On the separation of simultaneous-source data by inversion

Introduction

Conventionally, seismic data acquisition involves a single seismic source and an array of receivers. However, recent advances in acquisition technology enable seismic acquisition with multiple sources (Womack et al., 1990; Hampson et al., 2008; Beasley, 2008). By using simultaneous sources, it is possible to achieve longer offsets, better shot-sampling, and improved time and cost efficiency (van Mastrigt et al., 2002; Berkhout et al., 2008; Howe et al., 2009).

Although direct imaging of simultaneous-source data has several desirable properties, it also suffers from several pitfalls. The most important limitation of direct imaging is the introduction of crosstalk artifacts from incongruous sources. Under certain conditions, crosstalk artifacts may be sufficiently attenuated by stacking (Hampson et al., 2008; Beasley, 2008). Linearized inversion can attenuate crosstalk artifacts significantly (Ayeni et al., 2009; Dai and Schuster, 2009; Tang and Biondi, 2009). However, linearized inversion assumes that the true seismic velocities are known, which is not the case in any practical application. Therefore, most practitioners opt to separate simultaneous-source data sets into independent shot records followed by conventional processing.

Data separation may be treated as a filtering (Huo et al., 2009; Moore et al., 2008) or an inversion (Akerberg et al., 2008; Abma et al., 2010) problem. In this paper, we take an inversion approach, in which components of the simultaneous-source data are predictable from a single model. In our formulation, the simultaneous-source data are modeled by a composite Radon operator based on the recording geometries and relative shot times of the simultaneous sources. We solve the resulting regression using a robust hybrid-norm solver (Li et al., 2010). Model sparsity, introduced by the hybrid-norm, significantly improves the quality of the recovered data sets relative to those from an $l_{2}$ solver.

The quality of the separated data is further improved by introducing model regularization, which may be implemented in either the Radon or the shot space. In this paper, for the single-survey problem, we consider regularization by damping and by directional Laplacians (Hale, 2007). In our problem, non-stationary directional Laplacians are used to enforce smoothness along local dips. First, we solve the inversion problem using a damping regularization. Then, using the estimated independent data, we compute dip-components along constant-offset panels. From these dip estimates, regularization operators for the next inversion step are generated. These operators are used to regularize the inversion and generate new results that serve as inputs to the next inversion step. This procedure can be repeated as many times as necessary.

One potential application of simultaneous-source acquisition is in time-lapse seismic reservoir monitoring (Ayeni et al., 2009). For example, because this method reduces seismic acquisition cost, monitoring data sets can be acquired at shorter time intervals. However, because time-lapse monitoring requires high-quality data, amplitudes of separated data must be reliable. For the time-lapse seismic problem, we consider a spatio-temporal regularization scheme that utilizes a combination of directional Laplacians and temporal smoothness constraints.

In this paper, we first describe the inversion formulation of our separation approach. Next, we briefly discuss possible regularization schemes for this inversion problem. Finally, using data sets from 2D sections extracted from the SEAM geophysical model, we show that our method can produce high-quality results for both single and time-lapse surveys.

On the separation of simultaneous-source data by inversion