Journal of South American Earth Sciences 88 (2018) 144–156

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Journal of South American Earth Sciences

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Low-parametric modeling of the 2015, MW 8.3 , T ∗ Celeste Bollinia,b, , Nora Sabbionea, Vladimir Plickac,Jiří Zahradníkc a Department of Seismology, FCAG, National University of La Plata, b Consejo Nacional de Investigaciones Científicas y Técnicas, CONICET, Argentina c Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic

ARTICLE INFO ABSTRACT

Keywords: The MW 8.3 (GCMT) Illapel megathrust earthquake is investigated. The objective is to find out which features of Illapel earthquake the previously published rupture scenarios can be resolved by using a regional strong-motion network (epi- Chile central distances 130–260 km) and source models with a few parameters only. Low-frequency waveforms Low-frequency modeling (< 0.05 Hz) at nine stations (Centro Sismológico Nacional, Chile) are subjected to modeling. Various re- Multiple-point source models presentations of the source are used: (i) multiple-point source models based either on iterative deconvolution or Empirical Green's functions simultaneous inversion of source pairs, (ii) models of circular and elliptical uniform-slip patches, employing Fault segmentation Rupture speed synthetic and empirical Green's functions, respectively. This variety of methods provides consistent results. The earthquake appears to be a segmented rupture progressing from an early (deep) moment release to a later (shallow) one, towards the northwest. The source models of slip-uniform patches synchronously suggest a low rupture speed of 1–2 km/s. Despite the different data sets and methods used in this study, the estimate of rupture speed is consistent with independent publications. As for ambiguity in literature regarding the depth and timing of the rupture, our paper clearly prefers the models including a ∼20–30 s delay of the shallow moment release compared to the initial deep one. The strong-motion data set and low-parametric models proved to be compe- titive with more sophisticated approaches like multi-parameter slip models using a variety of regional geo- physical observables. These results, together with the results from other studies for smaller events, show that strong-motion networks can be useful for studying rupture processes in a wide range of magnitudes, thus pro- moting the improvement of regional strong-motion networks in poorly instrumented regions.

1. Introduction and references therein) eighteen years after the MW 7.1, Punitaqui earthquake (Pardo et al., 2002). The Illapel earthquake caused 15 ca- Large attract attention because they cause loss of lives sualties, and 2440 houses were destroyed (ONEMI, 2015). The earth- and damage, but also because they reveal links between long- and quake also caused significant strong ground motions, ∼1 g at a distance short-term geodynamic processes, for example subduction and faulting. of 130 km from the epicenter (Suppl. of Melgar et al., 2016), and a In particular, megathrust events yield invaluable information about the with an 11-m runup (Melgar et al., 2016). These two effects spatial and temporal heterogeneity of the slab (such as seismic gaps, were most likely caused by a combined effect of rupturing a deep inter-seismic locking) as well as specific features of its co-seismic rup- (∼30 km) and shallow (∼15 km) slip patch, respectively, thus in- turing (slip segmentation). One of the fundamental questions is whether dicating an along-dip segmentation of the megathrust (Melgar et al., deep and shallow portions of the slab differ in their physical properties. 2016). For instance, why do these portions radiate seismic waves in different A large amount of data has been produced by the Illapel event. frequency ranges (Lay et al., 2012). Chile belongs to a few natural la- These data range from free oscillations of the globe (Zábranová and boratories in the world that are well suited for this kind of studies Matyska, 2016), via seismic records of various distances and frequency (Cisternas et al., 2005; Vigny et al., 2009). bands, to tide gauge tsunami records and geodetic data, such as GPS

The MW 8.3 (Illapel) earthquake occurred on September 16, 2015, and InSAR. in central Chile, filling-in the seismic gap (Vigny et al., 2009) Since the first rapid evaluations (SCARDEC solution and the USGS and releasing inter-seismic coupling of the region (Zhang et al., 2016, quick finite-fault model), it has been known that the earthquake source

∗ Corresponding author. Departamento de Sismología e Información Meteorológica, Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La Plata, Paseo del Bosque S/N, B1900FWA, , Argentina. E-mail addresses: [email protected] (C. Bollini), [email protected]ff.cuni.cz (J. Zahradník). https://doi.org/10.1016/j.jsames.2018.08.006 Received 16 September 2016; Received in revised form 1 June 2018; Accepted 7 August 2018 Available online 11 August 2018 0895-9811/ © 2018 Published by Elsevier Ltd. C. Bollini et al. Journal of South American Earth Sciences 88 (2018) 144–156 process lasted approximately 80–120 s. SCARDEC (Vallée et al., 2011; longitude −72° E (Fig. 1a). By comparison, seismic catalogs for the Vallée and Douet, 2016) is an automated near-real time technique for same region, range of magnitude and period of time but in the absence the rapid robust determination of large earthquake source parameters of a large earthquake, show a seismicity of about 10% of the seismicity from broadband teleseismic P and S waves, including the source-time recorded after a large earthquake like the Illapel one. functions. The USGS finite-fault model indicated a single major slip Relatively little attention has been paid to seismic source in- patch (∼150 × 50 km, slip ∼5 m) at a relatively shallow depth of vestigations with strong-motion acceleration data, freely accessible ∼10 km (GEOSCOPE, 2015; USGS, 2015). from Centro Sismológico Nacional (CSN, 2015), and also partially ac- The automated backprojection of IRIS teleseismic stations also in- cessible from Center for Engineering Strong Motion Data (CESMD, dicated a significant high-frequency radiation (∼1 Hz), produced 2018). Okuwaki et al. (2016) used a single strong-motion record (CO03 mainly at ∼30 s after origin time, from a spot situated ∼50 km towards station, peak-ground-acceleration of 0.98 g) to illustrate the onset of the the east of the epicenter, at a greater depth than the hypocenter (IRIS, second slip episode determined by the inversion of teleseismic records. 2015). This episode started ∼25 s after the origin time with a deep-seated Many papers have already been published about the Illapel earth- high-frequency radiation and continued as an up-dip rupture propa- quake (Di Giacomo et al., 2014; ISC, 2017). By combining seismic, gation (25–90 s), creating a shallow slip patch depleted in the high- tsunami and geodetic data sets, the published models agree in small frequency radiation. Melgar et al. (2016) included strong-motion ac- number of patches, for example one slip patch (Benavente et al., 2016; celerograms in their joint kinematic source inversion based on a large Heidarzadeh et al., 2016; Okuwaki et al., 2016; Tilmann et al., 2016; variety of data: high-rate GPS, tide gauge tsunami, strong-motion re- Zhang et al., 2016) or two patches (Li et al., 2016; Melgar et al., 2016; cords and interferograms from Sentinel-1A satellite. They inverted in- Ye et al., 2016), with a peak slip of ∼10 m. The backprojection analyses tegrated strong-motion acceleration, i.e. velocity, in frequency range (Melgar et al., 2016; Okuwaki et al., 2016; Tilmann et al., 2016; Ye from 0.02 to 0.5 Hz, basically fitting a normalized form of the signal at et al., 2016) synchronously confirm high-frequency radiation from a frequencies below ∼0.1 Hz. As shown in their resolution tests (shown deeper part of the Illapel fault zone. A common feature of the published in Fig. S4 of their supplementary material), strong-motion velocities models is a rupture speed of ∼2 km/s. themselves cannot resolve spatial details of the order of 30–50 km (cells According to Centro Sismológico Nacional (CSN), Universidad de of their checkerboard test) but rather complement the other data.

