J. Zahradník

Iterative Deconvolution of Regional Waveforms and a Double-Event Interpretation of the 2003 Lefkada Earthquake, Greece

The moment tensor inversion for multiple point sources, based on Kikuchi and Kanamori (1991), was extended to full waveform data at regional (or local) distances. The new code proved to be efficient for retrieving major source contributions of the 2003 Lefkada, Greece, earthquake. The source model was derived from five three-component regional stations (epicentral distances <140 km), at periods 10–20 s. Two main events dominated the rupture process, one at the Lefkada Island (comprising three subevents of total moment 0.9 × 1018 N m) and the other at the Cephalonia Island (comprising one subevent of 0.5 × 1018 N m). Their spatial and temporal separation is 40 km and 14 s, respectively. They can be understood as two earthquakes. The uncertainty estimate based on reduced data sets (repeatedly excluding a station) shows that the Cephalonia subevent and the major Lefkada subevent are very well resolved regarding their position, time, and focal mechanism. The source model explains well the aftershock distribution, characterized by two clusters at the Lefkada and Cephalonia Islands, respectively. The focal mechanisms of the two main subevents are predominantly right-lateral strike slip of south-southwest–north-northeast orientation. The Cephalonia subevent occurred on a less steeply dipping fault with a small thrust component. Large deviations from pure double couple were found but interpreted as artifacts. The new software developed in this article (Fortran code and Matlab graphic user interface) is freely available. Online material: Color graphics and 3D visualization of the 2003 Lefkada earthquake sequence.

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.

The Athens Earthquake of 7 September 1999

Based on detailed aftershock monitoring, the first model of the Athens earthquake is formulated, which is consistent with global, regional, and local strong-motion data of the mainshock, and fits with geological setting. The 30-station temporary network located 450 aftershocks. During the first 20 observation days the aftershocks identified the mainshock fault plane dipping 52° and striking 117°, consistently with the teleseismic fault-plane solution. A formal upward continuation of the fault plane intersects the surface close to the Fili fault. Numerical modeling of the broadband regional data at 10 stations (epicentral distances 140 to 370 km) estimates the centroidal source depth of 10 km and yields an average source duration of 5 to 6 sec. The interstation variability of the apparent duration indicates source directivity. The empirical Green9s function modeling at the closest broadband station suggests a fault length of 20 or 10 km. Both the numerical and empirical modelings give a very short rise time of 0.1 to 0.3 sec. The short rise time seems to favor the nearly complete stress release of an asperity. A 10 km asperity (stress drop of 2.7 M Pa) is in agreement with a gap, identified during the first 12 observation days between two aftershock clusters. The strong-motion accelerograms in Athens also indicate a short apparent duration due to directivity (about 3 sec), and confirm an abrupt rupture beginning. There is no evidence for an abrupt stopping. The short rise time and short apparent source duration were two principal factors determining the damaging ground motions in Athens.

