Anisotropic complex Padeacute hybrid finite-difference depth migration

Author(s)

Amazonas, Daniela ^[1] ; Aleixo, Rafael ; Schleicher, Joerg ^[2] ; Costa, Jesse C. ^[1]

Affiliation

^[1] Fed Univ Para, Fac Geophys, BR-66059 Belem, Para - Brazil

^[2] Univ Estadual Campinas, Dept Appl Math, Inst Math Stat & Sci Comp, IMECC, Campinas, SP - Brazil

• Document type: Journal article
• Source: GEOPHYSICS; v. 75, n. 2, p. S51-S59, MAR-APR 2010.
• Web of Science Citations: 4

Abstract

Standard real-valued finite-difference (FD) and Fourier finite-difference (FFD) migrations cannot handle evanescent waves correctly, which can lead to numerical instabilities in the presence of strong velocity variations. A possible solution to these problems is the complex Padeacute approximation, which avoids problems with evanescent waves by rotating the branch cut of the complex square root. We have applied this approximation to the acoustic wave equation for vertical transversely isotropic media to derive more stable FD and hybrid FD/FFD migrations for such media. Our analysis of the dispersion relation of the new method indicates that it should provide more stable migration results with fewer artifacts and higher accuracy at steep dips. Our studies lead to the conclusion that the rotation angle of the branch cut that should yield the most stable image is 60 degrees for FD migration, as confirmed by numerical impulse responses and work with synthetic data. (AU)

• FAPESP's process: 06/04410-5 - Image-wave equations for remigration in anisotropic media
• Grantee: Rafael Aleixo de Carvalho
• Support Opportunities: Scholarships in Brazil - Doctorate