REFLECTION, REFRACTION, AND DIFFRACTION OF WAVES IN MEDIA WITH AN ELLIPTICAL VELOCITY DEPENDENCE

Assuming media having a velocity dependence on angle which is an ellipse, previously reported time-distance relations are confirmed for reflections from single interfaces, for reflections from sections of beds separated by horizontal interfaces, and for refraction arrivals, and the expression for diffractions is added. Expressions for plane-wave reflection and transmission coefficients at an interface separating two transversely isotropic media are also derived. None of the properties differs greatly from those for isotropic media. However, velocities found from seismic surface reflections or refractions are horizontal components. There seems to be no way of obtaining vertical components of velocity from surface measurements alone and hence no way to compute depths from surface data.