Migração FFD 3D em profundidade usando aproximação de Padé complexa

Abstract

Fourier finite-difference (FFD) migration implementations use splitting techniques to accelerate performace and save computational cost. However, such techniques introduce numerical anisotropy which leads to mispositioning of dipping reflectors along directions not used for splitting the migration operator. We implement 3D FFD continuation migration without splitting in the frequency-space domain using the complex Padé approximation and implicit finite differences. This approach eliminates numerical anisotropy at the expense of a computationally more intensive solution of a large banded linear system. Numerical experiments in homogeneous and heterogeneous models show that splitting techniques produce noticiable positioning erros for models with strong lateral velocity variation. We compare the performance of the iterative stabilized biconjugate gradient (BICGSTAB) and the multifrontal massively parallel direct solver (MUMPS). It turns out that the use of the complex Padé approximation provides an effective preconditioner for the BICGSTAB, reducing the number of iterations relative to the real Padé expansion. The iterative BICGSTAB method is more efficient than the direct MUMPS method when solving for a single term in the Padé expansion. For wide angle approximations more terms are required to represent the migration operator, in this case direct methods are required. The algorithm is validated and the properties evaluated computing the migration impulse response in the SEG/EAGE salt model.