Perturbation theory has been widely used in many applications in seismology, more recently for time-lapse problems. We have formulated a scheme for modeling linear and nonlinear elastic time-lapse difference amplitude variation with offset data. We have expressed this framework as an expansion in orders of the baseline interface properties and time-lapse changes from the time of the baseline survey to the time of the monitor survey. We have examined our formulation with the numerical data used in literature for real time-lapse data. The results indicated to the first order that our framework for time-lapse difference data is in agreement with Landrø’s linear approximation. The higher order terms represented corrections appropriate for large P- and S-wave velocities and density contrasts in the reservoir from the time of the baseline survey to the time of the monitor survey. A physical modeling data set was acquired simulating a time-lapse problem to validate our theoretical results. Plexiglas, polyvinyl chloride (PVC), and phenolic slabs were used as proxy materials to simulate the cap rock and reservoir at the time of the baseline and monitor surveys, respectively. Reflected amplitudes were picked at Plexiglas-PVC and Plexiglas-phenolic interfaces and were corrected for geometric spreading, emergence angle, free surface, transmission loss, and radiation patterns. Our results indicated that higher order expansion terms, involving products of elastic time-lapse perturbation and baseline medium perturbation, matched laboratory data with significantly reduced error in comparison with linearized forms. We have concluded that in many plausible time-lapse scenarios, the increase in accuracy associated with higher order corrections that we observed enhanced the time-lapse modeling.

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