Reflection and transmission approximations for monoclinic media with a horizontal symmetry plane

Abstract

We have considered a horizontal plane interface bounded by two monoclinic half-spaces to approximate the reflection and transmission (R/T) responses normalized by the vertical energy flux. We assume the monoclinic media have a horizontal symmetry plane, and the exact R/T coefficients can be analytically obtained for P-, S1-, and S2-waves. The exact R/T coefficients depend on the absolute model parameters of both half-spaces, whereas the R/T responses indicate the heterogeneity at the interface and, thus, can be characterized with model parameter contrasts across the interface. Compared with the exact R/T solutions, appropriate approximations with desirable accuracy can be determined by fewer model parameter contrasts and facilitate the parametric analyses and inversions. We first consider the weak-contrast assumption and use the perturbation method to obtain first-order approximations based on the homogeneous monoclinic background medium. To accommodate the strong-contrast interface, the published second-order approximations are then revised for the monoclinic media. For weakly anisotropic media, the first- and second-order approximations are proposed based on the isotropic background medium. Two pseudowaves are introduced as intermediate waves to legitimize our approximations for S1, S2, and converted waves in the applications. The derived approximations are verified on monoclinic models numerically. The second-order approximation method based on the monoclinic background medium is proven to have the overall best accuracy.