Chile, 2674 aftershocks of magnitude mL > 3 were recorded within 6 Although the above state-of-art review has identified several months after the event, extending about 100 km eastward of the trench, common features of the referenced papers, some aspects of the quan- at depths of less than 50 km (CSN, 2016). The aftershocks demonstrate titative source models, such as the position of the main slip patches, a gap ∼50 × 50 km, centered approximately at latitude −31° N and remain ambiguous. This means that the Illapel earthquake definitely

Fig. 1. The Illapel earthquake. Basic data and a typical waveform fit. a. The epicenters determined by USGS and CSN are shown by the yellow and red stars, respectively. The GCMT centroid is plotted by a red circle and red beachball. The aftershocks from the CSN catalog for a 6-month period and magnitude mL > 3 are shown by aquamarine circles. An aftershock gap surrounding the GCMT centroid is clearly visible. The blue beachball corresponds to the EGF aftershock. The white diamond represents the point of maximum beam power obtained by backprojection of Ye et al. (2016). This point matches very well the edge of the aftershock zone. The CSN stations equipped with strong-motion instruments and used in this paper are presented by green triangles. The black rectangle is the whole USGS grid used in their slip-distribution calculation. The green rectangle is a schematic representation of the USGS finite slip model (approximating the 4-m slip contour), while the locus of the major slip is shown by a small green square. The grid range employed in our multiple-point source modeling (orange rectangle) is also shown. The upper- left corner inset marks the location of the studied area on the map of South America. The upper-right corner inset shows that the position of the GCMT centroid agrees with the Slab 1.0 model (Hayes et al., 2012). The profile is E-W and passes through the GCMT centroid. Aftershocks are shown by aquamarine circles. b. The waveform match for all the stations obtained by iterative deconvolution for 0.01–0.02 Hz frequency range is shown. Strong-motion data was integrated to dis- placement prior the inversion and t = 0 s corresponds to the origin time of the event. The traces not included in the inversion due to instrumental disturbances are shown in gray. The blue numbers are the variance reduction for each station. The fitting was obtained with an overall value of VR = 0.68. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

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Table 1 Basic parameters for the September 16, 2015 Illapel earthquake. Hypocenter location by CSN, centroid determination by GCMT and finite fault model by USGS.

Hypocenter location Origin Time (UTC) Latitude (°N) Longitude (°E) Depth (km) Mw 22:54:31 −31.637 −71.741 23.3 8.4 Centroid parameters Centroid Time Latitude (°N) Longitude (°E) Depth (km) Mw Mo (Nm) Strike (°) Dip (°) Rake (°) DC (%) (UTC) 22:55:23 −31.130 −72.090 17 8.3 3.23 × 1021 7 19 109 93 Finite fault model Peak slip (∼8m) Moment rate function Latitude (°N) Longitude (°E) Depth (km) Distance from epicenter Maximum (Nm/s) Time of the max. Total duration (s) Main moment release (km) after OT (s) duration (s) −31.074 −72.218 5 60 7.2 × 1019 50 160 80 deserves more attention. Therefore, the objective of this paper is to time, being interested in a robust model of the source complexity, we develop low-parametric models of this earthquake, aiming to answer use the lowest frequencies enabling deterministic modeling specific questions like the following: (i) was most of the seismic mo- (0.01–0.05 Hz). To further validate the ISOLA MPS results, we also ment released in a single patch, and was this patch located close to the apply the empirical Green's function technique to calculate apparent surface and northwest of the epicenter, or also in a deeper patch si- source functions and invert them into finite source models composed of tuated closer to the epicenter (hence also closer to the locus of the high- slip-uniform elliptical patches. frequency radiation identified by the backprojection techniques), and At this point we observe that the data set used in this work and the (ii) if two patches represent a correct source model, then what was the objectives exposed above lead us to raise a more general objective: timing of the two moment-release episodes? Answering these kind of contributing to the assessment of the potential of regional strong-mo- questions is important because source studies, including better knowl- tion networks in terms of source studies. edge of the position and timing of subevents together with the focal The paper is structured as follows. First, in Section 2 we present the mechanisms, provide key information both for ground motion simula- basic parameters that characterize the Illapel earthquake. Then, in tions of future events and seismotectonic analysis. Sections 3 and 4 we characterize the data and modeling methods used To accomplish these goals, we are aware that multi-parameter slip- in our study. In Section 5 we apply the methods to gain an insight into distribution source models (Melgar et al., 2016; Tilmann et al., 2016) the source process. Finally, in Section 6 we compare our modeling re- are attractive since they may reveal important details of the rupture sults with those obtained by other authors, and confirm the results of process (mainly if resulting from a combination of various data types) those papers that indicated two moment-release episodes. like slip distribution and radiation patterns. On the other hand, complex models of various earthquakes differ from one another (Clévédé et al., 2. Basic parameters of the 2015 Illapel earthquake 2004), which applies even for synthetic blind inversion benchmarks of the Source Inversion Validation project (SIV, 2018). Fortunately, any Parameters of the Illapel earthquake are summarized in Table 1. source model can be decomposed into its stable and unstable parts Hypocenter locations by USGS and CSN are in good agreement, being (comprising singular vectors belonging to the so-called co-image and only 10 km from each other. Both are close to the coast, roughly 100 km null space, related to large and small singular values, respectively), and eastward of the trench. Because the CSN location includes regional it is only the co-image part of the model which is common to various distance records, we prefer the location from this agency. The Global studies of the same earthquake (Gallovič and Ampuero, 2015). The Centroid Moment Tensor (GCMT) solution (Dziewonski et al., 1981; main source complexities can be revealed even with very simple Ekström et al., 2012) is also shown in Fig. 1a. models, e.g. the models parametrized by two elliptic patches (Twardzik By observing the inset of Fig. 1a and the aftershock profiles pre- et al., 2012). sented in the technical report by Barrientos (2015), and also taking into The idea of low-parametric robust models of complex events was account that, in general, for megathrusts it is reasonable to suppose the first conceived by Vallée and Bouchon (2004). Even simpler than fault plane as the shallow dipping nodal plane of the focal mechanism, models consisting of slip patches are multiple-point source solutions. it is possible to assume that the strike, dip and rake in Table 1 corre- For example, a five-point representation was included in the Global spond to the fault plane of the event. CMT catalogue for the 2004, M 9.3, Sumatra earthquake (Ekström W The USGS finite-fault model has a single well-defined slip maximum et al., 2012) by using the analysis of Tsai et al. (2005). More recently, of 8 m at latitude −31.074° N, longitude −72.218° E, depth of 5 km, Duputel et al. (2012) and Meng et al. (2012) constructed a two-point i.e. ∼60 km northwest of the epicenter. The slip contour of ∼4 m (i.e. model of the 2012, M 8.6, Sumatra mainshock. Multiple-point source W half the maximum value) extends roughly ± 100 km northward and modeling at regional distances is one of the basic tools of ISOLA soft- southward from the epicenter, at depths that are shallower than 10 km. ware (Sokos and Zahradník, 2008, 2013; Zahradník and Sokos, 2018). This region is schematically shown in Fig. 1a. The moment-rate func- The software includes two main methods: iterative deconvolution and tion attains its maximum of 7.2 × 1019 Nm/s at ∼50 s after the origin joint inversion of source pairs (Zahradník and Sokos, 2014). ISOLA is an time. About 85% of the moment release occurred within the first ∼80 s, established code, so far applied to events ranging from micro- the total duration being ∼160 s. The time function by the SCARDEC earthquakes up to M > 7 megathrust events, e.g. M 7.6 in Costa W W method, already mentioned in Section 1, is shorter (of about 80 s). As Rica (Quintero et al., 2014) and M 7.1 in Chile (Hicks and Rietbrock, W such, at first glance, the earthquake appears to be characterized as 2015), also including intra-plate events (Dias et al., 2016) and an ap- predominantly rupturing along its strike, and in the up-dip direction. plication to the MW 9, Tokohu earthquake (Zahradník et al., 2011). Therefore, in this study we propose a low-parametric modeling as a suitable tool for the Illapel earthquake. Specifically, we apply ISOLA 3. Data multiple-point source (MPS) modeling. With the aim of obtaining some insight into the source complexity, we use near stations, i.e. the strong- Strong-motion acceleration records of the Illapel mainshock were motion records at epicentral distances of 130–260 km. At the same modeled in this paper. The nine stations that were used are shown in Fig. 1a. The epicentral distances range from 130 to 260 km. The stations

