True-amplitude, angle-domain, common-image gathers from one-way wave-equation migrations

Abstract

True-amplitude wave-equation migration provides a quality migrated image of the earth’s interior. In addition, the amplitude of the output provides an estimate of the angular-dependent reflection coefficient, similar to the output of Kirchhoff inversion. Recently, true-amplitude wave-equation migration for common-shot data has been proposed to generate amplitude-reliable, shot-domain, common-image gathers in heterogeneous media. We present a method to directly produce angle-domain common-image gathers from both common-shot and shot-receiver wave-equation migration. Generating true-amplitude, shot-domain, common-image gathers requires a deconvolution-type imaging condition using the ratio of the upgoing and downgoing wavefield, each downward-projected to the image point. Producing true-amplitude, angle-domain, common-image gathers requires, instead, the product of the upgoing wavefield and the complexconjugate of the downgoing wavefield in the imaging condition. Since multiplication is a more stable computational process than division, the new methods proposed provide more stable ways of inverting seismic data. Furthermore, the resulting common-image gathers can be directly used for migrated amplitude-variation-with angle analysis and tomography-based velocity analysis. Shot-receiver wave-equation migration requires new true-amplitude, one-way wave equations with one depth variable and transverse variables for the coordinates corresponding to sources and receivers, hence, two transverse coordinates in 2D and four transverse coordinates in 3D. We propose a modified double-square-root one-way wave equation to produce true amplitude common-image angle gathers. We also demonstrate the new methods with some synthetic examples. Some numerical examples show that the new methods we propose give better amplitude performance on the migrated angle gathers.