Ambiguities in AVO inversion of reflections from a gas‐sand

Abstract

We examine the reflections from a thick sand layer embedded in shales deposited in an open marine environment of Miocene age. Borehole data indicate that the sand bed is gas saturated. Making the assumptions of single interface reflections, plane‐wave propagation in elastic and isotropic media, and correct amplitude recovery of the actual seismic data, we try to invert the amplitude variation with offset (AVO) response for the compressional velocity [Formula: see text], shear velocity [Formula: see text], and density [Formula: see text] of the gas‐sand layer, knowing the parameters of the upper layer and the calibration constant. The actual reflections reach incidence angles up to 54 degrees at the farthest offset. Notwithstanding the large range of incidence angles, the outcomes of the inversion are ambiguous for we find many solutions that fit equally well, in a least‐squares sense, the observed AVO response. We present the locus of the solutions as curves in compressional velocity [Formula: see text], shear velocity [Formula: see text], and density [Formula: see text] space. To gain a better understanding of the results, we also perform the same inversion experiment on synthetic AVO data derived from the borehole information. We find that when inverting the AVO response in the same range of incidence angles as in the real data case, the exact solution is found whichever starting point we choose; that is, we have no ambiguity. However, if we limit the incidence angle range, e.g., to 15 degrees, the invention is no longer able to find a unique solution and the set of admissible solutions defines regular curves in [Formula: see text], [Formula: see text], [Formula: see text] space. We infer that residual noise in the recorded data is responsible for the ambiguities of the solutions, and that because of numerical noise, a wide range of incidence angle is required to obtain a unique solution even in noise‐free synthetic data.