A wave‐equation splitting algorithm for seismic modeling with applications to anisotropic media

1998 ◽  
Author(s):  
Irshad R. Mufti ◽  
Ricardo A. R. Fernandes
Keyword(s):  
Wave Equation ◽  
Anisotropic Media ◽  
Seismic Modeling ◽  
Splitting Algorithm

A hybrid method applied to a 2.5D scalar wave equation

2008 ◽  
Vol 45 (12) ◽  
pp. 1517-1525
Author(s):  
P. F. Daley ◽  
E. S. Krebes ◽  
L. R. Lines
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Heterogeneous Medium ◽  
Integral Transform ◽  
P Wave ◽  
Acoustic Wave Equation ◽  
Seismic Modeling ◽  
Subsurface Structures ◽  
Spatial Dimensions ◽  
Finite Integral

The 3D acoustic wave equation for a heterogeneous medium is used for the seismic modeling of compressional (P-) wave propagation in complex subsurface structures. A combination of finite difference and finite integral transform methods is employed to obtain a “2.5D” solution to the 3D equation. Such 2.5D approaches are attractive because they result in computational run times that are substantially smaller than those for the 3D finite difference method. The acoustic parameters of the medium are assumed to be constant in one of the three Cartesian spatial dimensions. This assumption is made to reduce the complexity of the problem, but still retain the salient features of the approach. Simple models are used to address the computational issues that arise in the modeling. The conclusions drawn can also be applied to the more general fully inhomogeneous problem. Although similar studies have been carried out by others, the work presented here is new in the sense that (i) it applies to subsurface models that are both vertically and laterally heterogeneous, and (ii) the computational issues that need to be addressed for efficient computations, which are not trivial, are examined in detail, unlike previous works. We find that it is feasible to generate true-amplitude synthetic seismograms using the 2.5D approach, with computational run times, storage requirements, and other factors, being at reduced and acceptable levels.

Migration of P‐wave reflection data in transversely isotropic media

Geophysics ◽  
1994 ◽  
Vol 59 (4) ◽  
pp. 591-596 ◽  
Author(s):  
Suhas Phadke ◽  
S. Kapotas ◽  
N. Dai ◽  
Ernest R. Kanasewich
Keyword(s):  
Wave Equation ◽  
Dispersion Relation ◽  
Synthetic Data ◽  
Transversely Isotropic ◽  
Anisotropic Media ◽  
Limited Range ◽  
Horizontal Velocity ◽  
P Wave ◽  
Transversely Isotropic Media ◽  
Isotropic Media

Wave propagation in transversely isotropic media is governed by the horizontal and vertical wave velocities. The quasi‐P(qP) wavefront is not an ellipse; therefore, the propagation cannot be described by the wave equation appropriate for elliptically anisotropic media. However, for a limited range of angles from the vertical, the dispersion relation for qP‐waves can be approximated by an ellipse. The horizontal velocity necessary for this approximation is different from the true horizontal velocity and depends upon the physical properties of the media. In the method described here, seismic data is migrated using a 45-degree wave equation for elliptically anisotropic media with the horizontal velocity determined by comparing the 45-degree elliptical dispersion relation and the quasi‐P‐dispersion relation. The method is demonstrated for some synthetic data sets.

A two‐way nonreflecting wave equation

Geophysics ◽  
1984 ◽  
Vol 49 (2) ◽  
pp. 132-141 ◽  
Author(s):  
Edip Baysal ◽  
Dan D. Kosloff ◽  
J. W. C. Sherwood
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Forward Modeling ◽  
Conventional Approach ◽  
Reflection Coefficients ◽  
Constant Density ◽  
Acoustic Wave Equation ◽  
Seismic Modeling ◽  
Homogeneous Regions ◽  
Dominant Direction

In seismic modeling and in migration it is often desirable to use a wave equation (with varying velocity but constant density) which does not produce interlayer reverberations. The conventional approach has been to use a one‐way wave equation which allows energy to propagate in one dominant direction only, typically this direction being either upward or downward (Claerbout, 1972). We introduce a two‐way wave equation which gives highly reduced reflection coefficients for transmission across material boundaries. For homogeneous regions of space, however, this wave equation becomes identical to the full acoustic wave equation. Possible applications of this wave equation for forward modeling and for migration are illustrated with simple models.

Wave‐equation datuming

Geophysics ◽  
1979 ◽  
Vol 44 (8) ◽  
pp. 1329-1344 ◽  
Author(s):  
John R. Berryhill
Keyword(s):  
Wave Equation ◽  
Reference Surface ◽  
Seismic Modeling ◽  
Time Data ◽  
Efficient Procedure ◽  
Irregular Surfaces ◽  
Large Velocity ◽  
Seismic Reflections ◽  
Irregular Topography ◽  
Kirchhoff Integral

Wave‐equation datuming is the name given to upward or downward continuation of seismic time data when the purpose is to redefine the reference surface on which the sources and receivers appear to be located. This technique differs from conventional datuming methods in the repositioning of seismic reflections laterally as well as vertically in response to observed time dips. The most interesting applications of the technique are those in which the redefined reference surface is an actual geologic interface having an irregular topography and a large velocity contrast. Wave‐equation datuming can remove the deleterious effect such an interface has on seismic reflections originating below it. Wave‐equation datuming also is applicable in seismic modeling. The computations required in wave‐equation datuming are related to those of migration. The Kirchhoff integral formulation of the wave equation can provide a basis for computation to deal with the irregular surfaces and variable velocities that are central to the problem. The numerical implementation of the Kirchhoff approach can be reduced to an efficient procedure involving summations and convolutions of seismic traces with short shaping and weighting operators.

scholarly journals ONE-STEP EXTRAPOLATION METHOD USING CHEBYSHEV’S RECURRENCE RELATION APPLIED TO SEISMIC MODELING

2016 ◽  
Vol 34 (4) ◽  
Author(s):  
Laura Lara Ortiz ◽  
Reynam C. Pestana
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Acoustic Wave ◽  
Difference Scheme ◽  
Chebyshev Polynomials ◽  
Finite Difference Scheme ◽  
Acoustic Wave Equation ◽  
Seismic Modeling ◽  
First Order ◽  
One Step

ABSTRACT. In this work we show that the solution of the first order differential wave equation for an analytical wavefield, using a finite-difference scheme in time, follows exactly the same recursion of modified Chebyshev polynomials. Based on this, we proposed a numerical...Keywords: seismic modeling, acoustic wave equation, analytical wavefield, Chebyshev polinomials. RESUMO. Neste trabalho, mostra-se que a solução da equação de onda de primeira ordem com um campo de onda analítico usando um esquema de diferenças finitas no tempo segue exatamente a relação de recorrência dos polinômios modificados de Chebyshev. O algoritmo...Palavras-chave: modelagem sísmica, equação da onda acústica, campo analítico, polinômios de Chebyshev.

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