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.

Depth migration from irregular surfaces with depth extrapolation methods

Geophysics ◽  
1991 ◽  
Vol 56 (1) ◽  
pp. 119-122 ◽  
Author(s):  
Moshe Reshef
Keyword(s):  
Wave Equation ◽  
Surface Topography ◽  
Time Shift ◽  
Extrapolation Methods ◽  
Irregular Surfaces ◽  
Depth Migration ◽  
Numerical Problem ◽  
Flat Interface ◽  
Interface Wave ◽  
Computationally Expensive

Nonflat surface topography introduces a numerical problem for migration algorithms that are based on depth extrapolation. Since the numerically efficient migration schemes start at a flat interface, wave‐equation datuming is required (Berryhill, 1979) prior to the migration. The computationally expensive datuming procedure is often replaced by a simple time shift for the elevation to datum correction. For nonvertically traveling energy this correction is inaccurate. Subsequent migration wrongly positions the reflectors in depth.

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.

Vertical seismic profile migration using the Kirchhoff integral

Geophysics ◽  
1988 ◽  
Vol 53 (6) ◽  
pp. 786-799 ◽  
Author(s):  
P. B. Dillon
Keyword(s):  
Wave Equation ◽  
Wave Field ◽  
Near Field ◽  
Synthetic Data ◽  
Real Data ◽  
Seismic Profile ◽  
Processing Strategies ◽  
Receiver Array ◽  
Vsp Data ◽  
Kirchhoff Integral

Wave‐equation migration can form an accurate image of the subsurface from suitable VSP data. The image’s extent and resolution are determined by the receiver array dimensions and the source location(s). Experiments with synthetic and real data show that the region of reliable image extent is defined by the specular “zone of illumination.” Migration is achieved through wave‐field extrapolation, subject to an imaging procedure. Wave‐field extrapolation is based upon the scalar wave equation and, for VSP data, is conveniently handled by the Kirchhoff integral. The migration of VSP data calls for imaging very close to the borehole, as well as imaging in the far field. This dual requirement is met by retaining the near‐field term of the integral. The complete integral solution is readily controlled by various weighting devices and processing strategies, whose worth is demonstrated on real and synthetic data.

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.

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.

scholarly journals Wave equation dispersion inversion of surface waves recorded on irregular topography

2019 ◽  
Vol 217 (1) ◽  
pp. 346-360 ◽  
Author(s):  
Jing Li ◽  
Fan-Chi Lin ◽  
Amir Allam ◽  
Yehuda Ben-Zion ◽  
Zhaolun Liu ◽  
...  
Keyword(s):  
Wave Equation ◽  
Surface Waves ◽  
Irregular Topography
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