An analysis of time-lapse phase shifts using perturbation theory

Shahin Jabbari, Kristopher A. Innanen

Scattering or perturbation theory has been widely used in many applications in seismology, including time-lapse problems. One of the main challenges in using scattering theory to predict the model for the difference data in a time-lapse problem is, the reference medium, the baseline survey, being a medium as complicated as the perturbed medium, the monitoring survey. We produce the linear and higher order terms in the forward scattering series for the difference data for the phase-shift changes between the baseline and monitor surveys in a reservoir. The baseline surveying is taken to be a homogeneous single layer for simplicity, but can be extended for a more complicated medium in future research. Green's function for characterizing the wavefield in this reference medium has a term describing the wave reflected from the interface at the time of the baseline survey. This leads to extra terms in the first and higher order approximations of the difference data when compared with a standard scattering problem. These extra terms are a function of the reflectivity of the single interface in the baseline survey and the perturbation due to production in the reservoir. Our perturbation theory for nonlinear time-lapse seismic inversion, which is the future steps in this research, will accommodate multidimensional and multi-parameter problems which will lead to more complete and general versions.