146 C. Bollini et al. Journal of South American Earth Sciences 88 (2018) 144–156 represent a part of the CSN collection from which those stations si- best-fit subevent is found and the corresponding synthetics are sub- tuated close to each other were eliminated. Some station components tracted from real data. Then, a second subevent is found, and so on. The with instrumental disturbances (Zahradník and Plešinger, 2005, 2010; application yields a single (best-fitting) set of subevents. In the iterative Vackář et al., 2015) were identified and excluded from modeling (gray deconvolution, as a rule, the first subevent (subevent 1, hereafter ab- traces in Fig. 1b). The data were downloaded from the CSN database breviated as S1) is the largest one, and then the subevent moments are (CSN, 2015), corrected for gain, aligned with the origin time, resampled systematically decreasing. At the same time, cumulative variance re- and integrated to velocity. Later, in the inversion process, the data were duction increases. The number of subevents is a user-fixed parameter further integrated (to displacement) by using various frequency ranges, and, in this paper, we stop the iterative deconvolution with n-th specified below. The same Butterworth 4th order causal filter was al- subevent if the cumulative variance reduction VR(n) for the first time ways applied both to the observed and synthetic data. reaches a value which is significantly greater than VR (1). The sig- In Section 4.3, the CSN records of an aftershock were also used. The nifi cance is evaluated statistically by the F-test. More details are de- aftershock was selected to satisfy the following criteria: to be located scribed in Section 5.1. The second method is newer and is known as the close to the mainshock, have a similar focal mechanism, and be re- Joint inversion of source pairs (Zahradník and Sokos, 2014). It is suitable corded at the same stations as the mainshock. We chose the event that if the studied earthquake is basically composed of one or two dominant occurred the same day as the mainshock: origin time 23:18:38 UTC, subevents. In this method a joint inversion is performed to obtain the latitude −31.602° N, longitude −71.646° E, and a depth of 35 km position and time functions of source pairs, assuming a given focal

(CSN), MW 7.1, strike 349°, dip 30° and rake 87° (GCMT). The Kagan mechanism of both members of each source pair, and a fixed total angle (Kagan, 1991) between the mainshock and this aftershock is small moment value. We systematically inspect all possible combinations of (14°). The location and focal mechanism of the EGF aftershock are two trial source positions on a grid and, for both members of the source shown in Fig. 1a. pair, we calculate the moment-rate function simultaneously. This function is modeled as a series of equally shifted elementary time 4. Methods and technical details functions whose relative weights are calculated by the non-negative least-squares (NNLS) method (Lawson and Hanson, 1974). The appli- Three different modeling attempts were performed to characterize cation yields a suite of subevent pairs, not only the best-fitting solution. the source process. As a first approach, we applied a multiple-point Below is a description of the technical details and additional data source modeling describing the rupture process as a sequence of points needed for the application of the MPS method. of moment release, called subevents. Then, we used a simple finite- source modeling with the aim of obtaining the basic parameters related 4.1.1. Velocity model to the geometry of the rupture, like the spatial extent, rupture velocity, The strong-motion data are inverted using a 1D velocity model. The stress drop, and mean slip. Finally, we tried a more sophisticated finite- model was provided by CSN, and it is relevant for the zone between source modeling to describe some other aspects of the rupture process latitude −26° N and −34° N (Pardo et al., 2002b). It is composed by 7 in more detail, like the slip distribution over the fault. The three homogeneous crustal layers, and 2 homogeneous layers and halfspace methods are described below, together with some other technical de- below the Moho, the latter being situated at a depth of 50 km. This tails. model was obtained by applying the VELEST method (Kissling et al., 1994) to 1041 events located with an RMS that is less than 0.25 s and 4.1. ISOLA multiple-point source (MPS) modeling by using data from a temporary local network in Chile and Argentina.

