stable retrieval of the rupture velocity, we choose here to use a fixed value of 0.7. [15] In summary, the second inversion step is realized in the frequency domain by fitting amplitude spectra in a larger frequency band, when the lower frequency corner is kept unchanged, while the upper corner is increased to a higher value (Table 1). The choice of the upper corner frequency is a compromise between parameters resolution and the simplification introduced within the Earth velocity model: a too high corner frequency may include specific data features which cannot be reproduced with the averaged 1 D model used to build the Green s functions, whereas the opposite case may smooth the seismograms features which can allow to resolve kinematic parameters. After testing different fitting procedures, L1 norm is here preferred to L2 norm, as this results more sensitive to high frequency spectra variation when changing kinematic parameters. Since differences between different extended source models may still be small, and owing to the excessive computational requirements, we prefer to realize a grid walk over possible configurations of the chosen kinematic parameters, rather than a detailed inversion as in inversion step 1a. A set of radiuses are tested, within a range of values defined in dependence on the scalar moment (e.g., only radiuses up to 8 km are considered for events with magnitude equal or below Mw 5.5), which has been chosen to include expected sizes according to Wells and Coppersmith [1994]. Similarly, we test a range of possible nucleation points within the rupture area, their number and distribution depending on the earthquake size. For instance, 3 nucleation points are tested for events with Mw < 5.5, up to 7 nucleation points for larger earthquakes in this study, in order to evaluate directivity effects Algorithm Characteristics and Main Tools [16] The inversion strategy here described has been implemented with the aid of the Kiwi (KInematic Waveform Inversion) tools, a set of Fortran routines handled within a Python interface, which have been developed at the University of Hamburg, Germany (see The strategy here adopted could be easily modified, thanks to the flexibility and of the code, which allows the implementation of a set of different source models, both for point source and kinematic source representation. We only discuss some of the available tools, which have been implemented within this application. Since the intention is to provide a relatively fast routine for continuous data analysis, computational efforts had to be minimized. Since the most time consuming step is the generation of Green s functions (GFs), these are calculated in advance, for a range of Earth models, source depths, and epicentral distances. GFs are then allocated into database structures, which can be fast accessed during the inversion. Different routines for GFs interpolation are build within the Kiwi tools, allowing the calculation of synthetic seismograms for any given source receiver configuration in between grid points. In the current approach a simple bilinear interpolation algorithm is used. The fast access to different phases infor- 6of24

