Seismic reflectivity and transmissivity parametrization with the effect of normal in situ stress

SUMMARY In situ stress has a significant effect on the properties of underground formations, including seismic wave velocity, porosity and permeability, and further affects seismic reflectivity and transmissivity. Research works on the effect of in situ stress are helpful to construct more precise seismic reflection and transmission coefficient equations. However, previous studies on seismic reflectivity equations did not take the effect of normal in situ stress into consideration. The mechanism of stress on seismic reflectivity and transmissivity is still ambiguous. In this study, we propose new explicit equations to help analyse the changes of seismic reflectivity and transmissivity under the effect of normal in situ stress. First, we deduce the Christoffel equation on the basis of solid acoustoelastic theory. Then, we utilize appropriate boundary conditions to formulate analytical equations of the reflectivity at the interface between two stressed formations, which can provide some new insights into the role of in situ stress. The shear wave birefringence will vanish because we assume that the wave propagates in the X–Z plane. Different rock models with different lithology and saturation are used to analyse the variation of seismic reflectivity and transmissivity with normal stress and incident angle at the interface. The main effect of normal stress on reflection and transmission coefficients is to change amplitude and critical incident angle. When the upper and lower layers are sandstones, the critical incident angle decreases with the increase of normal in situ stress, which is consistent with previous studies. In addition, the reflectivity equation can be degenerated to the Zoeppritz equation when the normal in situ stress vanishes, which further validates that the equation proposed is correct. Seismic reflectivity equations that couple the effect of stress can lay a foundation for direct prediction of in situ stress.