V. Plicka

Detailed Waveform Inversion for Moment Tensors of M∼4 Events: Examples from the Corinth Gulf, Greece

Moment tensors (MTs) of weak events are often calculated by a single agency (network), thus lacking independent validation. This article investigates how to increase reliability of the single-agency solutions through various multiple checks. It deals with the inversion of complete waveforms for six representative events (Mw 3.4-4.6) in the range of 0.08-0.15 Hz. Several three-station sets at near-regional distances (8-103 km) are used. The MTs are repeatedly calculated for two independent locations: from a regional and local network. The source depth is held fixed at the hypocenter and also grid searched to optimize the waveform match. Initially, large variations (instability) of the MT solution with the approach we used were found for some events. Later, the difficulties were understood and the solutions stabilized. It led to practical recommendations on how to detect or even avoid problematic MT solutions. First, avoid MT solutions for a single fixed depth (hypocenter). Second, optimize MT solutions by the depth grid search below epicenter (or better) for at least two alternative epicenters. Third, carefully analyze: (i) any rapid variation of the so- lution, (ii) major misfit of the first-motion polarities, (iii) low double-couple percen- tage (often correlating with (ii)), (iv) low values of the min=max eigenvalue ratio, and (v) departures of the MT-preferred depth from the location-derived depth. The MT-preferred depths, hence also the focal mechanism, may be misleading due to data problems (e.g., long-period disturbances, clipping) hidden in the band-pass wave- forms. The location-derived depth may be especially wrong for very shallow earth- quakes if the crustal model is inadequate in its shallow part and/or near stations are lacking. On the other hand, near stations (<20 km) should not be used in the wave- form inversion together with distant stations; because of their large amplitudes, the inversion can be easily biased due to instrumental data errors and small location errors. Online Material: Color figures and waveform match.

Asperity break after 12 years: The Mw6.4 2015 Lefkada (Greece) earthquake

The Mw6.4 earthquake sequence of 2015 in western Greece is analyzed using seismic data. Multiple point source modeling, nonlinear slip patch, and linear slip inversions reveal a coherent rupture image with directivity toward the southwest and several moment release episodes, reflected in the complex aftershock distribution. The key feature is that the 2015 earthquake ruptured a strong asperity, which was left unbroken in between two large subevents of the Mw6.2 Lefkada doublet in 2003. This finding and the well-analyzed Cephalonia earthquake sequence of 2014 provide strong evidence of segmentation of the major dextral Cephalonia-Lefkada Transform Fault (CTF), being related to extensional duplex transform zones. We propose that the duplexes extend farther to the north and that the CTF runs parallel to the western coast of Lefkada and Cephalonia Islands, considerably closer to the inhabited islands than previously thought. Generally, this study demonstrates faulting complexity across short time scales (earthquake doublets) and long time scales (seismic gaps).

The eGf method for dissimilar focal mechanisms: the Athens 1999 earthquake

Abstract The empirical Greens function method (eGf) is innovated to examine the rupture nucleation and propagation during the disastrous Athens earthquake of September 7, 1999 (ML=5.4). Waveforms recorded at seven regional broadband stations are studied. One of the two strongest aftershocks (ML=4) was selected as the eGf, but its focal mechanism differs from the mainshock mechanism. Therefore, the paper suggests an innovation of the classical eGf method. The assumption of the similarity of the mainshock and aftershock focal mechanisms is relaxed as follows: the mainshock is modeled by an eGf-like method using synthetic weak events, computed by discrete wave number method (DW), two times, once with the focal mechanism of the mainshock and again with the assumed focal mechanism of the aftershock. These computations are used to determine the subset of the stations at which the disparate focal mechanism results in a (station-dependent) multiplicative factor only, with minimum waveform distortion. Real data from that station subset are then inverted as if the mainshock and aftershock mechanisms were the same. The eGf synthetics are produced for constant-velocity radial rupture propagation starting at 36 trial grid points, regularly distributed on the fault plane, and the grid point providing the best fit to the observed waveforms is assumed to be the nucleation point. Synthetic tests show that success of the method strongly depends on the exact knowledge of the mainshock true fault-plane orientation, but that is fairly well known from the aftershocks distribution in this case. The aftershock sequence suggests two possible sizes of the fault: a large fault (20×16 km along strike and dip, respectively) and a small fault (8×10 km) that fills in the gap identified during the first 12 observation days between two aftershock clusters. The eGf modeling does not resolve a preferred fault dimension. However, for both sizes, the method locates the nucleation point at the western part of the fault plane, thus clearly indicating the rupture propagation toward Athens.

