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A Finite-difference method for simulation of sonic waves propagating in a vicinity of a borehole filled with fluid and surrounded by a 3D heterogeneous elastic medium is developed. The method utilizes an explicit second order of approximation FD scheme on staggered grids that approximates the elastodynamic system of equations in cylindrical coordinates. A… (More)

This paper presents a new approach to a local time-space grid refinement for a staggered-grid finite-difference simulation of waves. The approach is based on approximation of a wave equation at the interface where two grids are coupled. As no interpolation or projection techniques are used, the finite-difference scheme preserves second order of convergence.… (More)

- Galina V. Reshetova, Vladimir A. Tcheverda, Dmitry M. Vishnevsky
- 2008

In order to perform large scale numerical simulation of wave propagation in 3D heterogeneous multiscale elastic media Finite Difference techniques and its parallel implementation based on domain decomposition is used. A couple of typical statements of borehole geophysics are dealt with-sonic log and crosswell measurements. Both of them are essentially… (More)

In order to simulate the interaction of seismic waves with cavernous/fractured reservoirs, a finite-difference technique based on locally refined time-and-space grids is used. The need to use these grids is due primarily to the differing scale of heterogeneities in the reference medium and the reservoir. Domain Decomposition methods allow for the separation… (More)

4 This paper presents a problem-oriented approach, designed for numerical simulation of seismic wave propagation in models containing geological formations with complex properties such as anisotropy, attenuation, and small-scale heterogeneities. Each of the named property requires special treatment which increases computational complexity of the algorithm… (More)

In this paper, we apply an approach for numerical simulation of elastic waves in heterogeneous medium, based on the implementation of integral Laguerre transform with subsequent domain decomposition. Following the Laguerre transform, we obtain a system with strictly negative definite elliptic operator, which doesn't depend on separation parameter.… (More)

This paper describes the implementation of parallel computing to model seismic waves in heterogeneous media based on Laguerre transform with respect to time. The main advantages of the transform are a definite sign of the spatial part of the operator and its independence of the parameter of separation. This property allows one to efficiently organize… (More)

- Dmitry V. Pissarenko, Galina V. Reshetova, Vladimir A. Tcheverda
- J. Computational Applied Mathematics
- 2010

- B. Mikhailenko, Galina V. Reshetova
- J. Computational Applied Mathematics
- 2010