Abstract

We represent a reflecting medium as a stack of weak elastic scatterers embedded in a background medium of known elastic characteristics. The superposition of the backscattered wave field from this volume of scatterers observed at a receiver leads to specular reflection. Under Born formalism, this process linearizes the wave field with the resulting approximate reflection coefficient a simple function of scattering characteristics of the scatterers. We use the method of stationary phase to evaluate the Born integral. To test the validity of the concept, we derive the expression for the linear reflection coefficient for a horizontal interface separating two isotropic half spaces. Finally, we derive the expression for linear reflection coefficient for an interface separating an isotropic media from another transversely isotropic half space with tilted axis of symmetry. Our numerical results demonstrate that neglecting the dip of symmetry axis results in significant error in amplitude versus offset and azimuth analysis specially if the symmetry axis has moderate dips.