Jiří Zahradník

Elastic finite-difference method for irregular grids

Finite‐difference (FD) modeling of complicated structures requires simple algorithms. This paper presents a new elastic FD method for spatially irregular grids that is simple and, at the same time, saves considerable memory and computing time. Features like faults, low‐velocity layers, cavities, and/or nonplanar surfaces are treated on a fine grid, while the remaining parts of the model are, with equal accuracy, represented on a coarse grid. No interpolation is needed between the fine and coarse parts due to the rectangular grid cells. Relatively abrupt transitions between the small and large grid steps produce no numerical artifacts in the present method. Planar or nonplanar free surfaces, including underground cavities, are treated in a way similar to internal grid points but with consideration of the zero‐valued elastic parameters and density outside the free surface (vacuum formalism). A theoretical proof that vacuum formalism fullfills the free‐surface conditions is given. Numerical validation is per...

Northwestern Turkey Earthquakes and the Crustal Structure Inferred from Surface Waves Observed in Western Greece

Records of several earthquakes occurring in Turkey in 1999 obtained at broadband seismic stations in western Greece have been used to study the dispersion of surface waves, mainly Love waves. The observed group-velocity dispersion curves have been inverted into horizontally layered models of the Earths crust by a modified method of the single-parameter variation. As compared with a previous model for the territory of Greece, the dispersion data require significantly lower velocities in the uppermost crust and smaller crustal thickness. In particular, the resulting model displays S -wave velocities between 1.3 and 2.4 km/sec in the upper 2 km and a crustal thickness of about 33 km. Manuscript received 31 July 2000.

Long-Period Pulses in Broadband Records of Near Earthquakes

Broadband records of weak local earthquakes occasionally exhibit long-period, pulselike signals, appearing exclusively on horizontal components. Such signals have been recorded at station Sergoula in the Corinth Gulf by Guralp CMG-3T (100-sec) and Wielandt-Streckeisen STS-2 (120-sec) instruments. The pulses can be perfectly matched by the instrumental responses to a small step of acceleration. Similar pulses, observed during moderate near earthquakes at stations of the Greek National Network equipped with Lennartz Le-3D/20s (20-sec) sensors, can be explained in the same way. Numerical simulation of the pulses allows their removal, thus making the records fully utilizable for waveform inversion in seismic source studies. Prerequisite for that is precise knowledge of the instrument transfer function. We found that poles and zeros of the CMG-3T and STS-2 sensors were consistent with those given by the manufacturer, whereas those of the LE-3D/20s were not. We identified the latter by inversion of spontaneous pulses incidentally appearing in LE-3D/20s records without relation to any earthquake. What actually generates the earthquake-related horizontal acceleration steps remains unclear. Rapid and permanently lasting tilt is a very likely candidate. When we numerically model a coseismic near-field static displacement, we actually find a tilt step, but its amplitude is several orders below the observed values. We therefore rather speculate that it is a very local tilt, triggered by high-frequency ground vibrations.

Hybrid seismic modeling based on discrete-wave number and finite-difference methods

Any calculation of seismic wave propagation comprising the seismic source, the travel path, and the receiver site in a single finite-difference (FD) model requires a considerable amount of computer time and memory. Moreover, the methods currently available for including point sources in the 2D FD calculations are far-field approximations only. Therefore we have developed a new hybrid method for treating the seismic wave fields at localized 2D near-surface structures embedded in a 1D background medium, and excited by a point source. The source radiation and propagation in the background model is solved by the discrete-wave number (DW) method, while the propagation in the local 2D structure is calculated by the FD method. The coupling between the two sets of calculations is performed on a rectangular excitation box surrounding the local structure. We show the usefulness of the method in ground-motion studies where both near-field source effects and local site effects are important. Technical problems connected with the inconsistency between the 3D source radiation and the 2D FD calculation are minor for the relatively distant in-plane point explosive sources, but are more serious for the in-plane dislocation sources.

