PHASE VELOCITY DEPENDENT P-WAVE REFLECTION COEFFICIENT EQUATION FOR VTI/VTI MEDIA

Amplitude variation with offset (AVO) has become a commonly used seismic attribute in the petroleum exploration to reveal the lithology and estimate pore fluids underground. However, strata usually exhibit velocity anisotropy, thus the effect of anisotropy must be taking into account when applying the AVO analysis. Ruger's approximation of the P-wave reflection coefficient equation at an interface between two vertical transverse isotropic (VTI) layers, in welded contact, is widely used in anisotropic AVO analysis. Based on Ruger's approximate equation, a new anisotropic term of the P-wave reflection coefficient for VTI/VTI media is derived in this study which is only function of the velocity difference between the incident angle dependent phase velocity and the vertical velocity. Ruger's, Banik's and new derived approximate equations of the P-wave reflection coefficient for three commonly occurring in close in-situ proximity shale and gas sand models are calculated and compared. Study results show that the anisotropic effect is important in the reflection amplitude even though the anisotropies of the two layers are weak. Since the anisotropic effects of the P-wave phase velocity is dominated by the anisotropic parameter delta for VTI media within small incident angles, the anisotropic effect of the reflection P-wave amplitude within intermediate offset is also dominated by delta. All approximate equations fit the exact solution well within the intermediate offset except the anisotropic parameter epsilon is large. For the far offset, above approximate equations using to analyze the anisotropic reflection amplitude must be avoided except for analyzing the negative high acoustic impedance contrasts data by using the new derived approximate equation. In addition, this new derived approximate equation has a simple and direct physical meaning which is useful in understanding the effect of anisotropy on the AVO response.