Elastic parameter inversion of a sand body based on the exact reflection coefficient

Abstract Prestack seismic inversion is an important technology for oil and gas exploration that can provide accurate lithology and pore fluid information on underground media. Prestack inversion is theoretically based on the Zoeppritz equations, which establish the relationship between the seismic reflection coefficients of different offsets and elastic parameter contrasts between the interface of two lithologies. However, these are fourth-order matrix equations with a complex form and are difficult to be directly applied to inversion. Approximate analytical solutions have been used to establish a linear relationship between the seismic reflection coefficients and elastic parameters. And the approximations are based on the assumptions of a small angle and weak contrast, they cannot be applied to layers of high contrast, such as gas-bearing sandstones and coal seams. In this paper, we present an accurate prestack seismic inversion method that can be applied to a wider range of geological models. First, we derive the partial derivatives of the exact reflection coefficients of PP waves based on the Zoeppritz equations with respect to the elastic parameters and establish the exact Jacobian and Hessian matrices. Then, we use the least-squares algorithm to construct objective functions for the simultaneous inversion of three elastic parameters: The P-wave velocity, S-wave velocity, and density. Examples show that our inversion method is more accurate for strata with strong reflection interfaces than the approximate prestack inversion methods and stable under noisy conditions. The inversion method was applied in channel sand depositions of the Lower Permian Shanxi and Shihezi Formation of the Ordos Basin, and it was efficient to identify the gas-bearing sand layers and determine the range of potentially favorable areas.