Upper crustal structure of the western Corinth Gulf, greece, inferred from arrival times of the January 2010 earthquake sequence

The western part of the Corinth Gulf attracts attention due to its seismically active fault system and considerable seismic hazard. A moderate size earthquake occurred close to the town of Efpalio on January 18, 2010, followed by a sequence of smaller earthquakes. In the present paper we use this sequence to derive a local structural model for the region in the vicinity of Efpalio. The model is based on the minimization of traveltime residuals. In particular, we used arrival times from 51 selected events recorded on January 19 and 20 by at least 5 stations at epicentral distances less than about 25 km. A variant of the method of conjugate gradients has been used for this purpose. In comparison with several previous models, the new model is characterized by higher velocities to a depth of about 8 km. The velocity ratio in the model is vP / vS = 1.83. The hypocentres of the selected earthquakes lay at depths between about 5 and 9 km, but their distribution is rather irregular.

Earthquake location from P-arrival times only: problems and some solutions

Selected problems related to accurate hypocenter locations are discussed in the difficult case that only reliable P-wave readings are available. Near stations are usually only few, and often have a poor azimuthal coverage. As such, they are insufficient because the inversion is highly ill-posed, and the epicenter position strongly trades-off with depth. Thus more distant stations are also needed to obtain the correct epicenter. However, joint use of near and distant stations present another difficulty; it may yield a significantly incorrect depth estimate in case that the crustal model is not fully appropriate. In practice, the erroneous depth often remains unrecognized. An indication of the depth problem can be obtained by analyzing the travel-time residuals at individual stations. It is also useful to check fully independent depth estimates, for example those from the centroid-moment-tensor analysis. If the problematic crustal model is detected, and it is not easy to find a better one, the near- and distant station effects should be decoupled (a two-step location): the epicenter is calculated from all stations, kept fixed, and the source depth is grid-search beneath the epicenter by means of the near stations. The ideas are applied to the Mw 5.2 Efpalio (Western Greece) earthquake of January 18, 2010, and the following aftershock sequence.

The Patras earthquake (14 July 1993): relative roles of source, path and site effects

A damaging earthquake occurred on 14 July 1993 in Patras, Western Greece. The mainshock (local magnitude 5.1) was followed on the same day by two aftershocks of magnitudes 4.4 ML and 3.6 ML, respectively. The strong motion record of the mainshock is studied, based on the teleseismically determined seismic moment and focal mechanism. The Discrete Wavenumber (DW) and Empirical Greens Function (EGF) methods are used. The main conclusion is that the 1993 Patras mainshock had a complex S-wave group mainly due to structural (path and site) effect. However, some effects of the rupture stopping on the peak ground acceleration (0.2 g in the so-called S3 phase) cannot be ruled out. Two values of the source radius are suggested: R = 1.9 and 3.0 km. The strong motion record better agrees with R = 1.9 km. If the latter is true, the stress drop was of the order of 20 MPa, i.e., higher than often reported for comparable events in Western Greece. Regardless of the true source radius, the ratio of stress drops between the mainshock and aftershocks was about 1–2. The aftershock waveforms indicate significant lateral heterogeneities around Patras. Therefore, the ground-motion predictions of strong events in the area will remain highly non-unique until weak events from an immediate neighbourhood of the particular fault are recorded.

Ground motion modelling with a stochastically perturbed excitation

We present a new hybrid method combining deterministic and stochastic features. The aim is to describe the crustal propagation better than deterministic or stochastic methods can do separately. We start from the deterministic hybrid method based on Discrete- Wavenumber and Finite-Difference techniques (DW–FD). First we modify the DW–FD procedure by introducing topographical variations and a spatially varying Q factor. Then, to take into account effects due to small-scale heterogeneities of the crust, we add a stochastic noise (perturbation) to the deterministic signal propagated through the crust. The stochastic noise is constructed using a kind of Markov-like process generator with two physical constraints: to have the Brune spectrum, and to reproduce the spatial decay of coherence reported in literature for real sites. We have chosen a Markov-like technique because it allows us to get stochastic noise, with the given coherence spatial decay, directly in time domain. This new hybrid method is applied in a numerical test, the parameters of which approximate the case of the 12 June, 1995 Rome earthquake. It is found that the coherence decay with distance at the alluvial valley surface is slower than the prescribed coherence decay inside the bedrock.