7 mation at different inversion steps additionally required the development of arrival times databases. 3. Data Overview [17] The application of the proposed methodology to a set of earthquakes is first helpful to improve the choice of the numerical parameters of the inversion process, such as the bandpass at different inversion steps. The analysis of data sets from a range of different earthquakes, characterized by a different magnitude, location and focal mechanism will additionally allow to analyze the stability of the inversion process and its limits, depending on the earthquake point source parameters. To check the potential of the proposed method and to analyze effects of the mentioned parameters on the quality and stability of the inversion results, a set of trial earthquakes has been identified. Earthquake selection followed a set of given criteria. A time interval from January 2003 to June 2009 has been chosen, because of a better station availability. We limit our study to the case of shallow earthquakes, with hypocentral location within the crust, in order to use the eikonal source model constrained by the free surface and the Moho discontinuity (see par. 2.1). Finally, we choose two regional applications in Europe, owing to the interest of a further implementation of the algorithm at the BGR, in Germany. The full list of chosen earthquakes is shown in Figure 2 (event numbering here defined will be used through the text to identify each earthquake). Green s functions databases have been built, using PREM model [Dziewonski and Anderson, 1981] for applications to Greece and AK135 model with a continental crust [Kennett et al., 1995] for Germany. [18] The first region includes Greece and its surrounding areas (epicentral locations within latitude N and longitude E). It is one of the most active seismic regions within Europe, with a variety of different focal mechanisms and magnitudes above the threshold of Mw 5.5, which was chosen for the application to seismic data at regional distances (here defined as below 3000 km). A combined search through Global CMT catalog [Dziewonski et al., 1981] and the availability of seismic data through the Incorporated Research Institutions for Seismology Data Management System (IRIS DMS) yielded a list of 20 events. [19] The second region is centered in Germany and its surrounding areas (46 55 latitude N and 5 16 longitude E). Seismic broadband stations operated by the BGR, partly in cooperation with research institutions, provide a wide set of seismic data at local distances (here, below 500 km). Lowermagnitude earthquakes represents a challenge for the inversion method and offer a chance to identify the limits of its applicability. An earthquake search within the BGR catalog [Henger and Leydecker, 1978] yielded to a list of 21 events in the chosen time span, with magnitude above a threshold of Ml Modeling of Regional Earthquakes: Greece [20] The data set for Greece includes 20 earthquakes, with magnitudes ranging from Mw 5.1 (event 4, Kalamata) and Mw 6.8 (event 17, SE Peloponnesos). Focal mechanism solutions are provided by the Global CMT, USGS, INGV RCMT and ETHZ moment tensor catalogs offer a good benchmark to compare our solutions. Additionally, specific studies have been published, concerning some of the selected events, either discussing the local seismicity and tectonics, aftershock distribution and proposing kinematic models. They offer a chance to discuss the kinematic source parameters retrieved here Point Source Inversion [21] Point source parameters are retrieved following the procedure described in section 2.2. Frequency bandpass, range of epicentral distances (Table 1) and the adoption of distant dependent weights have been chosen after preliminary tests using different configurations. Two indicators were then identified and considered to evaluate and compare the quality of different solutions. The first indicator was the misfit, which indicates the capacity of the model to reproduce observations. Although the misfit value reflects the quality of the solution, its absolute value is also affected by the number of stations, the available traces and the station configuration. For this reason we have additionally considered an indicator of the stability of the point source solution, on the basis of the flatness of relative misfit curves for strike, dip and rake perturbations (see, e.g., Figure 3). This stability indicator prefers solutions, for which a common perturbation of strike, dip or rake angles will induce a major variation of the misfit value. Additionally to these numerical indicators, as the chosen earthquakes have been processed by moment tensor inversion routines from different institutions, it was possible to compare the retrieved solutions to those provided in these catalogs, using these indications to confirm our selection criteria. Owing to instabilities for very shallow sources and based on the application to shallow events, depth is constrained below 5 km. Solution quality is classified in three categories on the base of the L2 norm misfit. Categories A (best solutions), B, and C, with misfits below thresholds of 0.4, 0.5, and 0.6, respectively, are accepted as provided by the automatic routine, while category D solutions (misfit above 0.6) require a manual inversion, with proper selection of data traces. Figure 3 presents the typical output after inversion step 1, here shown for the application to the 12 April 2004, Mw 5.5, Zakynthos earthquake (event 13). Inversion step 1b (polarities and centroid location) is realized in the time domain, fitting 60 s length time window centered on S phases. Reference traces are shifted to a maximum of ±10 s to better align with synthetic seismograms assuming the different possible source mechanisms after inversion step 1a. Later, unshifted data windows are fitted assuming 2541 centroids: relative latitude and longitudes are varied in the range between 25 and 25 km, while relative origin time is varied in the range between 2 and 18 s. Figure 4 presents the output after inversion step 2 in the case of Zakynthos earthquake (event 13). [22] Results from automated application of the routine to the selected 20 earthquakes in the Greek region are summarized in Figure 5 and in Table 2. All solutions present a good fit to data, with L2 norm misfits below 0.5, with the exception of event 9 (misfit 0.611). According to the mentioned classification, 11 events have quality A, 8 quality B, and 1 quality D. All solutions from the automated inversion are accepted and used for the following kinematic inversion 7of24

8 Figure 3. Example of focal mechanism retrieved after inversion step 1a for the 11 April 2006 Mw 5.4 Zakynthos earthquake (event 13). (top) Inversion results include point source parameters estimation, focal mechanism, and curves of relative misfits versus depth, strike, dip, and rake angles. (bottom) Fit of the amplitude spectra for the used traces: gray shaded spectra represent observed spectra, and thick black lines represent synthetics. 8of24

9 Figure 4. Example of centroid location retrieved after inversion step 1b for the 11 April 2006 Mw 5.4 Zakynthos earthquake (event 13). (top) Inversion results include centroid parameters estimation, focal mechanism (including compression and dilatation quadrant), relative centroid location, and relative centroid time offset. The size of the gray dots increases with fit quality; the best solution is identified by a black circle. (bottom) Fit of S wave windowed displacements for the used traces: thin traces represent observed displacements, thick lines represent synthetics, and the gray shaded area represents the applied taper. 9of24

