Moveout-based wave-equation migration velocity analysis

Introduction

Wave-equation migration velocity analysis (WEMVA) methods aim to utilize velocity information from the migrated images to improve the velocity model. Using the wave equation is potentially more accurate than ray-based methods becauses it better describes wave-propagation physics and will give a more physically realistic senstivity kernel for the velocity update. Evaluating the flatness of the angle-dommain common image gathers (ADCIGs) (Biondi and Symes, 2004) is so far the most favored choice when forming WEMVA optimization problems.

Several WEMVA methods have been proposed, but there is no consensus on the best method. The maximum-stack power method (Chavent and Jacewitz, 1995) directly maximizes the angle stack of the ADCIGs, but similar to the Full Waveform Inversion (FWI) (Tarantola, 1984) method, it is prone to cycle-skipping when the velocity error is too large. The differential-semblance optimization (DSO) (Shen and Symes, 2008; Symes and Carazzone, 1991; Shen et al., 2005) penalizes the first derivative along the angle axis on the ADCIGs. This objective function is easy to implement but will falsely over-penalize an already flat angle gather with variant amplitudes; and the differential operator significantly amplifies the noise in the image, thus generating unwanted artifacts in the velocity upgrade. Sava (2004) uses prestack Stolt residual migration to help construct the image perturbation. The cycle-skipping problem is avoided this way, however the user is required to pick a $\rho$ parameter at each model point, and the picking is not trivial. Furthermore the Stolt migration can only migrate images using constant velocity for the entire velocity model. There is some question whether the $\rho$ parameters picked with these image-$\rho$ cubes always represent the correct trend of the velocity update.

In this report, we propose a new method which extends from the theory in Biondi (2010,2011). This method extracts the velocity-focusing information in the angle domain and tries to maximize the angle-stack power of ADCIGs as well. To tackle the cycle-skipping issue, we present a new way to construct the image perturbation by introducing an intermediate moveout parameter that describes the kinematics change of the ADCIGs caused by the velocity change; and that kinematic change then links to the change of objective function. The rest of the paper is divided into two parts: first the theoretical framework is explained; then we demonstrate the effectiveness of our method with several synthetic examples.

Moveout-based wave-equation migration velocity analysis