The point source contributions are called subevents, which re- 4.1.2. Frequency range present points of moment release. The moment tensors (MT) of sube- The usable frequency range is determined by the quality of the vents are inverted in full-MT mode (6 independent components, re- velocity model, and by the epicentral distances and noise. We made presenting an unconstrained mechanism), deviatoric-MT mode (a zero- several preliminary tests, and for our stations, which are at epicentral trace moment tensor), or DC-constrained mode (imposing the double distances of 130–260 km, we decided to use the frequency range of couple part to be close to 100%, representing a pure shear mechanism). 0.01–0.05 Hz and/or sub-ranges. The reasons of our choice are the Alternatively, 100% DC focal mechanisms of the subevents can be kept following: standard problem at low frequencies is the low S/N ratio, fixed (prescribed). The moment tensors are calculated by least-squares, mainly when using strong-motion accelerographs, whose intrinsic low- while the position and time of subevents are calculated by a spatio- frequency noise is always greater than in broad-band records. However, temporal grid search. The spatial grids are either linear or planar, and for the Illapel earthquake we can use frequencies as low as 0.01 Hz can be designed along horizontal planes or assumed fault planes. The because the event is large (ground motion is strong), so the S/N at these subevent moment-rate time function, also called elementary time low frequencies improves. At the same time, being aware that in- function, is supposed to be known (delta function, or a single triangle of accurate velocity models cause Green's function modeling errors (Halló a prescribed duration). Alternatively, the time function can be calcu- and Gallovič, 2016) which enable us to model just up to a few minimum lated from waveform data, assuming a known focal mechanism. Green's shear wavelengths (MSW), the upper frequency for inversion is de- functions, including near, intermediate and far-field terms, are calcu- termined by the maximum epicentral distance. By considering no more lated by the discrete wavenumber method (Bouchon, 1981; Coutant, than 4 MSW, for an epicentral distance of 260 km we are modeling 1990) by using a 1D velocity model (i.e. parallel layers with constant MSW of ∼60 km which, for a reference S-wave velocity of 3 km/s, parameters). Waveform agreement between the observed and synthetic corresponds to a frequency of 0.05 Hz. Considering both a characteristic data is quantified by the variance reduction (VR). The resolution of the source length of the entire earthquake of ∼200 km (Wells and moment tensor is expressed by the condition number (Sokos and Coppersmith, 1994) and typical slip patches of ∼50 km, we can Zahradník, 2013). MT uncertainty (including, for example, nodal lines roughly estimate that the MSW of 60 km is short enough to be sensitive and DC%) is computed from covariance matrix (Zahradník and to the overall source complexity (for example, to experience direc- Custódio, 2012). Inversion stability with respect to the space position tivity). At the same time, the MSW of 60 km is large enough to allow and time of subevents is tested by repeatedly removing stations, or modeling of each major ∼50 km patch as a point-source subevent. components (jackknifing). The resulting focal mechanisms are checked The multiple-point source modeling is also possible because the for their agreement with polarities. nearest stations are located at distances that are larger than the sube- Subevents are calculated by two methods. The first one, which is vent size (Table A1). We also considered an intermediate frequency standard, is the Iterative deconvolution (Kikuchi and Kanamori, 1991). A (0.02 Hz) to analyze the different multiple-points approaches according

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Fig. 2. Multiple-point source models. The models were calculated by iterative deconvolution in three frequency ranges (see headers), keeping the focal mechanism (GCMT) fixed. The subevents are shown by circles, color-coded according to their moment release time, while their radii scale with scalar moment. The black circle serves as the moment scale. The grid (orange rectangle in Fig. 1a) is represented by the trial sources (red diamonds) and their corresponding source numbers. The CSN epicenter and GCMT centroid are shown by red star and circle, respectively. The top panels are the inversions made with all stations, while the bottom panels show nine repeated inversions, each time eliminating one station (jackknifing). Three subevents (one 3-point source model) and 27 subevents (nine 3-point source models) are shown in the top and bottom panels, respectively. The significant number of subevents for each model is explained in the main text. On the left bottom panel, a 30–40 s separation between the early and late moment release episodes occurring in the bottom and top parts of the fault is clearly noticeable. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.) to variable frequency ranges. Thus, we considered three frequency 4.2. Equivalent uniform-patch (EUP) modeling ranges in our study: 0.01–0.02 Hz, 0.02–0.05 Hz and the full range 0.01–0.05 Hz. Although iterative deconvolution modeling assesses major rupture episodes in terms of subevent moments and times, it does not provide any information about the space extent (i.e. the geometrical size) of the 4.1.3. Elementary time function rupture. Therefore, the slip value remains undetermined, and so does Several elementary time functions of subevents were tested. We the stress drop. To remove this limitation, we suggest the concept of tried delta function and fixed-duration triangles with different lengths, uniform patch (a patch with homogeneous slip), representing the sim- observing that they just have little effect upon the results in the studied plest finite-fault model. The patch is an improved equivalent of a pre- frequency range. All the results are shown for 20-s elementary triangle viously identified MPS model. This method is a simplified version of the time functions, which is the shortest resolvable period for the maximum MuFEx method (Gallovič and Zahradník, 2012) and it was implemented frequency of 0.05 Hz. by using some codes from ISOLA. First, the position of the dominant subevent of the multiple-point source model is identified. Next, a circular patch is constructed, cen- 4.1.4. Grid of trial source points tered at this position. Radial rupture propagation with constant speed is The grid has been designed in a plane passing through GCMT cen- assumed to start at origin time in the hypocenter which, in general, may troid, at an average depth of 18 km and having a strike and dip cor- be situated inside or outside the patch. The model is parameterized by responding to the fault plane of the GCMT solution. Several grid sizes the patch radius and rupture velocity, and it is discretized (if a part of and spacings were tested. The results shown in Section 5 were obtained the circle falls out of the grid, that part is discarded). Green's functions by using a grid composed of 11 × 6 nodes with a step of 10 km along are calculated from every discrete point of the patch, and they are the strike and dip directions. Thus, the grid size is 100 km along the summed up with time shifts due to the assumed rupture propagation. strike and 50 km along the dip (Figs. 1a and 2). This sum is convolved with six elementary moment tensors. In this sense, the whole patch is formally represented by six elementary

