Calibrating the 4D signal at the well with information obtained from production data is essential for it to be used quantitatively. We have developed a model-based inversion method to estimate the changes of elastic parameters in the reservoir due to production at the well. Our scheme is based on the observation that flow behavior is constrained by the dynamic properties of the layer (i.e., permeability), and, therefore, a layered model should be used to parameterize the inversion. The inversion scheme considers traveltime (inside and below the reservoir, but not in the overburden) and impedance effects implied by the change of elastic parameters (inside the reservoir). Therefore, even at zero offset, we can separate changes in density from changes in P-velocity. When using multiple offset data, we can use an exact formulation for the reflectivity if the base logs (density, P-velocity, and S-velocity) are available, otherwise, an approximation to the exact form can be used. Theoretical and practical analyses have shown that P-velocity is the best resolved parameter followed by density and, finally, S-velocity. Compared to classical data-driven inversion, our procedure introduces fewer artifacts and is less sensitive to tuning because the layered model parameterization introduces the missing low and high frequencies (although the seismic bandwidth plays an essential role in the resolution). This 4D inversion at the well is part of a larger scheme that uses the results obtained by this scheme to extend the inversion to the whole data set.

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