Residual moveout-based wave-equation migration velocity analysis in 3-D

Introduction

Wave-equation migration velocity analysis (WEMVA) (Biondi and Symes, 2004; Biondi and Sava, 1999) belongs to a family of methods for solving the reflection tomography problem. These methods aim to estimate migration velocity by employing wave-equation operators. WEMVA formulates velocity estimation as an optimization problem. Evaluating the flatness of the angle-domain common-image gathers (ADCIGs) is currently the most favored choice when formulating WEMVA objective functions. The WEMVA objective function is optimized by applying gradient-based algorithms. The computation of the gradient is performed in two steps:

1. Computation of a perturbation in the migrated image.
2. Back-projection of the image perturbation into the velocity model using the image-domain wave-equation tomographic operator.

In the previous report (Zhang and Biondi, 2011), we proposed a new WEMVA method for maximizing the angle-stack power of ADCIGs. The key innovations in this method are as follows: first, we approximate the ADCIG, $I(s)$ (migrated using the current slowness $s$ ), with the initial ADCIG $I(s_0)$ followed by an RMO(Residual Moveout) on $I(s_0)$ ; then we design a new image-space tomography operator that describes the kinematic relation between the model slowness perturbation and the RMO parameters. Using several 2-D examples, we have shown that this method: 1) avoids cycle-skipping, 2) does not require manual picking of the moveout parameters, and 3) can robustly improve the flatness of the angle gathers.

Although the three-dimensional extension of our method is conceptually straightforward, to actually implement a 3-D prototype requires substantial efforts on both the theoretical and practical aspects. In this paper, we present our initial work toward a 3-D implementation of our approach. The rest of the paper is organized as follows: First, we present the upgraded theory of our RMO WEMVA method for handling 3-D ADCIGs. Second, we discuss some of the challenges of transforming 3D common-image gathers (CIGs) between the offset and angle domains. We show a synthetic example as a prove of concept for our 3-D RMO WEMVA formulation.

Residual moveout-based wave-equation migration velocity analysis in 3-D