Joint wave-equation inversion of time-lapse seismic data

Introduction

Hydrocarbon exploration and production has gradually shifted from simple to complex geological environments. Relatively simple imaging and monitoring objectives (e.g. anticlinal-type traps) have been replaced by more complex ones (e.g., sub-salt reservoirs and stratigraphic traps). Since most of the current time-lapse seismic imaging technologies are inadequate in many emerging frontiers, new imaging and monitoring methods are required. In addition, differences almost always exist between acquisition geometries of different seismic datasets. Such geometry differences may be due to new (or more efficient) acquisition systems and design, production facilities (absent at the time of the baseline survey) or nature (e.g., ocean currents).

Our goal is to attenuate artifacts from two major sources:

1. poor and uneven sub-surface illumination in reservoirs under complex overburden, and
2. disparities in acquisition geometries of the baseline and monitor surveys.

We achieve these objectives by simultaneously inverting migrated images from different vintages with a target-oriented approximation (Valenciano, 2008) to the linear least-squares wave-equation Hessian. The Hessian operator in this problem can be regarded as a set of non-stationary deconvolution filters in a single survey, or a concatenation of sub-matrices built from such filters in multiple surveys. We discuss two joint-inversion formulations of the seismic monitoring problem:

1. regularized joint-inversion for image differences (RJID):
   • input: staggered sums of migrated images, and
   • output: inverted baseline image and image differences between successive surveys;
2. regularized joint-inversion of multiple images (RJMI)
   • input: migrated images for all surveys,
   • output: inverted images for all input surveys.

Solving a single joint-inversion problem enables the incorporation of prior knowledge of the reservoir location, extent and geometry, temporal constraints or information from other sources (e.g., production history-matching).

As previously noted, inputs into the RJID formulation are staggered sums of migrated images from multiple surveys and the outputs are inverted baseline and time-lapse images between successive surveys. Since the imaging and monitoring objectives are decoupled, different regularization schemes can be defined for the baseline and time-lapse images. Inputs and outputs to RJMI are migrated images and corresponding inverted images respectively. RJMI differs from separate inversion, because a coupling operator introduces desirable temporal constraints during inversion.

In order to arrive at both formulations, we have assumed that the background baseline velocity model is known and that it changes slowly between surveys. We also assume that such small velocity changes have negligible impact on wave propagation through the earth, at least to the top of the reservoir. Where there are noticeable displacements between images -- as a result of significant velocity changes or geomechanical effects around the reservoir -- an event alignment step (Hale, 2007) can be applied prior to inversion.

In this paper, we briefly summarize the seismic monitoring problem, and then we discuss the basic theory of linear least-squares inversion and its extension to the RJID and RJMI formulations for an arbitarary number of surveys. Finally, using six datasets from a 2D-synthetic sub-salt model, we show that both joint-inversion formulations yield noticeably improved results over migration or separate inversion.

Joint wave-equation inversion of time-lapse seismic data