Zoltán Wéber

Seismic traveltime tomography: a simulated annealing approach

Abstract Seismic traveltime tomography involves finding a velocity model that minimizes the error energy between the measured and the theoretical traveltimes. When solving this nonlinear inverse problem, a local optimization technique can easily produce a solution for which the gradient of the error energy function vanishes, but the energy function itself does not take its global minimum. Other methods such as simulated annealing can be applied to such global optimization problems. The simulated annealing approach to seismic traveltime tomography described in this paper has been tested on synthetic as well as real seismic data. It is shown that unlike local methods, the convergence of the simulated annealing algorithm is independent of the initial model: even in cases of virtually no prior information, it is capable of producing reliable results. The method can provide a number of acceptable solutions. When prior information is sparse, the solution of the global optimization can be used as an input to a local optimization procedure, such as, e.g., simultaneous iterative reconstruction technique (SIRT), producing an even more accurate result.

Optimizing model parameterization in 2D linearized seismic traveltime tomography

Abstract In seismic traveltime tomography, a set of linearized equations is solved for the unknown slowness perturbations. The matrix of this set of equations (the tomographic matrix) is usually ill-conditioned, because the model space contains more details than can be resolved using the available data. The condition of the tomographic matrix can be characterized by its singular value spectrum: the larger the normalized singular values and the greater the rank of the matrix, the smaller the null space and the better the condition of the inversion problem. The structure of the tomographic matrix depends on the source–receiver configuration and the model parameterization. Since the source–receiver geometry is often fixed (e.g. in earthquake tomography), conditioning can only be influenced through the model parameterization, i.e. the structure of the model space. In this paper, we demonstrate a method for finding an optimal, irregular triangular cell parameterization that best suits the raypath geometry. We define a practical cost function, whose minimization is equivalent to the minimization of the null space of the tomographic matrix. Since the cost function depends on the model discretization in a highly nonlinear manner, a simulated annealing algorithm is used to find the optimal parameterization. We show that the cost value for the optimal triangulated model is about two times smaller than that for the regular gridded model with the same dimension, resulting in more accurate and reliable inversion results. The method is demonstrated through some cross–borehole tomographic examples with given acquisition geometries.

One-dimensional P-wave velocity model for the territory of Hungary from local earthquake data

We determined a new one-dimensional P-wave velocity model for the territory of Hungary based on the first arrival times of local earthquakes. During the computations 910 P-wave arrival data of 86 events from the time period between 1985 and 2010 have been used. The applied methodology is a combination of a genetic algorithm based procedure and an iterative linearized joint inversion technique. The preferred velocity profile has been chosen from the best models based on the data of a series of controlled explosions.The resulting flat-layered model consists of three crustal layers and a half-space representing the uppermost mantle. The crustal compressional velocities vary in the range of 5.3–6.3 km/s, while the uppermost mantle velocity was found to be 7.9 km/s. The Moho is located at an average depth of 26 km.Additionally, the Vp/Vs ratio was calculated by the Wadati-method, which gave a value of 1.74±0.05.

AlpArray in Hungary: temporary and permanent seismological networks in the transition zone between the Eastern Alps and the Pannonian basin

In the last few decades dense large-scale seismic networks showed their importance in studying the structure of the lithosphere and the upper mantle. The better understanding of the Apennines–Alps–Carpathian–Dinarides system is the main target of the AlpArray European international initiative in which more than 50 institutes are involved. The core of AlpArray is the AlpArray Seismic Network (AASN). With its

Probabilistic local waveform inversion for moment tensor and hypocentral location

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Estimating source time function and moment tensor from moment tensor rate functions by constrained L1 norm minimization

∼600 broadband seismic stations (

Source Properties of the 29 January 2011 ML 4.5 Oroszlány (Hungary) Mainshock and Its Aftershocks

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