N. I. Khokhlov

Numerical simulation of seismic activity by the grid-characteristic method

Seismic activity in homogeneous and layered enclosing rock masses is studied. A numerical mechanical-mathematical model of a hypocenter is proposed that describes the whole range of elastic perturbations propagating from the hypocenter. Synthetic beachball plots computed for various fault plane orientations are compared with the analytical solution in the case of homogeneous rock. A detailed analysis of wave patterns and synthetic seismograms is performed to compare seismic activities in homogeneous and layered enclosing rock masses. The influence exerted by individual components of a seismic perturbation on the stability of quarry walls is analyzed. The grid-characteristic method is used on three-dimensional parallelepipedal and curvilinear structured grids with boundary conditions set on the boundaries of the integration domain and with well-defined contact conditions specified in explicit form.

Monitoring the State of the Moving Train by Use of High Performance Systems and Modern Computation Methods

The objective of this work has been to study the propagation of elastic waves in rails. It presents the comparison of calculations obtained by the grid-characteristic and discontinuous Galerkin methods. The propagation of elastic waves in the presence and absence of the karst inclusion in the ground under the embankment, diagnosed in these cases from the rails, are compared. The wave pictures and diagnosed signals for four types of defects of a fractured character: vertical and horizontal head layering, cross fracture in the head and cracks in the rail web are given. The grid-characteristic method on the curvilinear structural meshes and the discontinuous Galerkin method on the nonstructured triangular meshes make it possible to solve efficiently the tasks on monitoring the state of the moving train and rail, including a great number of integrity violations, dynamic interactions in the train-rail system, and obtain the full wave picture.

Numerical computation of wave propagation in fractured media by applying the grid-characteristic method on hexahedral meshes

Wave propagation in fractured rock in the course of seismic exploration is studied. The grid-characteristic method on hexahedral meshes is extended to the case of an elastic medium with empty and fluid-saturated cracks. The crack effect on wave propagation in the medium is taken into account by introducing cracks at the stage of grid generation with boundary conditions and conditions on the crack edges specified in explicit form. This method is used to obtain wave patterns near an extended inclined crack. The problem of numerically computing the seismic effect produced by a cluster of vertical and subvertical cracks is given in a complete three-dimensional formulation. The structure of the resulting pattern and the influence exerted by the crack-filling substance on the signal recorded on the surface are examined.

Simulation of elastic wave propagation in geological media: Intercomparison of three numerical methods

For wave propagation in heterogeneous media, we compare numerical results produced by grid-characteristic methods on structured rectangular and unstructured triangular meshes and by a discontinuous Galerkin method on unstructured triangular meshes as applied to the linear system of elasticity equations in the context of direct seismic exploration with an anticlinal trap model. It is shown that the resulting synthetic seismograms are in reasonable quantitative agreement. The grid-characteristic method on structured meshes requires more nodes for approximating curved boundaries, but it has a higher computation speed, which makes it preferable for the given class of problems.

Simulation of seismic processes inside the planet using the hybrid grid-characteristic method

The problem of the propagation of seismic waves in the Earth is studied. The authors propose a method to simulate numerically dynamic processes based on the solution to determine the system of elastic body equations by a grid-characteristic method on structural curvilinear computational meshes. A set of calculations of the propagation of a perturbation (set as a local extension area) in a layered two-dimensional Earth model are carried out. Wave patterns and characteristics of wave responses are compared to analytical solutions and the published analogous results.