148 C. Bollini et al. Journal of South American Earth Sciences 88 (2018) 144–156 seismograms (with unit scalar moment) like any single-point source in in the multiple-point model, we performed the standard statistical F-test standard ISOLA. Finally, also in ISOLA, we prescribe a fixed focal me- (for technical details of the application, we referred to Suppl. Text S5 of chanism and construct synthetic seismograms. Matching the synthetics Sokos et al., 2016) and, as a reference, we selected the 99% confidence with real seismograms provides both an optimized scalar moment of the level. The results in this frequency range, given in Table 2c, show that it patch and a time shift with respect to origin time. Repeated inversions is enough to add two subevents to S1 to obtain the simplest model with varying circle radii and rupture speeds enable optimization of reaching the 99% confidence (hereafter, 3-point model, Fig. 2, top left these parameters in terms of waveform fit. panel). The cumulative scalar moment of the 3-point model is approxi- 4.3. Two-patch finite-source EGF modeling mately one third of the GCMT value (Table 1), because our data do not have frequencies as low as those used in the GCMT solution (Quintero

This technique is based on the Empirical Green's Functions (EGFs), et al., 2014), i. e 0.002 Hz for MW >8(Ekström et al., 2012). representing a well-established seismological tool (Courboulex et al., The 3-point model (MW 8.0) explains the data with variance re- 1997; Plicka and Zahradník, 1998, 2002; Roumelioti et al., 2009). Its duction VR = 0.68 (Table 2a). The VR is an overall value of the wa- advantage is that velocity models and synthetic Green's functions are veform match and it was formally obtained taking into account all the not required. If a ‘strong’ event used as a target event and another stations and components, even those which were excluded from the ‘small’ event (called the EGF event) are recorded at the same stations, inversion because of instrumental disturbances (gray traces in Fig. 1b). the latter can substitute the synthetic Green's functions. The EGF event The variance reduction was also obtained for the individual compo- should have a similar focal mechanism as the target event. nents (blue numbers in Fig. 1b) and in some cases it was a negative The EGF is used to calculate the apparent source time functions value due mainly to slight shifts between synthetic and observed wa- (ASTFs) which describe the seismic moment rate released by the source. veforms. Nevertheless, those components were not excluded from the Due to directivity effects, the duration of the ASTFs varies from one inversion because we did not find any reason to remove them (no in- station to another according to the azimuth. The ASTFs are calculated strumental disturbances and good S/N). The time shifting may be a as explained in the appendix of Sokos et al. (2016): each ASTF is ex- consequence of the inaccuracies in the velocity model, which may be pressed as a weighted sum of identical, equally shifted isosceles trian- reflected in some stations more than in others. gles. The target record at each station is a linear combination of the A characteristic feature of the 3-point model is that, as time pro- convolutions between the EGF record and every triangle. The positive gresses, the subevents ‘move’ from the bottom of the grid towards the coefficients of this combination are calculated by the NNLS method for trench (updip) and towards the northwest. As validated by jackknifing each station, as cited above. In this paper, the ASTF is calculated in the (Fig. 2, bottom left panel), this important feature is robust, especially as frequency range of 0.03–0.5 Hz. This is a common interval (found by regards the up-dip temporal progression. However, the position of both trial and error) with a good S/N ratio for both the strong and weak the early (deep) and late (shallow) subevents is less certain in the strike event. direction. The total time function has a duration of 60 s with a max- Finally, the ASTFs are inverted into a model of two elliptical patches imum moment rate of 6.7 × 1019 Nm/s at a time of 50 s after origin of uniform slip (Vallée and Bouchon, 2004; Sokos et al., 2016). The time. model parameters are the following: (i) the position of the centers, the axes lengths, and the slip values of the two ellipses; (ii) constant speed 5.1.2. Sub-range of 0.02–0.05 Hz of rupture propagating radially from the hypocenter. If the two ellip- As in the previous case, the deviatoric inversion was unstable as tical patches partly overlap with each other, the slip in the overlapping regards the focal mechanisms of minor subevents. Thereafter, we fo- region is the sum of both. The inverse problem is non-linear, and the cused on the results with the fixed-mechanism inversion. In this fre- parameters are searched by the Neighborhood Algorithm (Sambridge, quency range, the subevent S1 had an even stronger dominance (Fig. 2, 1999). The algorithm provides not only the parameter set leading to the top center panel) than in the previous case, having a moment that is 3.5 best fit of the ASTFs, but also a family of so-called acceptable solutions times larger than the other subevents, compared to a 1.9 ratio seen fitting the ASTFs within a chosen limit. before (Table 2b). The subevent S1 is situated 10 km southward with Both the EUP and EGF modeling were performed using the same respect to the GCMT centroid. By applying the F-test (Table 2c) we velocity model and similar grids as those of the MPS modeling. found that the 99% confidence level is never reached, independently of how many events we added to S1. We interpret this result as a con- 5. Results sequence of the strong dominance of S1. Minor subevents just cause minor improvement of the waveform fit and thus they formally increase 5.1. Inversion by iterative deconvolution the VR (Table 2a).

Therefore, we claim a single-point model (MW 7.5) that fits the data All the inversions were carried out by prescribing a number of six with VR = 0.50 as a result for this frequency range. The jackknifing subevents, and in all the cases the last three subevents proved to be results are shown in Fig. 2, bottom center panel. The time function has a insignificant with respect to both the seismic moment and the im- duration of 90s (its main part is 30-s long) with a maximum moment provement of waveform fit. For this reason, Fig. 2 and Table 2 show rate of 2.2 × 1019 Nm/s at time of 40 s. results for the first three subevents. 5.1.3. Range of 0.01–0.05 Hz 5.1.1. Sub-range of 0.01–0.02 Hz In the whole frequency range, the inversion with the GCMT fixed The deviatoric inversion in this range provided a dominant subevent mechanism did not yield any dominant subevent (Fig. 2, top right

(S1) of MW 7.9 at a distance of approximately 15 km southward from panel), providing the moments of the first three subevents in the same the GCMT centroid. Its mechanism was similar to the GCMT. However, order of magnitude. The waveform match was characterized by lower the free focal mechanisms of the following subevents featured a dra- VR values than in the previous cases (Table 2a), therefore being less matic variation (Kagan angle > 42°), thus indicating that they are very reliable. Also, the F-test never reached the 99% confidence level poorly constrained. Therefore, we repeated the inversion with focal (Table 2c). mechanisms fixed at the GCMT strike, dip and rake values. The posi- tion, size and timing of the three largest subevents were found similar 5.2. Joint inversion of source pairs by NNLS method to the free deviatoric case, hence indicating that these are stable fea- tures of the inversion. To determine how many subevents are required In the frequency range of 0.02–0.05 Hz we found that the MPS

