Converted‐wave true amplitude prestack Kirchhoff migration

Abstract

Preserving amplitudes in converted wave prestack migration is important for subsequent AVO processing and interpretation. However, it has not received as much attention as amplitude preservation for P wave migration. In this paper, we derive common offset true amplitude weight functions in a v(z) medium for two and one half, and three dimensional converted wave Kirchhoff migration. The weight formulas are then simplified into the terms invovling travel time, ray path and velocity functions for efficient computation. The simplified weight functions are also examined with numeric modeling data for depth migration, which demonstrated well-controlled amplitude behavior in offset and depth.

3D Seismic Survey Design, Second edition

“…This loss of resolution represents NMO stretch; therefore, the NMO stretch factor S fact,C for C-wave data can be written as [The relationship (cosi + g cos j = √1 + g 2 + 2g cos 2y is used in Miao et al (2005) but without a derivation.] Note that equation 6.6 is a generalization of the equation for P-waves because it is also valid for g = 1.…”

Converted-wave prestack time migration with a new approximate migration weight

“…PS case: The exact constant-velocity weight for PS migration, analogous to eq. 1, can be obtained beginning with the expression for the horizontal layering case in Miao et al (2005) and simplifying it for the case of a homogeneous medium. Like eq.…”

“…1 the resulting expression must again be evaluated in the inner migration loop; however it is more complicated than the PP expression, so that it would be even more time-consuming to apply. Miao et al (2005) suggest that the PS weight could be approximated following the same practice as in the PP case. Presumably they refer to the fact that in the CMP geometry (i.e.,…”

“…For P-waves an approximate method which balances efficiency and accuracy was presented by Dellinger et al (2000) and Zhang et al (2000), and this is in common use throughout the industry. Miao et al (2005) presented an extension of the exact migration weight for PS data collected from horizontally layered media, and also sought to develop an efficient and accurate approximation similar to that used in the P-wave case. Their analysis did not examine the issue in detail however, and a more satisfying and optimal approximation is still desired.…”

Anisotropic converted wave amplitude-preserving prestack time migration by the pseudo-offset method

“…Vanelle and Gajewski (2001) developed the converted wave, true amplitude, migration based on travel times. Goertz, and Riede (2005) and Miao et al (2005) derived the 3D converted wave Kirchhoff amplitude-preserving migration equation. However, all of these methods are for isotropic media.…”