Target-oriented joint inversion of incomplete time-lapse seismic data sets

Introduction

There is a wide range of published work on the most important aspects of time-lapse seismic imaging. Some of these works include studies of seismic properties of reservoir fluids (Batzle and Wang, 1992), processing and practical applications (Rickett and Lumley, 2001; Calvert, 2005), and successful case studies (Lefeuvre et al., 2003; Whitcombe et al., 2004; Zou et al., 2006). Because of many successful applications, time-lapse seismic imaging is now an integral part of many reservoir management projects.

A recurring problem in many field time-lapse seismic applications is the presence (and sometimes changing locations) of production and development facilities. Such facilities prevent perfect geometry repetition for different surveys and can pose a major challenge when they are directly located above producing reservoirs. In order to circumvent this problem, it is common practice to undershoot the facilities using two or more boats. However, the undershoot approach does not work in all situations, mainly because the shot/receiver offset distributions cannot be perfectly matched.

Incomplete time-lapse seismic data sets also arise from intentional subsampling of seismic data sets. Such regularly (Smit et al., 2006; Calvert and Wills, 2003) or randomly (Arogunmati and Harris, 2007) subsampled data sets reduce the overall acquisition cost requirement for multiple seismic surveys. Successful field application of regularly sub-sampled time-lapse data sets has been demonstrated by previous authors (Smit et al., 2006; Calvert and Wills, 2003). Although regularly sampled data sets removes unnecessary redundancy in time-lapse data sets and can sufficiently sample low frequency spatial changes in reservoir properties, high frequency changes will likely not be captured. Acquiring seismic data sets randomly can ensure that all parts of the evolving reservoir are sampled, but with different densities/folds for any given survey. Randomly sampled data sets can be interpolated and then processed as full-volume data sets (Arogunmati and Harris, 2007), or they can be directly used to reconstruct the reservoir using compressive sampling (Candes and Romberg, 2007; Candes and Wakin, 2008) principles.

We propose a joint inversion method, based on an iterative least-squares inversion of the linearized wave-equation, for direct imaging of randomly sparse/incomplete time-lapse seismic data sets. The method utilizes a system of non-stationary filters derived from an explicitly computed target-oriented approximation (Valenciano, 2008) to the linear least-squares wave-equation Hessian. A joint inversion scheme enables incorporation of structural constraints (e.g., reservoir location and geometry) and temporal constraints (e.g., smooth temporal changes) in time-lapse image estimation. The proposed method, regularized joint inversion of multiple images (RJMI), and related methods have been applied to other time-lapse seismic imaging problems (Ayeni et al., 2009; Ajo-Franklin et al., 2005; Ayeni and Biondi, 2008).

We assume that the background baseline velocity model is known and that it changes slowly between surveys. Large velocity changes and geomechanical shifts can be handled by including an event alignment step prior to or during inversion. Integration of geomechanical shifts into the joint inversion formulation is ongoing and will be discussed elsewhere. A solution of the joint inversion problem using a robust (reweighted least-squares) L1-framework is also ongoing.

In this paper, using matrix-vector notations, we first review linear wave-equation modeling, iterative least-squares migration/inversion, and the RJMI method. Then, using a subset of the 2D Marmousi model (Versteeg, 1994), we show that RJMI gives good quality time-lapse images from incomplete seismic data sets.

Target-oriented joint inversion of incomplete time-lapse seismic data sets