First-order approximation of seismic parameters in AVO intercept and gradient changes are not sufficient to estimate changes in saturation and pressure accurately. Analysis from an unconsolidated reservoir and a compacting reservoir show that we need to consider higher order terms in seismic parameters to reduce the inaccuracy of the estimates. Here, in this paper, we implement the non-linear optimization method to estimate changes in saturation and pressure using reflectivity equation directly. We test the applicability of this non-linear optimization method on synthetic data for both the reservoir scenarios over an wide range of saturation and pressure changes. We observe that the inversion results using the new method are reasonably good in both reservoir scenarios.
Changes in saturation (?S) and pressure (?P) can be estimated by using time-lapse amplitude variation with offset (AVO) seismic data (Landrø, 2001). The method requires near- and faroffset stacked data of base and monitor surveys as inputs and then directly invert for time-lapse ?S and ?P. The method is based on the linearized AVO equation of Smith and Gidlow (1987) and considers only the first order approximation in the relative changes of the seismic parameters ([equation]). Trani et al. (2011) observed that the Landrø’s method (considering 1st order approximation of seismic parameters in Smith and Gidlow (1987) equation) under-predicts the gradient reflectivity changes (?G) leading to strong leakage between estimated pressure-saturation changes. Recent work by Bhakta and Landrø (2014) showed that the Landrø’s method under predicts both ?G and ?R0 due to saturation changes, for unconsolidated shallow sand reservoir. Therefore, it is necessary to include second order terms in Landrø’s approximation to increase the accuracy in ?R0 and ?G (Bhakta and Landrø, 2014).
As both ?G and ?R0 have quadratic terms or the products between the relative changes in seismic parameters ([equation]) and reservoir parameters (S, P), the whole expression becomes highly non-linear. Trani et al. (2011) used the Gauss- Newton algorithm to invert for ?S and ?P considering up to second order terms in the seismic parameter changes and replacing them by the changes in reservoir parameters (i.e., ?S and ?P). Whereas, Bhakta and Landrø (2014) presented a method to estimate time-lapse ?S and ?P by replacing Landrø’s one-step method with a multi-step inversion approach that can directly use Smith and Gidlow (1987) equation without any approximation in it. Here, in this paper we implement the non-linear optimization method (the Levenberg-Marquardt (LM) method (Aster et al., 2013)) to estimate ?S and ?P using the Smith and Gidlow (1987) equation directly. We test the applicability of this non-linear optimization method on synthetic data for two different reservoir scenarios: one is an unconsolidated shallow sand reservoir and another one is a compacting chalk reservoir. Inversion results using the LM method are reasonably good in both the reservoir scenarios.