Correlation analysis of statistical facies fault models

Doklady Earth Sciences - This paper addresses seismic imaging of fault zones and analysis of the seismic data with the use of the fault facies model developed at Uni Research CIPR. Simulated and...     

REMOTE SENSING METHODS IN THE STUDY OF SOILS IN BELARUS'

Applications of remote sensing in the study of soils of Belarus' are investigated. The focus is upon ascertaining relationships between phototone of cultivated soils and various soil characteristics (humus content, texture, etc.); upon ensuring the best times for imaging; on the revision of existing soil maps from remote sensing imagery; and on determinations of humus content from spectral reflectance values. Translated by Edward Torrey, Alexandria, VA 22308 from: G. V. Dobrovol'skiy and V. L. Andronikov, eds., Aerokosmicheskiye metody v pochvovedenii i ikh ispol'zovaniye v sel'skom khozyaystve: sbornik nauchnykh trudov [Remote Sensing Methods in Soil Science and Their Utilization in Agriculture: A Collection of Scientific Works]. Moscow: Nauka, 1990, pp. 109–116.     

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.     

On the interface error analysis for finite difference wave simulation

A common way to construct a finite difference scheme is to satisfy a desired order of approximation, typically as high as possible. For linear wave propagation problem approximation together with stability delivers convergence of the same order as approximation. If a wave propagation proses is considered convergence to a plane wave solution can be derived analytically by means of the dispersion analysis. However, mentioned techniques are applicable only to homogeneous media and provide no knowledge of reflection/transmission coefficients. In this paper we prove that the only way to get second order accuracy of the solution for media with discontinuous parameters is to use a conservative finite difference scheme of the second order, and the only way to do this is to use the arithmetic mean for the density and the harmonic mean for the bulk modulus in the vicinity of the interface.     

Attenuation mechanisms in fractured fluid-saturated porous rocks: a numerical modelling study

Seismic attenuation mechanisms receive increasing attention for the characterization of fractured formations because of their inherent sensitivity to the hydraulic and elastic properties of the probed media. Attenuation has been successfully inferred from seismic data in the past, but linking these estimates to intrinsic rock physical properties remains challenging. A reason for these difficulties in fluid-saturated fractured porous media is that several mechanisms can cause attenuation and may interfere with each other. These mechanisms notably comprise pressure diffusion phenomena and dynamic effects, such as scattering, as well as Biot's so-called intrinsic attenuation mechanism. Understanding the interplay between these mechanisms is therefore an essential step for estimating fracture properties from seismic measurements. In order to do this, we perform a comparative study involving wave propagation modelling in a transmission set-up based on Biot's low-frequency dynamic equations and numerical upscaling based on Biot's consolidation equations. The former captures all aforementioned attenuation mechanisms and their interference, whereas the latter only accounts for pressure diffusion phenomena. A comparison of the results from both methods therefore allows to distinguish between dynamic and pressure diffusion phenomena and to shed light on their interference. To this end, we consider a range of canonical models with randomly distributed vertical and/or horizontal fractures. We observe that scattering attenuation strongly interferes with pressure diffusion phenomena, since the latter affect the elastic contrasts between fractures and their embedding background. Our results also demonstrate that it is essential to account for amplitude reductions due to transmission losses to allow for an adequate estimation of the intrinsic attenuation of fractured media. The effects of Biot's intrinsic mechanism are rather small for the models considered in this study.     

Numerical simulation of seismic waves in models with anisotropic formations: coupling Virieux and Lebedev finite-difference schemes

Anisotropy is widespread in the Earth’s interior. However, there is a number of models where anisotropic formations comprise as few as 10–20?% of the volume, and this includes fractured reservoirs, thin-layered packs, etc. while the major part of the medium is isotropic. In this situation, the use of computationally intense anisotropy-oriented approaches throughout the computational domain is prodigal. So this paper presents an original advanced finite-difference algorithm based on the domain decomposition technique with individual scheme used inside subdomains. It means that the standard staggered grid scheme or the Virieux scheme is used in the main part of the model which is isotropic, while the anisotropy-oriented Lebedev scheme is utilized inside domains with anisotropic formations. Finite-difference consistency conditions at the artificial interface where the schemes are coupled are designed to make the artificial reflections as low as possible, namely, for the second-order scheme, the third order of convergence of the reflection coefficients is proved.     

Lebedev scheme for the numerical simulation of wave propagation in 3D anisotropic elasticity‡

This paper presents a Lebedev finite difference scheme on staggered grids for the numerical simulation of wave propagation in an arbitrary 3D anisotropic elastic media. The main concept of the scheme is the definition of all the components of each tensor (vector) appearing in the elastic wave equation at the corresponding grid points, i.e., all of the stresses are stored in one set of nodes while all of the velocity components are stored in another. Meanwhile, the derivatives with respect to the spatial directions are approximated to the second order on two‐point stencils. The second‐order scheme is presented for the sake of simplicity and it is easy to expand to a higher order. Another approach, widely‐known as the rotated staggered grid scheme, is based on the same concept; therefore, this paper contains a detailed comparative analysis of the two schemes. It is shown that the dispersion condition of the Lebedev scheme is less restrictive than that of the rotated staggered grid scheme, while the stability criteria lead to approximately equal time stepping for the two approaches. The main advantage of the proposed scheme is its reduced computational memory requirements. Due to a less restrictive dispersion condition and the way the media parameters are stored, the Lebedev scheme requires only one‐third to two‐thirds of the computer memory required by the rotated staggered grid scheme. At the same time, the number of floating point operations performed by the Lebedev scheme is higher than that for the rotated staggered grid scheme.