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Table 2 Multiple-point source model, iterative deconvolution, GCMT mechanism. Models with a variable number of subevents (1–3) are compared in three frequency ranges. a. Cumulative variance reduction, VR(n). b. Dominance of S1 with respect to the other subevents.c.Confidence level (CL), calculated by the F-test. Parameter n in all sub-tables shows the number of considered subevents (e.g. n = 2 means that we consider the first two subevents, S1 + S2). The model that is significant at 99% level and the simplest in terms of the number of subevents is shown in bold.

a

Frequency range (Hz) VR(n)

n=1 n=2 n=3 0.01–0.02 0.44 0.53 0.68 0.02–0.05 0.50 0.55 0.59 0.01–0.05 0.21 0.30 0.37

b

Frequency range (Hz) Mo (1)/M’ (a)

0.01–0.02 1.9 0.02–0.05 3.5 0.01–0.05 1.3

c

Frequency range (Hz) Confidence level, CL(n) (%) (b)

n=2 n=3 0.01–0.02 80 99 0.02–0.05 65 80 0.01–0.05 75 85 a M′ is the maximum moment among subevents 2 and 3, thus Mo (1)/M′ is a measure of the dominance of S1. b Confidence level CL(n) refers to the improvement of the waveform fit when comparing cumulative variance reduction of n subevents, VR(n), with the variance reduction of the first subevent, VR (1). inversion is characterized by a single dominant subevent. Since the find an appropriate rupture velocity Vr, we assumed that the source dominance may be artificially enhanced by the iterative deconvolution duration is close to 60 s, as obtained in Section 5.1 for the 3-point method, as shown in Zahradník and Sokos (2014), we also performed source model, and we tested several values of the patch radius R and Vr the inversion by means of an independent NNLS technique. Pairs of by providing the 60-s duration. We found that, for the radius R = 50 km sources (S1 and S2) were searched simultaneously, which is generally (Fig. 4a) and rupture velocity Vr = 2 km/s, we fit the waveforms with better than the consecutive iterative deconvolution. The focal me- VR = 0.77 (variance reduction was calculated as in Section 5.1). The chanism and the total moment was constrained to the GCMT values, waveform fitting provided the moment-rate peak of 5.5 × 1019 Nm/s at 21 and time functions were calculated by using 20-s elementary triangles, time 45 s and the total moment of Mo = 2 × 10 Nm (MW 8.2) separated from each other by 10 s. The maximum waveform fit was (Fig. 4b). These values are in good agreement with the USGS finite-fault 19 VRopt = 0.55. This value is relatively low due to a formal reason: it model (moment-rate peak of 7.2 × 10 Nm/s at 50 s, MW 8.3). This includes all the components, even those excluded from the inversion, as model is equivalent to a uniform slip of 5.6 m and stress drop of 7 MPa. was explained in the previous Section. All the solutions in the interval between 0.95 VRopt and VRopt are shown in Fig. 3a. In 75% of the solutions, the moment ratio of both sources in a pair is between 0.5 and 5.4. EGF inversion of elliptical patches 2. Hence, as expected, this technique prevents the strong dominance of fi the first subevent previously observed in the iterative deconvolution. By using the aftershock speci ed in Section 3, the apparent source This result shows that, in this frequency range, the iterative deconvo- time functions (ASTFs) were derived as shown in Fig. 5a. The inversion – lution biased the results. Therefore, the NNLS is a more reliable method was performed in the frequency range of 0.03 0.5 Hz. Since an inver- in this frequency range. Fig. 3a shows that although the solution is non- sion based on similar ASTFs from two mutually near stations would be unique, most of the pairs provided the same robust feature: an early equivalent to an inversion from a single station with a doubled weight, event occurs in the bottom part of the fault, later followed by another we removed the stations C09O and C11O due to their proximity to event of comparable size in the top part. This indicates evolution of the C01O and CO03, respectively. Moreover, C11O mainshock was not moment release upward and towards the northwest. This scenario is available in NS component. similar to that obtained with iterative deconvolution in the frequency The azimuthal coverage is limited due to the lack of stations in the range of 0.01–0.02 Hz. As an example, the time functions for a selected west. Thus, our inference about source directivity cannot be very point-source pair (Fig. 3b) are presented in Fig. 3c. strong. Nevertheless, Fig. 5a shows some variability of the ASTF dura- tion and amplitude. In particular, the northern stations C01O and CO03 are characterized by a short duration and large amplitude, indicating a 5.3. Inversion by equivalent uniform-patch method (EUP) northward rupture process. This is supported by the longest duration of ASTF at the southern MT05 station. We applied this method in the frequency range of 0.01–0.02 Hz to The ASTFs were inverted into 75250 models of two elliptical pat- estimate the space extent and rupture velocity of a single circular patch ches. The result is presented for the models whose variance reduction equivalent to the 3-point model of Section 5.1. The results are shown in was between 0.95 VRopt and VRopt (30 two-ellipse models), where Fig. 4. The patch was centered at the largest subevent of that model. To VRopt = 0.86 is the optimum value for the variance reduction. Two

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Fig. 3. Two-point source models. The models were calculated by a joint inversion of the source pairs (NNLS method) in the frequency range of 0.02–0.05 Hz. The total moment of each model is constrained by the GCMT value.a.An assembly of all the source-pair models fitting the waveforms within a prescribed limit (the so- called acceptable models, as explained in the main text). For the grid and subevent's color and size coding, see Fig. 2. Although the solution is non-unique, most of the pairs are characterized by an early event in the bottom part of the fault (blue), and the late event in the top part (pink), respectively. The CSN epicenter is shown by a red star. The result indicates the evolution of the moment release upward from hypocenter and towards the northwest. b. An example of a single solution corre- sponding to a source pair (6,39); the numbers refer to the grid points. c. An example of the moment-rate time function of the selected source pair (6,39); the blue-dot dashed line and green-dotted line correspond to the early (deep) source 39 and the late (shallow) source 6, respectively. Note the almost same moment of both subevents (same area under the curves), while the shallower source is 20–30 s delayed with respect to the deeper one. The total moment-rate time function of that pair is plotted with the red-solid line. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

151 C. Bollini et al. Journal of South American Earth Sciences 88 (2018) 144–156

representations were used. The best-fit model of two ellipses is shown in Fig. 5b, while the mean of the 30 models is plotted in Fig. 5c. All 2- patch models are similar: each one consists of an almost circular patch (slip 2–8 m) and an elongated patch. The elongated patches were less stable as regards their slip (1–15 m) and, in the mean of the 30 models, they produced an unrealistic extension of the source along its strike, with slip values below 4.5 m which is half the maximum slip. That is why, in Fig. 5c, the most reliable result is the mean slip above 4.5 m. The almost circular patches are similar to the EUP circular model. Rupture speed varies between 1.5 and 2.0 km/s, the best-fitting solution being Vr = 1.6 km/s.