10 Table 2. Summary of Point Source Inversion for the Greece and Surrounding Region Data Set a Event Latitude (deg N), Longitude (deg E) Type/Category Dep (km) Two Configurations of Strike, Dip, and Rake (deg) M0 (Nm) Mw Dur (s) toff (s) Rel.Loc. N E (km) Misfit Step 1 NSt Ntr 1. East Aegean 38.25, automatic/a , 79, , 40, e , , Gulf of Saros 40.19, automatic/a , 75, , 84, e , , Lefkada 38.84, automatic/a , 52, 7 199, 84, e , , Kalamata 37.15, automatic/b , 38, , 53, e , , Crete 34.45, automatic/b , 62, , 89, e , , Dodecanese 37.15, automatic/a , 32, , 57, e , , Kas 35.89, automatic/a , 48, , 79, e , , Ionian Sea 37.36, automatic/b , 55, , 34, e , , North Albanian 42.37, manual/a , 19, , 70, e , , East Aegean 38.17, automatic/a , 76, , 52, e , , Zakynthos 37.61, automatic/b , 62, , 28, e , , East Aegean 38.15, automatic/a , 76, , 47, e , , Zakynthos 37.64, automatic/b , 62, , 28, e , , Zakynthos 37.60, automatic/b , 62, , 35, e , , Zakynthos 37.63, automatic/a , 63, , 27, e , Kerkyra 39.19, automatic/a , 19, , 76, e , , SW Peloponnesos 36.24, automatic/b , 86, , 4, e , SW Peloponnesos 36.24, automatic/b , 85, 82 8, 9, e , , SW Peloponnesos 36.24, automatic/a , 74, , 68, e , , NW Peloponnesos 37.93, automatic/a , 79, 1 212, 89, e , 39 a Here Dep indicates depth, Dur indicates duration, Rel.Loc.N E indicates relative location NE, and Nst Ntr indicates number of stations/number of traces. 10 of 24

11 Figure 5. Summary of point source focal mechanism inversion (Greece). (top) Focal mechanisms plotted on the map of reference region. (bottom) Comparison of obtained solutions (black focal mechanisms, thick line circles) with those provided by main catalogs (gray beach balls; symbols are defined according to the legend) showing focal mechanisms, centroid depths, and scalar moments. 11 of 24

