Predicting rugged water-bottom multiples through wavefield extrapolation with rejection and injection

Introduction

Seismic multiples can directly contaminate the stacking velocity and obscure the primary images in stack sections. Even worse, the energy of seismic multiples can smear into the target zones during seismic migration and result in a suboptimal result during seismic inversion. Therefore, seismic multiple attenuation has been a primary concern in marine seismic data processing.

In recent years, both the geophysical industry and academia have made significant progress in seismic multiple attenuation, including multiple prediction and adaptive multiple subtraction. As a result, a diverse toolkit for multiple attenuation is available in marine seismic data processing today. However, the effectiveness and efficiency of some multiple attenuation methods are still a challenge in practice.

In theory, 3D surface-related multiple elimination, or SRME, can predict surface-related multiples accurately from the seismic data itself without a priori knowledge of the subsurface (Verschuur and Berkhout, 1997; van Dedem and Verschuur, 2001). For a trace of a given shot-receiver pair, convolution-based SRME predicts the multiple model trace by convolving the common-shot gather related to the given shot point with the common-receiver gather related to the given receiver point. Ideally this method requires that the source and receiver are co-located, the source signatures are consistent, and the seismic data are completely acquired and well sampled. However, for most 2D and 3D marine streamer data, this is not the case, because of boat steering that deviates from the designed sail line, cable feathering and near offset gap, among other causes. Therefore, either data pre-processing for SRME or built-in processing during SRME is required, either of which reduces the computational efficiency.

As a complementary approach to 3D convolution-based multiple prediction, WEM-modeling-based multiple prediction employs downward and upward wavefield extrapolation between the sea surface and the water bottom to predict water-bottom multiples and peg-legs based on a previously produced near-surface model (Stork, 2006; Wiggins, 1988; T. Weisser, 2006). This method theoretically is independent of seismic acquisition geometry and ideally requires a near-surface velocity model with water velocity, water-bottom topography and subsurface velocities. Unfortunately, in practice, it is not easy to estimate the subsurface velocities. Therefore, to allow wavefield extrapolation using only the water velocity and the water bottom topography, conventional wave equation modeling generally performs an approximation to the sea floor surface prior to wavefield continuation. In general, the Kirchhoff integral and finite-difference methods require dipping and horizontal flat sea floor surfaces respectively. Obviously, in the case of a structured or rugged sea floor, this approximation will result in suboptimal multiple modeling.

With the aim of improving the effectiveness and efficiency of wave-equation multiple modeling, I employ the so-called wavefield rejection and injection technique to perform wavefield extrapolation, so that I can use only the water velocity and the water-bottom topography to predict rugged water-bottom multiples and peg-legs. To best match this technique, I also present an algorithm for recursive Kirchhoff wavefield extrapolation in the space-frequency domain.

Predicting rugged water-bottom multiples through wavefield extrapolation with rejection and injection