Joint inversion of simultaneous source time-lapse seismic data sets

Introduction

Time-lapse (4D) seismic is an established technology for monitoring hydrocarbon reservoirs. It is central to most field development and management plans, and many successful applications have been published (Whitcombe et al., 2004; Zou et al., 2006). However, in many time-lapse seismic applications, inaccuracies in replication of acquisition geometries for different surveys (non-repeatability) is a recurring problem. Although modern acquisition techniques can improve repeatability of shot-receiver positions, field conditions usually prevent perfect repeatability.

Recently, several authors have suggested acquisition with multiple simultaneously shooting seismic sources. Although, not a new technology (Womack et al., 1990; Beasley et al., 1998), modern acquisition and imaging techniques now make simultaneous source (or blended) acquisition both appealing and practical. Some advantages of this acquisition method include:

• Improved shot-sampling: reduces shot-interpolation requirements in conventional narrow-azimuth data.
• Lower acquisition cost: enables acquisition of several azimuths in 3D wide-azimuth data sets at lower cost.
• Longer offsets and full-azimuth: enables better imaging and improved AVO information.
• Shorter acquisition time-window: makes acquisition practical where operational, climatic, political or other uncontrollable factors could have prevented it.

Different processing schemes have been proposed for simultaneous source data sets. Most of these schemes rely on separation of the data sets into different shot components before standard processing (Spitz et al., 2008; Hampson et al., 2008). Processing schemes that require no separation have also been suggested (Berkhout et al., 2008; Tang and Biondi, 2009). However, there has been little discussion on the implications of this acquisition technique for time-lapse seismic.

We introduce the term relative shot-timing non-repeatability to describe a potential source of artifacts in simultaneous source time-lapse seismic data sets. Because current simultaneous source acquisition designs generally rely on randomized shot-timings, it will be difficult to accurately reproduce the relative shot-receiver positions and at the same time maintain the relative shot-timing for different surveys. Shot-receiver non-repeatability, together with the predicted relative shot-timing non-repeatability, will lead to strong degradation of time-lapse seismic images. Because of the complexity introduced by non-repeatability of both shot-receiver positions and relative shot-timing, conventional cross-equalization methods for time-lapse seismic data sets will fail. Therefore, we explore least-squares inversion methods of such data sets.

Iterative data-space linear least-squares migration/inversion can improve structural and amplitude information in seismic images (Kühl and Sacchi, 2003; Clapp, 2005; Nemeth et al., 1999; Plessix and Mulder, 2004). An extension of image-space least-squares inversion (Valenciano, 2008) to time-lapse imaging has been shown to improve time-lapse seismic images (Ayeni and Biondi, 2008). In this paper, we propose a data-space joint inversion method for imaging simultaneous source time-lapse seismic data sets. The proposed method combines the cost-saving advantages of both simultaneous source acquisition and phase encoded migration (Romero et al., 2000). We further demonstrate that preconditioning with non-stationary dip filters and temporal smoothness constraints further improves the time-lapse seismic images.

We assume a known, slowly changing background baseline velocity. Because a close approximation of the background velocity is essential, we propose baseline data acquisition with separate or few simultaneous sources and monitor data acquisition with several simultaneous sources. We assume careful processing of the baseline data such that the data can be used for velocity estimation and the image can be used for dip estimation or interpretation. Furthermore, we assume that the shot-receiver positions and relative shot-timing are known for all surveys. Integration of background velocity and geomechanical changes into the joint inversion formulation is ongoing and will be discussed elsewhere.

In this paper, we first discuss Born modeling of phase-encoded data as an approximation of simultaneous source acquisition. Then, using a phase-encoded modeling/migration formulation, we discuss joint linear least-squares inversion of multiple simultaneous source seismic data sets. We also summarize a spatio-temporal preconditioning scheme based on spatial non-stationary dip-filters and temporal leaky integration. Finally, using a modified version of the 2D Marmousi model (Versteeg, 1994), we show that solving the preconditioned joint inversion problem yields optimal time-lapse seismic images.

Joint inversion of simultaneous source time-lapse seismic data sets