An explicit, unconditionally stable, 15‐degree depth migration and modeling algorithm implemented in poststack, directional, and prestack modes

Geophysics ◽  
1991 ◽  
Vol 56 (9) ◽  
pp. 1412-1422
Author(s):  
Alvin K. Benson
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Three Dimensional ◽  
Inhomogeneous Media ◽  
Unconditional Stability ◽  
Data Sets ◽  
Unconditionally Stable ◽  
Depth Migration ◽  
Implicit Schemes ◽  
Modeling Algorithm

An explicit, unconditionally stable, finite‐difference depth migration and modeling algorithm is formulated and implemented for the fifteen‐degree wave equation in poststack, directional (rotational), and prestack modes for inhomogeneous media. It is about two times faster than implicit schemes. The simplicity, unconditional stability, and speed of the algorithm are appealing for numerous applications, especially prestack and three‐dimensional data sets.

scholarly journals A Comparison of Splitting Techniques for 3D Complex Padé Fourier Finite Difference Migration

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Jessé C. Costa ◽  
Débora Mondini ◽  
Jörg Schleicher ◽  
Amélia Novais
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Computational Cost ◽  
Three Dimensional ◽  
Depth Level ◽  
Numerical Examples ◽  
The Cost ◽  
Comparable Quality ◽  
3D Problem ◽  
Dimensional Wave

Three-dimensional wave-equation migration techniques are still quite expensive because of the huge matrices that need to be inverted. Several techniques have been proposed to reduce this cost by splitting the full 3D problem into a sequence of 2D problems. We compare the performance of splitting techniques for stable 3D Fourier finite-difference (FFD) migration techniques in terms of image quality and computational cost. The FFD methods are complex Padé FFD and FFD plus interpolation, and the compared splitting techniques are two- and four-way splitting as well as alternating four-way splitting, that is, splitting into the coordinate directions at one depth and the diagonal directions at the next depth level. From numerical examples in homogeneous and inhomogeneous media, we conclude that, though theoretically less accurate, alternate four-way splitting yields results of comparable quality as full four-way splitting at the cost of two-way splitting.

MIGRATION BY FOURIER TRANSFORM

Geophysics ◽  
1978 ◽  
Vol 43 (1) ◽  
pp. 23-48 ◽  
Author(s):  
R. H. Stolt
Keyword(s):  
Fourier Transform ◽  
Wave Equation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Three Dimensional ◽  
Frequency Dispersion ◽  
Scalar Wave ◽  
Conjugate Space ◽  
And Migration

Wave equation migration is known to be simpler in principle when the horizontal coordinate or coordinates are replaced by their Fourier conjugates. Two practical migration schemes utilizing this concept are developed in this paper. One scheme extends the Claerbout finite difference method, greatly reducing dispersion problems usually associated with this method at higher dips and frequencies. The second scheme effects a Fourier transform in both space and time; by using the full scalar wave equation in the conjugate space, the method eliminates (up to the aliasing frequency) dispersion altogether. The second method in particular appears adaptable to three‐dimensional migration and migration before stack.

Delayed-shot 3D depth migration

Geophysics ◽  
2005 ◽  
Vol 70 (5) ◽  
pp. E21-E28 ◽  
Author(s):  
Yu Zhang ◽  
James Sun ◽  
Carl Notfors ◽  
Samuel H. Gray ◽  
Leon Chernis ◽  
...  
Keyword(s):  
Wave Equation ◽  
Real Data ◽  
Seismic Survey ◽  
Data Sets ◽  
Depth Migration ◽  
Planar Source ◽  
The Common ◽  
Streamer Data ◽  
Wavefield Extrapolation ◽  
2D And 3D

For 3D seismic imaging in structurally complex areas, the use of migration by wavefield extrapolation has become widespread. By its very nature, this family of migration methods operates on data sets that satisfy a wave equation in the context of a single, physically realizable field experiment, such as a common-shot record. However, common-shot migration of data recorded over dipping structures requires a migration aperture much larger than the recording aperture, resulting in extra computations. A different type of wave-equation record, the response to a linear or planar source, can be synthesized from all the common-shot records. Synthesizing these records from common-shot records involves slant-stack processing, or applying delays to the various shots; we call these records delayed-shot records. Delayed-shot records don't suffer from the aperture problems of common-shot records since their recording aperture is the length of the seismic survey. Consequently, delayed-shot records hold potential for efficient, accurate imaging by wavefield extrapolation. We present a formulation of delayed-shot migration in 2D and 3D (linear sources) and its application to 3D marine streamer data. This formulation includes a discussion of sampling theory issues associated with the formation of delayed-shot records. For typical marine data, 2D and 3D delayed-shot migration can be significantly more efficient than common-shot migration. Synthetic and real data examples show that delayed-shot migration produces images comparable to those from common-shot migration.

A New Efficient Unconditionally Stable Finite-Difference Time-Domain Solution of the Wave Equation

2017 ◽  
Vol 65 (6) ◽  
pp. 3114-3121 ◽  
Author(s):  
Seyed-Mojtaba Sadrpour ◽  
Vahid Nayyeri ◽  
Mohammad Soleimani ◽  
Omar M. Ramahi
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Unconditionally Stable ◽  
Difference Time

The finite-frequency sensitivity kernel for migration residual moveout and its applications in migration velocity analysis

Geophysics ◽  
2008 ◽  
Vol 73 (6) ◽  
pp. S241-S249 ◽  
Author(s):  
Xiao-Bi Xie ◽  
Hui Yang
Keyword(s):  
Wave Equation ◽  
Synthetic Data ◽  
Velocity Model ◽  
Migration Velocity ◽  
Data Sets ◽  
Velocity Analysis ◽  
Depth Migration ◽  
Sensitivity Kernel ◽  
Migration Velocity Analysis ◽  
Tomography Method

We have derived a broadband sensitivity kernel that relates the residual moveout (RMO) in prestack depth migration (PSDM) to velocity perturbations in the migration-velocity model. We have compared the kernel with the RMO directly measured from the migration image. The consistency between the sensitivity kernel and the measured sensitivity map validates the theory and the numerical implementation. Based on this broadband sensitivity kernel, we propose a new tomography method for migration-velocity analysis and updating — specifically, for the shot-record PSDM and shot-index common-image gather. As a result, time-consuming angle-domain analysis is not required. We use a fast one-way propagator and multiple forward scattering and single backscattering approximations to calculate the sensitivity kernel. Using synthetic data sets, we can successfully invert velocity perturbations from the migration RMO. This wave-equation-based method naturally incorporates the wave phenomena and is best teamed with the wave-equation migration method for velocity analysis. In addition, the new method maintains the simplicity of the ray-based velocity analysis method, with the more accurate sensitivity kernels replacing the rays.

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