I advocate to integrate all observations of a reservoirs into a single inversion for parameters. Seismic time lapse surveys are sensitive to saturation changes and, consequently, overlap with other subsurface measurements, such as the petroleum engineer's well tests. A joint inversion guarantees a consistent estimate and a framework of interpretation. Furthermore, the interference of independent information introduces new constraints and may make an integrated inversion feasible.
The integration may change traditional acquisition design, subsurface parameterization, and processing of the available observations. The various experiments ought to be reevaluated with respect to their contribution to the overall resolution of unknown reservoir properties. Overall, the inversion framework should help scientists to improve and harmonize the various experiments. In practice, the shear size of an integrated inversion may require separate inversions of the various data types. However, integrated studies should clarify the conceptual formulation. Any practical approximations and shortcuts should be chosen with a clear understanding of their consequences.
The current approach of interpreting difference sections of time-lapse experiments is an incomplete formulation of the underlying inversion problem. One might describe it as a first step of the more comprehensive inversion. I believe, that a clever approach to the integrated inversion may, however, very well include the formulation of such difference sections. I wonder if Symes' Difference Semblance Optimization 1991 could be extended to the time-lapse formulation.
This document discussed simulation models and partial differential equations for wave and fluid propagation in porous rocks. Among several alternative models, I emphasized Gassmann's model of elasticity and Darcy's fluid flow model for black oil. The models share similar parameterization and degree of parsimony. However, I implemented starkly simplified finite difference algorithms for both experiments. A future inversion of the simplified simulators should guide any necessary improvement of my implementations.