Least-squares wave-equation inversion of time-lapse seismic data sets - A Valhall case study

Introduction

Reservoir rock and fluid property changes can be obtained from seismic amplitude and/or travel-time changes. There is a wide range of published work on the most important considerations for time-lapse seismic imaging. For example, Batzle and Wang (1992) and Mavko et al. (2003) outline important rock and fluid relationships; Lumley (1995), Rickett and Lumley (2001), Calvert (2005), and Johnston (2005) discuss important processing and practical applications; and Lefeuvre et al. (2003), Whitcombe et al. (2004), Zou et al. (2006) and Ebaid et al. (2009) present successful case studies. Because of the recorded successes, time-lapse seismic imaging is now an integral part of many reservoir management projects.

In practice, production-related changes in time-lapse seismic images can be masked by non-repeatability artifacts (e.g., changes in geometry, ambient noise) or by effects of complex overburden (e.g., salt canopy). 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 the geometries used to acquire the 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 manner (Tang, 2009; Valenciano et al., 2006). For the time-lapse imaging problem, we can either invert for the complete baseline and monitor images or invert for a static baseline and time-lapse images between surveys. Inputs in the resulting formulations are migrated images (or combinations thereof) and the outputs are the inverted images (or time-lapse images). The operators are a concatenation 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 and data preprocessing is required prior to inversion. Furthermore, we assume compaction and velocity changes between surveys are small relative to the baseline; therefore the effects of these--which inherently neglected by migrating all data sets with the baseline velocity--can be removed by multidimensional warping of the monitor images to the baseline.

First, we summarize wave-equation inversion of time-lapse data sets. Then, we apply this method to a subset of the Valhall Life of Field Seismic (LoFS) data with a synthesized obstruction in the monitor. We show that the proposed method improves the image resolution (compared to migration) and that it attenuates obstruction artifacts in time-lapse images.

Least-squares wave-equation inversion of time-lapse seismic data sets - A Valhall case study