8 3 - D recursive extrapolation operators

1 3 - D recursive extrapolation operators

To visualize the 3-D subsurface of the earth 3-D migration algorithms are needed which give accurate results within a reasonable computation time. In this Chapter several recursive depth migration algorithms are discussed and compared with each other. The backbone of every recursive depth migration algorithm is a 3-D extrapolation algorithm. In lateral homogeneous media the extrapolation algori...

3-D recursive extrapolation operators: a comparison

3-D recursive extrapolation operators: an overview

with ∆z being a small extrapolation step. The advantage of computation in the kx, ky-ω domain is that the desired result is obtained by multiplication of the data with the operator. However, to allow laterally varying medium functions a space variant convolution operator in the x, y-ω (space-frequency) domain should be applied. When the spatial extrapolation operator is used in an explicit recu...

Matrix and Vector Sequence Transformations Revisitedc

Sequence transformations are extrapolation methods. They are used for the purpose of convergence acceleration. In the scalar case, such algorithms can be obtained by two diierent approaches which are equivalent. The rst one is an elimination approach based on the solution of a system of linear equations and it makes use of determinants. The second approach is based on the notion of annihilation...

Implicit 3-D depth migration by wavefield extrapolation with helical boundary conditions

Wavefield extrapolation in the (ω−x) domain provides a tool for depth migration with strong lateral variations in velocity. Implicit formulations of depth extrapolation have several advantages over explicit methods. However, the simple 3-D extension of conventional 2-D wavefield extrapolation by implicit finite-differencing requires the inversion of a 2-D convolution matrix which is computation...