High-performance computer simulation of wave processes in geological media in seismic exploration

Abstract

A class of problems arising in seismic exploration are investigated, namely, seismic signal propagation in multilayered geological rock and near surface disturbance propagation in massive rock with heterogeneities, such as empty or filled fractures and cavities. Numerical solutions are obtained for wave propagation in such highly heterogeneous media, including those taking into account the plastic properties of the rock, which can be manifested near a seismic gap or a wellbore. All types of explosion generated elastic and elastoplastic waves and waves reflected from fractures and the bound aries of the integration domain are analyzed. The identification of waves in seismograms recorded with near surface receivers is addressed. The grid characteristic method is used on triangular, parallelepi pedal, and tetrahedral meshes with boundary conditions set on the rock-fracture interface and on free surfaces in explicit form. The numerical method proposed is suitable for the study of the interaction between seismic waves and heterogeneous inclusions, since it ensures the most correct design of com putational algorithms on the boundaries of the integration domain and at media interfaces. A parallel software code implemented with the help of OpenMP and MPI was used to execute computations on parallelepipedal and tetrahedral grids.

Lipschitz optimization methods for fitting a sum of damped sinusoids to a series of observations

“…The problem (i) is a classical problem and is important in spectral analysis (see, e. g., [18,22,46]) and many applications, such as magnetic resonance spectroscopy, radioastronomy, antenna theory, prospecting seismology, and so on (see, e. g., [10,33,29,46]). The problem (ii) with d =0 can be considered as a simple extension of the Fourier expansion and hence can be applied in many different fields (see, e. g., [2,15]).…”

Deterministic approaches for solving practical black-box global optimization problems

“…We look for such a value of x that best fits the numerically simulated response V y (x, d i , t j ) to a measured one. Computational simulation can be performed by some numerical integration algorithm: for example, the grid-characteristic method (see, e.g., [58,46]) can be used for this scope, thus taking into account the physical features of the problem and allowing one to set correctly the boundary and contact conditions. Hereby, this particular problem can be formulated as the following least squares optimization problem (see, e.g., [80,85,51,62,64,77]):…”

Modelling the wave phenomena in acoustic and elastic media with sharp variations of physical properties using the grid‐characteristic method

“…A novel approach to modelling wave phenomena based on the grid‐characteristic method (grid‐characteristic method (GCM); Magomedov and Kholodov, ) was developed in Petrov et al . (), Golubev, Petrov and Khokhlov (a,b), Muratov and Petrov (), Kvasov and Petrov () and Favorskaya et al . ().…”

“…A novel approach to modelling wave phenomena based on the grid-characteristic method (grid-characteristic method (GCM); Magomedov and Kholodov, 1988) was developed in Petrov et al (2013), Golubev, Petrov and Khokhlov (2013a,b), Muratov and Petrov (2013), Kvasov and Petrov (2012) and Favorskaya et al (2014). The GCM approach is based on a linear transformation of the original hyperbolic system of equations, describing the wave phenomena in acoustic or elastic media, into a system of transport equations, for which the solution at later time can be determined as a linear combination of the displaced at the certain spatial-step solutions at some previous time moment.…”