Vadim Lisitsa

Local time-space mesh refinement for simulation of elastic wave propagation in multi-scale media

This paper presents an original approach to local time-space grid refinement for the numerical simulation of wave propagation in models with localized clusters of micro-heterogeneities. The main features of the algorithm are-the application of temporal and spatial refinement on two different surfaces;-the use of the embedded-stencil technique for the refinement of grid step with respect to time;-the use of the Fast Fourier Transform (FFT)-based interpolation to couple variables for spatial mesh refinement. The latter makes it possible to perform filtration of high spatial frequencies, which provides stability in the proposed finite-difference schemes.In the present work, the technique is implemented for the finite-difference simulation of seismic wave propagation and the interaction of such waves with fluid-filled fractures and cavities of carbonate reservoirs. However, this approach is easy to adapt and/or combine with other numerical techniques, such as finite elements, discontinuous Galerkin method, or finite volumes used for approximation of various types of linear and nonlinear hyperbolic equations.

Combination of the discontinuous Galerkin method with finite differences for simulation of seismic wave propagation

We present an algorithm for the numerical simulation of seismic wave propagation in models with a complex near surface part and free surface topography. The approach is based on the combination of finite differences with the discontinuous Galerkin method. The discontinuous Galerkin method can be used on polyhedral meshes; thus, it is easy to handle the complex surfaces in the models. However, this approach is computationally intense in comparison with finite differences. Finite differences are computationally efficient, but in general, they require rectangular grids, leading to the stair-step approximation of the interfaces, which causes strong diffraction of the wavefield. In this research we present a hybrid algorithm where the discontinuous Galerkin method is used in a relatively small upper part of the model and finite differences are applied to the main part of the model.

Finite-difference algorithm with local time-space grid refinement for simulation of waves

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. We have proved that this approach is low-reflecting, the artificial reflections are about 10 − 4 of an incident wave. We have also shown that if a successive refinement is applied, i.e. temporal and spatial steps are refined at different interfaces, this approach is stable.

Simulation of seismic waves propagation in multiscale media: impact of cavernous/fractured reservoirs

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 of the target area into subdomains containing the reference medium (coarse grid) and reservoir (fine grid). Computations for each subdomain can be carried out in parallel. The data exchange between each subdomain within a group is done using MPI through nonblocking iSend/iReceive commands. The data exchange between the two groups is done simultaneously by coupling the coarse and fine grids. The results of a numerical simulation of a carbonate reservoir are presented and discussed.

Reflectionless truncation of target area for axially symmetric anisotropic elasticity

This paper presents an approach to numerical simulation of seismic wave propagation in anisotropic elastic media in cylindrical coordinates by means of conservative finite difference scheme on staggered grids. An original low cost domain distension based on Optimal Grids is proposed to restrict computational domain.

Impact of Cavernous/Fractured Reservoirs to Scattered Seismic Waves In 3D Heterogeneous Media: Accurate Numerical Simulation And Field Study

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 is used in order to split the target area into subdomains containing the reference medium (coarse grid) and reservoir (fine grid). Computations for each subdomain is carried out in parallel. The data exchange between each subdomain within a group is done using MPI through nonblocking iSend/iReceive commands. The data exchange between the two groups is done simultaneously by coupling the coarse and fine grids and is implemented via Master Processors assigned to each . The results of a numerical simulation of a carbonate reservoir are presented and discussed.

Effect of CT image size and resolution on the accuracy of rock property estimates

In order to study the effect of the micro-CT scan resolution and size on the accuracy of up-scaled digital rock property estimation of core samples Bentheimer sandstone images with the resolution varying from 0.9 μm to 24 μm are used. We statistically show that the correlation length of the pore-to-matrix distribution can be reliably determined for the images with the resolution finer than 9 voxels per correlation length and the representative volume for this property is about 153 correlation length. Similar resolution values for the statistically representative volume are also valid for the estimation of the total porosity, specific surface area, mean curvature and topology of the pore space. Only the total porosity and the number of isolated pores are stably recovered, whereas geometry and the topological measures of the pore space are strongly affected by the resolution change. We also simulate fluid flow in the pore space and estimate permeability and tortuosity of the sample. The results demonstrate that the representative volume for the transport property calculation should be greater than 50 correlation lengths of pore-to-matrix distribution. On the other hand, permeability estimation based on the statistical analysis of equivalent realizations shows some weak influence of the resolution on the transport properties. The reason for this might be that the characteristic scale of the particular physical processes may affect the result stronger than the model (image) scale.

Accuracy Analysis of Finite-difference Staggered-grid Numerical Schemes For Elastic-elastic And Fluid-elastic Interfaces

Inaccurate treatment of sharp medium discontinuities introduces a significant error in finite-difference simulations of wave propagation. Such error can be significantly decreased if medium parameters are modified in the vicinity of the interface in some special way. Here we address the theory of how to modify the parameters to achieve the best accuracy. We perform the accuracy analysis of reflection and transmission coefficients and find the modification which provides the second order accuracy versus grid size for planar fluid-elastic and elastic interfaces parallel to the grid. Two widely used finite different schemes of the second and fourth orders are considered. We validate our theoretical results numerically.

Seismic imaging and statistical analysis of fault facies models

AbstractInterpretation of seismic responses from subsurface fault zones is hampered by the fact that the geologic structure and property distributions of fault zones can generally not be directly observed. This shortcoming curtails the use of seismic data for characterizing internal structure and properties of fault zones, and it has instead promoted the use of interpretation techniques that tend to simplify actual structural complexity by rendering faults as lines and planes rather than volumes of deformed rock. Facilitating the correlation of rock properties and seismic images of fault zones would enable active use of these images for interpreting fault zones, which in turn would improve our ability to assess the impact of fault zones on subsurface fluid flow. We use a combination of 3D fault zone models, based on empirical data and 2D forward seismic modeling to investigate the link between fault zone properties and seismic response. A comparison of spatial statistics from the geologic models and the s...

Local Time-Space Mesh Refinement for Finite Difference Simulation of Waves

This paper presents a new approach to a local time-space mesh refinement for a finite difference simulation of waves. The approach is based on the approximation of 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. We proved that this approach is low-reflecting and the artificial reflections are about 10−4 of incident wave. We also proved that if successive refinement is applied, i.e., temporal and spatial steps are refined at a different interfaces, the approach is stable.