Geometric spreading in orthorhombic media

Abstract

Geometric spreading is an important factor that needs to be taken into account in the analysis of seismic amplitudes. In particular, when using any modification of amplitude variation with offset or amplitude versus azimuth methods, the effect of geometric spreading is crucial to isolate the effect of reflection from a particular interface. The relative geometric spreading controls the amplitude of seismic waves passing through a velocity model. In the case of an anisotropic medium, geometric spreading becomes very complicated. Usually, geometric spreading is computed from ray tracing. I have derived simple analytical formulas to compute the relative geometric spreading of P-waves in a stack of acoustic orthorhombic layers with azimuthal variations in symmetry planes. I also analyzed the kinematic properties of the derived equations and performed sensitivity analysis with respect to three anelliptic parameters. A simple and accurate approximation for the relative geometric spreading is derived and tested against well-known approximation. My approximations give insight into the role that anelliptic parameters play into the azimuthal distribution of amplitudes and can be used for amplitude analysis in multilayered orthorhombic models.