Migration velocity analysis based on linearization of the two-way wave equation

Introduction

Seismic velocity analysis methods can be divided into two major groups. First, there are techniques that aim at minimizing the misfit in the data domain such as full waveform inversion (Tarantola, 1984; Luo and Schuster, 1990; Biondi, 2009). Second, there are other techniques that aim at improving the quality in the image domain such as migration velocity analysis (MVA)(Symes and Carazzone, 1991; Biondi and Sava, 1999; Shen, 2004). These techniques try to measure the quality of the image several ways and then invert the estimated image perturbation using a linearized wave equation operator. This tomographic operator is based on a Taylor expansion of the image around a background slowness model.

There are several advantages to minimizing the residual in image-space, such as increasing signal-to-noise ratio and decreasing the complexity of the data (Tang et al., 2008). The linearization in WEMVA is conventionally done based on the one-way wave equation. This approach has some advantages, such as the computational efficiency of one-way wave equation operators. However, it also suffers from disadvantages such as decreased accuracy or the inability to model wide-angle propagations.

In this paper, we show the derivation of a linearized tomographic operator that is based on the two-way wave equation. This operator is the essential part in constructing the gradient of any two-way wave equation based MVA, such as WEMVA by residual moveout fitting (Biondi, 2010). The two-way wave equation is linearized over slowness by dropping the second order slowness perturbation term. Also, the Born approximation is used to derive this operator. We also show a few ways to interpret and implement this operator. Finally, we show the resolution matrix of this operator.

Migration velocity analysis based on linearization of the two-way wave equation