6. Discussion and conclusion

A summary of the results is given in Table 3 and Fig. 5b–c. In the 0.01–0.02 Hz frequency range, the Illapel earthquake analyzed by iterative deconvolution appears to be well modeled as a 3-point source. This model is characterized by a dominant subevent (S1), close to the GCMT centroid, situated in-between the early (deep) and later (shallow) loci of the moment release, with time progression in the updip direction and, slightly less clearly, toward the northwest. An equivalent representation of the source by a single circular patch of uniform slip yields a mean slip of 5.6 m, a stress drop of approximately

7 MPa, and a rupture speed of 2 km/s. This model (MW 8.2) only slightly underestimates the GCMT magnitude (MW 8.3), and the moment-rate function agrees very well with the USGS finite-fault model (peak of 5.5 and 7.2 × 1019 Nm/s, at 45 and 50 s, respectively). At slightly higher frequencies (0.02–0.05 Hz), iterative deconvolution has revealed just the dominant subevent (S1). However, a joint inversion of the source pairs has shown that even in these frequency ranges, we may detect a similar temporal rupture progression as before (i.e. an initial deep-se- ated episode followed after ∼30 s by a shallow one) while the two episodes may have released a comparable amount of seismic moment. By using the EGF method, in which apparent source time functions are inverted into models of two slip-uniform elliptical patches, we have confirmed the position of the main slip region and validated the low rupture speed (1.5–2.0 km/s). As regards the frequencies used in this paper, it is necessary to in- crease the frequency range analyzed here if we wish to obtain models with higher resolution, for which it is also essential to combine diverse observations (Melgar and Bock, 2015) like most of the studies cited in Section 1. Nevertheless, the frequencies used in this work proved to be enough to retrieve the gross features of the rupture process. The lowest frequency range provided a model in which the largest subevent basi- cally represents the centroid. By slightly increasing the frequency range we were able to describe the source as composed of two points of comparable moment release. Both models reflect the progression of the rupture. Also, the area of main slip and rupture velocity is in good Fig. 4. Equivalent uniform patch. The model was obtained through the EUP agreement for both finite-fault models. method, by fitting waveforms (VR = 0.77) in the range of 0.01–0.02 Hz, while To compare these results with published ones, we have focused on keeping the focal mechanisms (GCMT) fixed. The used grid has increments of the most comprehensive papers by Melgar et al. (2016) and Ye et al. 20 km along the strike and dip. a. The black dotted-dashed line represents the ff 50-km-radius circular patch, centered at the grid point corresponding to S1. The (2016). Despite the di erent data sets and methods described in these 21 papers, our estimate of the rupture speed is consistent with these in- patch is characterized by a moment of 2 × 10 Nm, MW 8.2, uniform slip of 5.6 m, and constant rupture speed of Vr = 2 km/s. The patch correctly matches dependent studies (and also with other studies, cited in Section 1). the aftershock gap. The CSN epicenter and GCMT centroid are shown by red Moreover, as shown in Fig. 5c, the main slip region identified by our star and circle, respectively. The green square corresponds to the maximum slip methods overlaps the significant slip contours of both papers. While the of the USGS finite-fault model, and the white diamond corresponds to the point slip inversion of Ye et al. (2016) is characterized by a single patch, of maximum beam power obtained by backprojection in Ye et al. (2016). b. Melgar et al. (2016) reported two major slip episodes, which evolved at Moment-rate time function obtained by superimposing 20-s elementary trian- 30–50 s after origin time, and at 50–70 s, respectively. Our results (both gles of the 21 involved grid points of the fault corresponding to the patch model in Fig. 5b–c) have confirmed the latter space-temporal evolution of the shown in panel a. The value t = 0 s correspond to the origin time of the event. source process, including the same ∼30 s delay of the shallow moment- This time function has duration of ∼60 s with the maximum value at 45 s, being release episode compared to the deep one. in good agreement with the USGS finite-fault model (maximum moment rate of 7.2 × 1019 Nm/s at about 50 s after the origin time and 85% of the moment Therefore, we have answered the two main questions formulated in release occurred within the first ∼80 s). (For interpretation of the references to Section 1: the Illapel earthquake appears to have ruptured not only the color in this figure legend, the reader is referred to the Web version of this deep-seated segment, revealed by Ye at al. (2016), or the relatively article.) shallow segment reported in the USGS finite-fault model. The event

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(caption on next page) rather might have included both segments and progressed in time from of historical earthquakes along the central Chile subduction zone (Beck the deep patch to the shallow one, as also indicated by Melgar et al. et al., 1998). This work suggests that the zone between −29 and −32° (2016). Generally, the rupture propagated with a relatively low rupture N has a very heterogeneous style of faulting, and this portion of the speed. This scenario appears to be consistent with the results of a study plate boundary may consist of small to moderate-size asperities that can

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Fig. 5. Elliptical patch modeling and comparisons. a. Apparent source time functions (ASTFs) obtained by the Empirical Green's Function method (black) and their approximation calculated with the best two-patch slip model (red). b. The dashed ellipses represent the best-fit EGF model. The small colored circles are the MPS solution copied from Fig. 2 (top left panel). The dot-dashed circle is the circular uniform patch model copied from Fig. 4a. The GCMT centroid is plotted by a red dot, and the CSN epicenter by a red star. c. The colored background plot is the distribution of the mean slip in the EGF models whose waveform fit is within a prescribed limit. The most reliable result is the slip distribution above 4.5 m (i.e. half of the maximum slip) due to the less stability of the EGF elongated patches as regards their slip. The dot-dashed circular uniform patch model is copied from Fig. 4a. Solutions by other authors are also included in order to make a comparison. The thin and thick black irregular curves are contours of the maximum slip (∼7 m) from Melgar et al. (2016) and Ye et al. (2016), respectively. The green rectangle and the small green square represent the USGS finite model, as in Fig. 1a. The GCMT centroid is plotted by a red dot, and the CSN epicenter by red star. Panels b and c also include a white diamond representing the point of maximum beam power obtained by the backprojection of Ye et al. (2016). The key point is that our low- parametric models, obtained with a few regional strong-motion stations, are in reasonable agreement with the other, more complex studies. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

Table 3 Summary of the results of the present paper by using four methods and three different frequency ranges.

