A Second-Order Approach for P-Wave Elastic Impedance Technology

Abstract

Previous formulation for P-wave elastic impedance (EI) technology considers only first-order effects in isotropic reflectivity. In this paper, Wang's pseudo-quadratic approximation for PP-wave reflection (RPP) coefficients is used, in order to incorporate nonlinear effects into EI equation. In comparison with coefficients computed with the conventional linear approximation, Wang's pseudo-quadratic formula shows higher accuracy at far incidence. A further nonlinear component in the intermediate region of incidence is responsible for the high accuracy achieved with the pseudo-quadratic Rpp coefficient formula. By applying the same procedures of previous linear formulation to Wang's pseudo-quadratic Rpp coefficient, a second-order approach for EI equation is obtained. This novel approach is formed by multiplication of two terms. The first term represents the previous linear approach for EI equation. As for the second term, it is interpreted as the correction of first-order EI formula to second-order effects. As expected, specialization of the second-order EI equation to normal incidence results in the well-known acoustic impedance (AI). Assumption of invariability in fundamental elastic properties leads to simplification of mathematical procedures. However, high contrasts possibly found within the log window under investigation may corrupt the computation of EI logs by introducing numerical errors. Although two procedures are proposed to cope with numerical errors, modeling shows that the second-order approach for EI is robust enough to handle high contrasts in elastic parameters. Actual well logs are used to verify performance of the novel EI equation in reproducing the amplitude-versus-offset (AVO) response of a mature, oil-bearing sandstone resevoir. As a result, influence of nonlinear effects, which are incorporated into EI equation, is observed on amplitudes and on frequency bandwidth of synthetic seismograms generated at a high angle of incidence. Further experiments with actual well data focus on crossplotting EI logs against fundamental elastic parameters. In terms of accuracy, the outcomes reveal that lithofacies classification can benefit from using the elaboration of EI technology derived in this work.