Analysis of the source scanning algorithm with a new P-wave picker

We analyze the location of earthquakes in near regional networks using complete seismic records. The method is based on the source scanning algorithm (SSA) of Kao and Shan (2004), but similarly to Grigoli et al. (2013), seismograms are substituted by a P-wave picker trace. The picker traces in a network are repeatedly stacked using grid of trial source positions, and hypocenter is identified with the point providing the best stack (the largest brightness). The first innovation of this paper is a new picker, measuring the ratio of the summed absolute values of seismogram in the right and left part of a moving time window, the RPA/LPA picker. The brightness maps based on this picker are clearer than those based on the STA/LTA picker. The second innovation is a simple theoretical model of the brightness maps. It makes it easy to identify how individual stations contribute to form the brightness spot. It is shown on synthetic tests that the performance of the method depends on focal mechanism, progressively improving from normal to reverse and strike-slip events. The method is successfully applied to four events of different mechanisms and depths, recorded at different ranges of epicentral distance by either broad-band sensors or accelerographs. The events have been located close to previously published epicenters. The brightness maps provide an estimate of the relative uncertainty of the (non-linear) location problem. The uncertainty estimate is also applicable without measured arrival times, “without earthquakes”, thus useful when designing or upgrading seismic networks for better location performance.

Inverting full waveforms into 1D seismic velocity model of the upper crust by neighborhood algorithm - Corinth Gulf, Greece

We investigated inversion of full waveforms into formal 1D velocity models. ‘Formal’ means that the models are primarily intended to simulate complete seismograms close to real records, rather than to reflect the true crustal structure from the geological point of view. The method is demonstrated for a magnitude Mw 5.3 earthquake (centroid depth of 4.5 km), recorded at 8 three-component stations in the Corinth Gulf region, Greece, spanning the epicentral distance range from 15 to 102 km, and frequency range from 0.05 to 0.2 Hz. The forward problem was solved by the discrete wavenumber method, while the inversion was performed with the neighborhood algorithm. As such, not only the best-fit models, but also suites of the models almost equally well satisfying data were obtained. The best resolution was found in the topmost ∼10 km. Extensive testing of the model parametrization enabled identification of the most robust features of the solution. The P- and S-wave velocities are characterized by a strong increase with depth in the topmost ∼4–5 km. This part of the model can be approximated by a layer with constant velocity gradient. Compared to a previously existing model of the region, the satisfactory waveform match was extended from the maximum frequency of 0.1 Hz up to 0.2 Hz. This extension will improve calculation of the seismic source parameters in the region, e.g. determination of source time functions and slip distributions of potential future Mw > 6 events.

Generalized Source Model of the North Korea Tests 2009–2017

The 2017 North Korea test is analyzed together with the previous 2009–2016 tests, and a generalized source model is derived using waveform data. Data are represented by lowfrequency records of 11 broadband near-regional stations (epicentral distances 140–310 km), bandpassed from 0.03 to 0.09 Hz. The events feature a significant degree of similarity. Therefore, mean records can be calculated by averaging the five tests, using the cross-correlation shifts and amplitude scaling. The mean records are inverted for the full moment tensor in terms of its posterior probability density function. The meansource model reveals significant uncertainties and parameter tradeoffs, due to well-known resolution problems at shallow depths and long wavelengths. Nevertheless, the moment tensor is undoubtedly dominated by its nonshear parts, that is, the isotropic component, and compensated linear vector dipole (inclined ∼15° to the vertical). The source type is very close to an opening crack, consistent with existing physical models of explosive shallow sources, accompanied by material damage. The generalized source model presented here is new. It can be used as a prior, realistically constrained model, applicable in early discriminations between natural earthquakes and explosions at the test site. Users at any station (not involved in this study) could precompute template synthetics in their preferred frequency ranges and velocity models. If fitting with real data by a single-constant source scaling, a real-time indication of an explosion similar to the previous Democratic People’s Republic of Korea (DPRK) tests can be obtained. Electronic Supplement: Tables and figures illustrating details of the individual 2009–2017 tests and of the mean-source model.