Resolvability of isotropic component in regional seismic moment tensor inversion

We propose a new approach to resolve the isotropic component of the seismic moment tensor and its uncertainty. In linearized inversion problems, where the earthquake or explosive-source location and origin time are fixed (e.g., assumed to be known), the uncertainty of the moment tensor can be studied through the eigenvalues and the eigenvectors of the design matrix, which allows the representation of the theo- retical misfit by means of a 6D error ellipsoid. Because the design matrix depends only on the structural model and receiver source geometry, the analysis can be performed using recorded seismic waveforms, or without. In the nonlinear inversion problems, where the free parameters are eight (e.g., the six elements of the moment tensor, depth, and origin time), we propose a waveform-inversion scheme in which the trace of the moment tensor varies systematically and the remaining seven free parameters are opti- mized for each specific value of the trace. In this way, a 1D experimental probability density function of the moment tensor trace is constructed. To demonstrate the appli- cability of the method, we apply it to two shallow earthquakes (Mw 4.9 and 4.7) with epicenters close to the Columbo volcano, located 20 km northeast of the island of Santorini, Aegean Sea, Greece. We use 15 near-regional (60-310 km) records at frequencies below 0.1 Hz and two alternative crustal models. We conclude that the main uncertaintiesare attributed to the crustal modeland tothe trade-off betweenthe isotropic component and the source depth.

Robust finite-difference scheme for elastic waves on coarse grids

SummaryAn explicit scheme for 2-D problems of P-SV waves is proposed, 4th order accurate in space and 2nd order accurate in time. The elastodynamic equations are discretized without destroying their self-adjoint nature. Twenty—four effective parameters are introduced at every grid point that make the scheme sensitive enough to spatial variations of the actual Lamé parameters. The scheme is of the same form everywhere, including discontinuities. In particular, also the free surface is described without special formulas; the so-called vacuum formalism is developed. These features make the method simple and widely applicable. However, boundary conditions are only approximately satisfied. Nevertheless, comparisons with independent methods indicate satisfactory results. They include, for example, local Rayleigh waves and bidimensional resonances in basin-like models with strongly curved interfaces of a high velocity contrast (1 : 5), whose principal features were modelled by the present method well.

Seismic response analysis of two-dimensional absorbing structures

SummaryA computational method (based on finite differences) is proposed for the seismic response analysis of the Earths structures. The method is applied to the earth fill and the sedimentary basin. It was found that the lateral inhomogeneity of non-absorbing structures caused remarkable effects on synthetic seismograms, viz. strong “horizontal reflections” at later arrivals. In absorbing structures these effects are much less pronounced and the response is determined primarily by the variable thickness of the structures. The responses of structures with non-causal or causal absorption differ only slightly, but they are strongly influenced by the magnitude of the absorption itself.

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.

A recent deep earthquake doublet in light of long-term evolution of Nazca subduction

Earthquake faulting at ~600 km depth remains puzzling. Here we present a new kinematic interpretation of two Mw7.6 earthquakes of November 24, 2015. In contrast to teleseismic analysis of this doublet, we use regional seismic data providing robust two-point source models, further validated by regional back-projection and rupture-stop analysis. The doublet represents segmented rupture of a ∼30-year gap in a narrow, deep fault zone, fully consistent with the stress field derived from neighbouring 1976–2015 earthquakes. Seismic observations are interpreted using a geodynamic model of regional subduction, incorporating realistic rheology and major phase transitions, yielding a model slab that is nearly vertical in the deep-earthquake zone but stagnant below 660 km, consistent with tomographic imaging. Geodynamically modelled stresses match the seismically inferred stress field, where the steeply down-dip orientation of compressive stress axes at ∼600 km arises from combined viscous and buoyant forces resisting slab penetration into the lower mantle and deformation associated with slab buckling and stagnation. Observed fault-rupture geometry, demonstrated likelihood of seismic triggering, and high model temperatures in young subducted lithosphere, together favour nanometric crystallisation (and associated grain-boundary sliding) attending high-pressure dehydration as a likely seismogenic mechanism, unless a segment of much older lithosphere is present at depth.

Scisola: Automatic Moment Tensor Solution for SeisComP3

An automatic moment tensor is a significant product of regional seismic networks and an essential piece of information for real‐time seismological applications, like shake maps or tsunami warning. In this article, we present scisola, a new software for automatic moment tensor (MT) retrieval, based on the ISOLated Asperities (ISOLA) MT inversion code and SeisComP3 real‐time processing system. Scisola connects SeisComP3 with the ISOLA FORTRAN codes by retrieving event, station, waveform, and instrumental response data from SeisComP3 and passing the information to ISOLA. The Green’s function calculation and centroid spatiotemporal grid search are done in parallel mode in scisola, thus the computational time is significantly reduced. The user has full control of all calculation aspects, for example, frequency range of inversion and station selection through the creation of magnitude‐based rules. Scisola is programmed in Python and provides a complete graphical user interface (GUI) and a database for storing the results. The automatic solution is stored in the database, and the user is able to revise it through a GUI. The software provides a complete logging of processing steps, extended graphical output, a text file useful for e‐mail dissemination, and a handful of quality indexes of the solutions. The code’s performance was tested against manual MT solutions and proved to be efficient.