Impedance-type approximations of the P-P elastic reflection coefficient; modeling and AVO inversion

The normal-incidence elastic compressional reflection coefficient admits an exact, simple expression in terms of the acoustic impedance, namely the product of the P-wave velocity and density, at both sides of an interface. With slight modifications a similar expression can, also exactly, express the oblique-incidence acoustic reflection coefficient. A severe limitation on the use of these two reflection coefficients in analyzing seismic reflection data is that they provide no information on shear-wave velocities that refer to the interface. We address the natural question of whether a suitable impedance concept can be introduced for which arbitrary P-P reflection coefficients can be expressed in a form analogous to their acoustic counterparts. Although no closed-form exact solution exists, our analysis provides a general framework for which, under suitable restrictions of the medium parameters, possible impedance functions can be derived. In particular, the well-established concept of elastic impedance and the recently introduced concept of reflection impedance can be better understood. Concerning these two impedances, we examine their potential for modeling and for estimating the AVO indicators of intercept and gradient. For typical synthetic examples, we show that the reflection impedance formulation provides consistently better results than those obtained using the elastic impedance.