Numerical Modeling of Wave Processes During Shelf Seismic Exploration

The attention to Arctic shelf is explained by the real need of exploration and development of oil-fields and gas-fields. The computer modeling is a single appropriate approach because the physical experiments in Arctic are expensive and sometimes difficult or impossible to make. In this research, the wave processes during seismic exploration of Arctic shelf are studied. The up-to-date numerical simulation by gird-characteristic method was applied. This method allows to obtain all types of elastic and acoustic waves (longitudinal P-waves, transverse S-waves, Stoneley, Rayleigh, Love, scattered PP-, SS-, and converted PS- and SP-waves) in the heterogeneous media, using mathematically correct conditions on boundaries and interfaces. Also a comparison of acoustic and elastic wave processes during shelf seismic exploration was implemented. The experiments show that it is more precise and informative to solve the elastic wave equation in geological media and the acoustic wave equation in the sea water layer only despite of sources and receivers, which are located in the water layer near the surface. The experiments demonstrate the opportunity to measure the reflections in the water from the converted PS-waves and the reflected SS-waves, using receivers in the water layer. The software based on grid-characteristic method was developed. It is possible to use different interface and boundary conditions and obtain full wave pattern.

Grid-characteristic method on embedded hierarchical grids and its application in the study of seismic waves

The grid-characteristic method on a sequence of embedded hierarchical grids is used to study the reflection and diffraction of elastic seismic waves propagating from an earthquake hypocenter to the Earth’s surface. More specifically, the destruction caused by seismic waves in complex heterogeneous structures, such as multi-story buildings, is analyzed. This study is based on computer modeling with the use of the grid-characteristic method, which provides a detailed description of wave processes in heterogeneous media, takes into account all types of emerging waves, and relies on algorithms that perform well on the boundaries of the integration domain and material interfaces. Applying a sequence of hierarchical grids makes it possible to simulate seismic wave propagation from an earthquake hypocenter to ground facilities of interest—multi-story buildings—and to investigate their seismic resistance.

Modeling 3D seismic problems using high-performance computing systems

This paper examines some issues in numerical modeling of seismology in three-dimensional space on high-performance computing systems. As a method of modeling, the grid-characteristic method is used. This method allows accurate staging of different contact conditions and is suitable for the most physically correct solutions of problems of seismology and seismic prospecting in complex heterogeneous media. We use the grid-characteristic schemes up to the 4th order accuracy inclusive. The software package is parallelized for work in a distributed clustered medium using the MPI technology. We present the results of the simulation of the Love and Rayleigh surface seismic waves, as well as the passage of seismic waves initiated by an earthquake’s hypocenter to the earth’s surface through a multilayer geological formation.

Approximate solutions of acoustic 3D integral equation and their application to seismic modeling and full-waveform inversion

Abstract Over the recent decades, a number of fast approximate solutions of Lippmann–Schwinger equation, which are more accurate than classic Born and Rytov approximations, were proposed in the field of electromagnetic modeling. Those developments could be naturally extended to acoustic and elastic fields; however, until recently, they were almost unknown in seismology. This paper presents several solutions of this kind applied to acoustic modeling for both lossy and lossless media. We evaluated the numerical merits of those methods and provide an estimation of their numerical complexity. In our numerical realization we use the matrix-free implementation of the corresponding integral operator. We study the accuracy of those approximate solutions and demonstrate, that the quasi-analytical approximation is more accurate, than the Born approximation. Further, we apply the quasi-analytical approximation to the solution of the inverse problem. It is demonstrated that, this approach improves the estimation of the data gradient, comparing to the Born approximation. The developed inversion algorithm is based on the conjugate-gradient type optimization. Numerical model study demonstrates that the quasi-analytical solution significantly reduces computation time of the seismic full-waveform inversion. We also show how the quasi-analytical approximation can be extended to the case of elastic wavefield.

Numerical modeling of wave processes in layered media in the Arctic region

The aim of this work is the numerical simulation of wave propagation in media with linear-elastic and acoustic layers as exemplified by the seismic prospecting problems in the Arctic region and the explosive impact on an iceberg. The complete system of equations describing the state of a linearly elastic body and the system of equations describing the acoustic field are solved. The grid-characteristic method is used to provide the contact and boundary conditions, including the contact condition between acoustic and linear-elastic layers, to be correctly described.