Wave-equation inversion of time-lapse seismic data sets

Introduction

Reservoir rock and fluid property changes can be obtained from seismic amplitude and/or travel-time changes (Lumley, 1995; Calvert, 2005). Several successful applications of time-lapse seismic imaging to reservoir monitoring have been published by previous authors (Lefeuvre et al., 2003; Whitcombe et al., 2004; Ebaid et al., 2009).

However, in practice, production-related changes in time-lapse seismic images can be masked by non-repeatability artifacts (e.g., changes in geometry, ambient noise). To correctly interpret time-lapse seismic differences, such artifacts must be attenuated --a prerequisite conventionally achieved through image cross-equalization methods (Rickett and Lumley, 2001). Although cross-equalization methods are well developed and provide reliable results in many practical applications, they are inadequate where large inconsistencies exist between time-lapse data sets or where the reservoir overburden is complex. Where these conventional methods fail, wave-equation inversion provides a way to attenuate unwanted artifacts in time-lapse images, thereby enhancing production-related changes.

The proposed method is based on linear least-squares migration/inversion of seismic data sets (Clapp, 2005; Kühl and Sacchi, 2003; Nemeth et al., 1999). Because each iteration of a data space implementation of least-squares migration/inversion is approximately twice the migration cost, this approach is expensive. However, by posing this problem in the image space, it can be efficiently solved in a target-oriented way (Tang, 2008; Valenciano et al., 2006). For the time-lapse imaging problem, we can either invert for the complete baseline and monitor images or we can invert for a static baseline and time-lapse images between surveys. The input vectors in the resulting formulations contain the migrated images (or combinations thereof) and the output vector contains the inverted images. The operators are a concatenations of target-oriented approximations to the Hessian of the least-squares objective function (Ayeni and Biondi, 2010). We regularize the inversion using spatial (dip) and temporal (difference) constraints.

Because we assume that the data contain only primaries, robust multiple/noise attenuation is required prior to inversion. Furthermore, we assume compaction and velocity changes between surveys are small, therefore these can be removed by warping of the monitor images to the baseline.

First, we discuss linearized wave-equation inversion of time-lapse data sets. Then, we apply this method to a North Sea field time-lapse data set. We show that even with the presence of a gap (caused by a simulated obstruction) in the monitor data-set, wave-equation inversion give improved results over conventional methods.

Wave-equation inversion of time-lapse seismic data sets