Focal Mechanisms of Weak Earthquakes from Amplitude Spectra and Polarities

Abstract — The ASPO method (Amplitude Spectra and POlarities) for the focal-mechanism retrieval from relatively weak events is based on a widely available instrumental setup: A few broadband stations within a denser short-period network. Collectively all stations provide the epicenter location. Complete records are taken from three-component broadband stations, without selecting a particular wave type, or picking amplitudes. It makes the method suitable for automated data processing, and enables studies of the interference crustal phases. Only the amplitudespectra are inverted. This is a robust feature which makes the method insensitive to any timing problems (such as those due to uncertain origin time, or due to technical failures). The first-motion polarities serve as an additional constraint of the amplitude-spectra inversion; only few (clear) polarities are taken from the nearest stations, wher e they mostly belong to direct P waves. The method seeks five parameters: The focal depth, scalar moment, strike, dip, and rake. Greens function, automatically including possible near-field effects and interference (e.g., surface) waves, is calculated by the discrete wavenumber method. ASPO works below the corner frequency, and the time function is not being retrieved. This feature not only minimizes the number of the inverted parameters, but also speeds up the calculation, because the lower the frequency, the faster the discrete wavenumber run. Instead of an exceedingly slow 5-parameter grid search, the inversion is organized in two steps: (i) the depth and moment determination with a coarse grid search of the strike, dip and rake, and (ii) a fine grid search of the three source angles. Uncertainty of the best-fitting solution is assessed from the minimum error value and from the scatter of the nodal lines (and/or P and T axes) between min and min + 10%. The method was tested on the clustered M ≈ 3.5 earthquakes recorded by a temporary network of three CMG3-T broadband stations in western Corinth Gulf. A fundamental problem is that the broadband stations suffer systematically from event-induced instabilities at horizontal components if earthquakes of the studied magnitudes occur at short distances, 10–30 km. Therefore, the ASPO method could not be applied below 0.1 Hz. As such, the results are sensitive with respect to unknown crustal structure details, and the focal mechanisms remain rather uncertain (minimum error higher than 0.34). Compared to synthetic tests with perturbed data, in which the error is lower than 0.2, it is concluded that the crustal model needs further improvement.

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).

Simple method for combined studies of macroseismic intensities and focal mechanisms

A simple method is presented for the computation of theoretical models of the macroseismic field, approximately valid close to the epicentre of a weak crustal earthquake. It is assumed that the intensity is logarithmically proportional to the energy flux of a complete directS wave. A circular source is used, whose energy-flux directivity is weak and thus simply predictable. The focal mechanism influences the solution through standard far-field double-couple radiation patterns. For the wave propagation in the layered crust the ray method is used, and a simple absorption correction is applied. Conversion coefficients at the earths surface are included. To speed up repeated computations of the theoretical macroseismic fields for varying focal mechanisms, the ray quantities are computed (and stored) separately. This makes the program fast and simple enough even for routine applications on small microcomputers, whenever observed macroseismic fields, focal mechanisms, and hypocentre locations need joint interpretation.

Finite-difference schemes for elastic waves based on the integration approach

The authors present a second order explicit finite‐difference scheme for elastic waves in 2-D nonhomogeneous media. These schemes are based on integrating the equations of motion and the stress‐free surface conditions across the discontinuities before discretizing them on a grid. As an alternative for the free‐surface treatment, a scheme using zero density above the surface is suggested. This scheme is first order and is shown to be a natural consequence of the integrated equations of motion and is called a vacuum formalism. These schemes remove instabilities encountered in earlier integration schemes. The consistency study reveals a close link between the vacuum formalism and the integrated/ discretized stress‐free condition, giving priority to the vacuum formalism when a material discontinuity reaches the free surface. The two presented free‐surface treatments coincide in the sense of the limit (grid size → 0) for lateral homogeneity at or near the free surface.

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.

From unstable to stable seismic modelling by finite-difference method

Abstract FD modelling of the two-dimensional P-SV seismic response is performed for the Volvi Lake sedimentary basin at EURO-SEISTEST site. The basin is 6 km long and 200 m deep. Viscoelastic linear rheology, with the attenuation described by Q proportional to frequency is used. The FD synthetics are accurate up to 4.6 Hz . This means 10 gridpoints per shortest S-wavelength corresponding to frequency of 4.6 Hz . The site is characterized by complex structure, with high velocity contrasts between individual blocks, ( v S = 2600 m/s)/( v S = 425 m/s); also the v p v s velocity ratio is up to 5. Numeric instabilities have been found at contacts between blocks with high and low v p v s ratios. A simple trick to stabilize the calculations for long FD runs (e.g. 20 000 time levels, or more) has been suggested. It consists of a special algorithmic treatment of the material discontinuities, preventing mixing of very large and very small values of the so-called effective material parameters within a grid cell. Appendix provides a comparison of the present FD method with an independent method for a model with non-planar topography and several v P v s ratios.

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.