12 step, with the exception of event 9, for which a manual inversion is suggested. The fit could be improved for this specific inversion, after removing few noisy traces; the retrieved focal mechanism was consistent with the automated solution. Polarity information is correctly interpreted in the second inversion step. Resulting focal mechanisms resemble the main stress field in the region, and are in agreement with solutions published by regional catalogs for all studied earthquakes (Figure 5, bottom). Large consistency is observed when comparing scalar moment estimations with published solutions. Centroid depths show a general agreement with the average behavior of available solutions, although a major scattering within the source depths proposed by different catalogs stresses the difficulties in the stable retrieval of this parameter. In few cases (events 1, 2, 10, 16) our solutions prefer slightly shallower sources than other solutions. [23] The chances for a successful inversion of centroid parameters are highly dependent on the data amount and the azimuthal coverage. For the application to Greek events, data quality was satisfactorily and results of inversion step 1b offer an improvement of the centroid location in time and space (Figure 6). Therefore, centroid time offsets and location shifts have been used during kinematic modeling at inversion step 2. Centroid locations show typical horizontal shifts up to 20 km and time delays of 0 to 10 s. The consistent retrieval of positive time offsets has to be associated with the duration of the rupture process, identifying the delay between the nucleation and centroid time. A subestimation of seismic waves velocities in the chosen model could also partially explain this observation. Relatively large spatial offsets of centroid locations may be partially consequence of uneven station distributions. The uncertainties of location estimations, based on a bootstrap approach, are typically in the range or below the retrieved offsets Kinematic Source Inversion [24] The last step of the inversion process refers to the retrieval of kinematic parameters of the earthquake source. Displacement traces are tapered as for inversion step 1a, but misfit estimation is now based on the L1 norm comparison of amplitude spectra. The range of tested models include both possible fault planes, toward a fault plane discrimination, and a range of radiuses and of nucleation points within the rupture surface, to better describe rupture kinematics; the number of tested models increases with the magnitude of the event, as it increases the chance to distinguish between different models. Given the current approach, the inversion is first biased by the fit of the rupture process duration, as discussed in section 2.4. This explains the difficulty to correctly resolve the risetime, the rupture time, the rupture velocity and the radius, which all affects the process duration. An example of the output after inversion step 2 is given in Figure 7 (event 13, Zakynthos). [25] Routine application to the Greek data set indicates acceptable fits through automated inversion for nine earthquakes (two more events could be improved after manual inversion). Finally, we get indications of the kinematic of the rupturing process for more than half of the studied events. Kinematics rupture models will be here discussed for the best solutions, which are shown in Figures 8 and 9. However, for completeness, results for all cases are listed in Table 3 (where f indicates parameters fixed within the inversion, m indicates that the parameter is either the minimum or maximum value assumed within the inversion, and two solutions for Lefkada earthquake refer to bandpass filters of Hz and Hz, respectively). For the same reason, for all events we list the best solutions for both possible fault planes. The best modeled earthquakes are mostly confined in two main areas, southern Ionian (ENE low angle dipping thrust mechanisms) and eastern Aegean Sea (NE SW strike slip mechanisms), possibly suggesting a more favorable data coverage in this area. An alternative explanation might be that the source process for the main seismic activity in these areas is consistent with the source model here proposed. Four more strike slip fault mechanisms are additionally discussed (events 2, 3, 19, 20). Retrieved rupture sizes are often larger than those predicted by empirical relations [e.g., Wells and Coppersmith, 1994]; these discrepancies highlight once more the discussed problems of distinguishing between rise and rupture time, although strong assumption on rupture velocity may play an additional important role. In the following, source models are discussed specifically for the 11 best events Southern Ionian Sea [26] Four earthquakes interested the area offshore the SW coast of Zakynthos Island. The first event (event 11) occurred on 18 October 2005, while the remaining three (event 13 15) occurred between the 11 and 12 April All events present a similar magnitude (Mw ). Events 11, 13 and 15 show consistent depth of about 25 km and thrust mechanism striking NNW SSE. The last event (event 14) is located at the slightly shallower depth of almost 17 km; its focal mechanism, slightly different from the other cases, is still consistent in the identification of a possible fault plane with low dipping angle toward ENE. This plane, common to the 4 earthquakes, is consistently identified as the fault plane through kinematic inversion. Its orientation, according to these results, has a strike of and a dip of Rake angles indicate pure thrust mechanisms for deeper events (rakes ), with a minor oblique component for the shallowest one (event 12, rake 53 ). Rupture radiuses varies between 6 and 8 km, increasing with scalar moment. According to the source geometry imposed by the eikonal model and the local crustal structure, this leads to rupture areas of km 2 and average slips of 2 4 cm. An interesting result, common to all four earthquakes, is the identification of rupture directivity processes, predicting almost unilateral rupture processes, starting at the northern edge of the rupture and propagating toward SSE. These may reflect common gradients in the shear stress resolved on the faults. Zahradnik et al. [2008] have studied earthquakes at Zakynthos from year 2006, with specific attention on nondouble couple source components. However, no extended source models have been previously proposed for these earthquakes, nor specific studies on aftershock distribution are available, in order to support or contrast the models here proposed. However, the focal mechanisms and the fault plane identified fit well with the Hellenic subduction structure at the Ionian Islands [Laigle et al., 2002] Northern Ionian Sea [27] The 14 August 2003, Mw 6.2, Lefkada earthquake (event 3) is a complex earthquake, which has been studied in detail using a variety of modeling approaches [e.g., Karakostas et al., 2004; Zahradnik et al., 2005; Benetatos 12 of 24

13 Figure 6. Summary of centroid location inversion results (Greece) using azimuthal equidistant projections. Symbols refer to locations by different institutions as listed in the legend. The common scale of 100 km is given at the bottom. 13 of 24

14 Figure 7. Example of kinematic model retrieved after inversion step 2 for the 11 April 2006 Mw 5.4 Zakynthos earthquake (event 13). (top) Main inversion results include kinematic parameters estimation, focal mechanism (including discrimination of the true fault plane, identified by a thick line), rupture shape and size, isochrones of the rupture process, curves of misfit versus source radius and relative rupture velocity, which is fixed here. (bottom) Fit of the amplitude spectra for the used traces: gray shaded spectra represent observed spectra, thick black lines represent synthetics. 14 of 24