Method Freq. range (Hz) Source model MW VR Slip (m) Rupture speed (km/s) Source duration (s) Time of peak moment rate (s)

ID 0.01–0.02 3-points 8.0 0.68 –– 60 50 EUP 0.01–0.02 Single circular patch 8.2 0.77 5.6 2 60 45 NNLS 0.02–0.05 2-points 8.3 (fixed) 0.55 –– 80 40 EGF 0.03–0.5 (a) Two elliptical patches 8.3 (fixed) 0.86 8.6 (b) 1.6 ––

a The range used in the calculation of apparent source time function. b Maximum slip value of the mean model in Fig. 5c. fail individually as single earthquakes or together, generating earth- Through MPS modeling Hicks and Rietbrock (2015) found that the quakes like, for example, the Ms 8.3, 1922, which was characterized by 2011, MW 7.1, Araucania earthquake, which was reported as a single a multiple asperity type rupture. event in global moment tensor solutions, was instead composed of two Besides low-frequency slip inversions, the cited papers included ruptures on two separate faults. Sokos et al. (2016) studied the 2015, high-frequency (0.5–2.0 Hz) back-projections of teleseismic data. For MW 6.4, Lefkada earthquake by using both the MPS and EGF modeling example, Ye et al. (2016) have identified a localized emitter of the in- to determine the complex rupture propagation and slip distribution. tense radiation from the deepest part of the fault, at approximately By considering the results achieved in this work together with the 50 km northeast of the epicenter. This locus, which is close to the cir- applications of the methods cited above, we can return to the more cumference of our EUP circular patch, might correspond to a high- general objective stated in Section 1 and claim that a strong-motion frequency emitter associated with the presence of a barrier, re- network can be useful on its own for studying rupture processes in a presenting an edge of the rupture area. Barriers are zones where the wide range of magnitudes. It is particularly interesting for moderate rupture process abruptly stops, and the so-called stopping phases are magnitude (MW < 6.5) earthquakes which do not have finite-fault generated. These phases are rich in high frequencies due to the sudden models from international agencies like the USGS, highlighting the change of the slip velocity on the fault (Madariaga, 1977; Bernard and need of independent studies. It is possible that, for smaller events (e.g

Madariaga, 1984). We believe that the circular patch model is legit- MW 5), the finite-fault models like the EUP and EGF will fail, but the imate, although it is the simplest finite-extent model, because this patch MPS solution might indicate some source multiplicity in a robust way. well agrees both with the main slip region depicted by the EGF method These results represent a strong motivation for improving regional and with the gap in the aftershock distribution (Figs. 4a, 5b and 5c). strong-motion networks in those parts of the world lacking in dense The previous papers published soon after the earthquake did not have instrumentation. For the purposes of illustration, in the southernmost the complete aftershock catalog, which was later released by CSN and region of South America the instrumentation is developing. This region which is also showed here, so they could not point out the obvious has a history of big events like the 1949, MW 7.8, Punta Arenas relation between the aftershock gap and the slip pattern. We should also earthquakes (Sabbione et al., 2007 and references therein), thus being mention that the position of the back-projection emitter is close to the in a moderate seismic hazard zone (Leyton, 2016). Given the low cost of relatively sharp termination of the aftershock distribution in the down- accelerometers compared to broadband sensors, the results presented dip direction. here are motivating for increasing the deployment of these instruments In summary, we can state that by using limited data (9 strong-mo- as part of less dense regional broadband networks. tion records at regional distances) and low-parametric models (3-point MPS models, 2-point NNLS models, a single uniform slip patch, and 2- elliptical patch models) we have been able to retrieve the same gross Acknowledgments features of the rupture process for a big event as in the independent papers, which were based on more abundant data and multi-parameter The authors thank to Centro Sismológico Nacional, Chile, for inversions. By gross features we mean the position of the main rupture making freely available their strong-motion records and for providing area, the dominant direction of rupture propagation, and the rupture the velocity model and the aftershocks catalog. The authors also wish to velocity. In particular, the segmentation of the source process into the thank Efthimios Sokos for his technical help. The figures were created early (deep) and later (shallow) episodes, indicated at low frequencies using Generic Mapping Tools. One of the authors (J.Z.) was supported in some of the published papers, has been unanimously detected. by the Czech Science Foundation, grant GACR-14-04372S during the At this point it is worth mentioning that some of the methods ap- first submission, and GACR-18-06716J during the revision, while V.P. plied here work well also for smaller events. Gallovič and Zahradník was supported by CzechGeo/EPOS (LM2015079). This research has (2012) used the MPS modeling and strong motion data to estimate the resulted from the stay of the first author (C.B.) at Charles University, size and extension of subsources within the rupture zone of the 2009, Prague, within the Scholarship Programme under a bilateral interna-

MW 6.3, L'Aquila earthquake. Quintero et al. (2014) fitted strong mo- tional agreement between the Ministry of Education of Argentina and tion data for a MPS modeling of the 2012, MW 7.6, Nicoya earthquake. Ministry of Education, Youth and Sports of the Czech Republic.

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Appendix

Table A1 Stations used in this work and epicentral distances with respect to the mainshock.

Station name Latitude (°N) Longitude (°E) Epicentral dist. (km)

C11O −30.696 −70.959 128 CO03 −30.834 −70.689 137 VA01 −33.023 −71.637 164 VA03 −32.764 −70.551 183 C01O −29.877 −71.238 195 MT05 −33.392 −70.738 230 VA05 −33.657 −71.614 234 C09O −29.510 71.200 234 MT09 −33.776 −70.989 260

Table A2 List of used acronyms

Acronym Explanation

ASTF Apparent source time function CSN Centro Sismológico Nacional DC Double couple EGF Empirical Green Function (method) EUP Equivalent Uniform Patch (method) GCMT Global Centroid Moment Tensor IRIS Incorporated Research Institutions for Seismology MPS Multiple-point source (method) MSW Minimum shear wavelength MT Moment tensor NNLS Non-negative least-squares (method) S1 Subevent 1 S/N Signal to noise ratio USGS United States Geological Survey VR Variance reduction

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