Three-dimensional depth migration by using finite-difference formulation of the linearly transformed wave equation

1994 ◽  
Author(s):  
Daniel L. Mujica R.
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Three Dimensional ◽  
Depth Migration ◽  
Finite Difference Formulation

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.

Sign in / Sign up

Export Citation Format

Share Document