15 Figure 8. Fault discrimination resulting from kinematic inversion for the Greek region. Original locations (crosses), centroid locations (black dots), and nucleation locations (white dots) are shown along with the focal mechanisms for the point source models (gray and white beach balls); true fault planes are identified by thick black lines upon the beach balls; dashed lines indicate horizontal projection of the rupture area for the eikonal source model. et al., 2005, 2007]. Kinematic models as well as the aftershock distribution support the identification of the northsouth striking plane as fault plane, in contrary of what is found here, using our standard approach. However, the rupture process is known to be quite complex for this event, with both Zahradnik et al. [2008] and Benetatos et al. [2007] suggesting a double event, with two subevents clearly separated in time and space by 40 km and 14 s. It is clear that such a rupture process cannot be simulated by means of a simple eikonal source model, what would explain the limit of our approach and its failure in this particular case, unless spatial and temporal discontinuities are smoothed through a proper filter. A second, manual inversion has been therefore carried out, using a more appropriate bandpass filter between 0.01 and 0.05 Hz, for the kinematic inversion. Results prefer now the NNE SSW fault plane, in agreement with the orientation of the Kefalonia fault. Additionally, we can predict the main rupturing direction, breaking along the fault plane NNE toward SSW, thus reproducing the effects of the two main events. The retrieval of a radius equal or larger than 21 km (upper radius), thus a rupture length of 42 km, would also fit with the extension of the smoothed double event. It remains open the important question on how to handle such cases, within an automated routine. One possibility for future approaches could be to include source time function estimation and its analysis to reveal complex rupture process, prior to the realization of the kinematic inversion Eastern Aegean Sea [28] On 10 April 2003, a Mw 5.7 earthquake occurred in the eastern Aegean (event 1). Two years later, in October 2005 a new seismic sequence struck the same area, with the two main events occurring on the 17 (Mw 5.7, event 10) and 20 October (Mw 5.8, event 12). All three earthquakes have been modeled here by strike slip focal mechanisms. Kinematic inversions could well identify the NE SW striking plane as the fault plane for all cases, although it was unable to stably retrieve the rupture size. The best solutions were found for radiuses of 14 km, which corresponds to the highest tested value; it is worth noting that excessive radius estimation, if this was the case here, would affect other parameters, leading to an excessive estimation of the rupture area and a subestimation of the average slip. The identified fault plane is consistent with the distribution of aftershocks for the 2005 events as observed by Benetatos et al. [2006], who associated the main seismic activity with the activation of dextral strike 15 of 24

16 Figure 9. Rupturing process resulting from kinematic inversion for the Greek region. Rupture process along the rupture areas for the selected earthquakes, showing the rupture geometry, the nucleation points, and the isochrones of the rupture front propagation (a complete plot legend is included). Solutions are grouped by epicentral regions (see Figure 8). slip faults. Bilateral rupture processes seems better fit data, with respect to unilateral models Northern Aegean Sea [29] The Mw 5.6 Gulf of Saros earthquake (event 2) occurred on 6 July 2003 offshore the NE coast of Gokceada Island, Turkey, in the Aegean Sea. A pure strike slip mechanism has been identified, with possible fault planes oriented WSW ENE and NNW SSE. Kinematic inversion prefers the fault plane with a strike angle of 252. Slightly large misfit can be improved by removal of most noisy traces, without significantly change the inversion result. The location and orientation of this fault plane would suggest its linkage with the eastern edge of the north branch of the North Anatolian fault, as suggested by Karabulut et al. [2006]. The centroid location is also consistent with this interpretation; inversion step 1b, in fact, shifts the centroid much to the north, with respect to the original location based on Global CMT catalog. Aftershock distribution and a detailed source model by Karabulut et al. [2006] give additional support to our fault plane identification. The rupture size (radius 14 km) seems to suffer to the typical ambiguity between rise and rupture time. Karabulut et al. [2006] modeled a slip patch of 10 km length for this event. However, the cloud of located epicenters of the seismic sequence elongates for about 25 km, a value which would be much more consistent with our extended source model. Finally, no directivity effects are revealed by the kinematic inversion, which prefers bilateral ruptures Peloponnesos [30] The Mw 6.2 and Mw 6.4 earthquakes (events 19, 20), occurred in SW and NW Peloponnesos, are strike slip earthquakes with planes oriented NW SE and SE NW. Kinematic inversion clearly prefer for both events the NE SW fault plane (see Table 3 for details). Directivity effects have been detected, indicating in both cases a rupture propagation toward NE. The rupture radius is resolved to 20 km (length about 40 km), corresponding to average slips of 6 7 cm. Two other major events (event 17 18, Mw ) occurred in SW Peloponnesos show a preference for low dip angle planes dipping toward NE. Results are not further discussed here, given the large misfits obtained during kinematic modeling. 5. Modeling of Local Earthquakes: Germany [31] The German data set consists of 21 earthquakes. Owing to the smaller magnitudes, fewer focal mechanism solutions are available for these events by regional moment tensor catalogs; these are provided by ETHZ and INGV RCMT. Magnitudes estimations range from Mw 3.4 to Mw 4.8, hypocentral depths from 4.0 to 24.0 km Point Source Inversion [32] A preliminary set of point source inversion tests with a reduced set of earthquakes allowed the identification of the 16 of 24