Three dimensional wave equation depth migration by a direct solution method

2006 ◽  
Author(s):  
Dan Kosloff ◽  
Hillel Tal‐Ezer ◽  
Allon Bartana
Keyword(s):  
Wave Equation ◽  
Solution Method ◽  
Three Dimensional ◽  
Direct Solution ◽  
Depth Migration ◽  
Direct Solution Method ◽  
Dimensional Wave

Compact High Order Accurate Schemes for the Three Dimensional Wave Equation

2019 ◽  
Vol 81 (3) ◽  
pp. 1181-1209 ◽  
Author(s):  
F. Smith ◽  
S. Tsynkov ◽  
E. Turkel
Keyword(s):  
Wave Equation ◽  
Three Dimensional ◽  
High Order ◽  
Dimensional Wave

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.

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