Diffraction modelling of 3-D lower-crustal reflectors

The length of the acoustic path and the limited band-width of the lower crustal reflections in near-normal-incidence profiles give a Fresnel Zone radius of the order of 2–3 km for the lower crust. In this situation, interpretations of the lower crust cannot be based solely on geometrical optics, which is a high-frequency approximation, but must take into account the effects of diffraction. A mathematical model based on the Kirchhoff Integral estimates diffraction effects in the acoustic field and allows the reflections observed from a laterally varying, first-order discontinuity to be calculated for arbitrary source and receiver locations. A simplified form of the Kirchhoff Integral provides a clear physical model for the form of the reflected field including diffraction effects. This model is used to study synthetic sections and several useful interpretational rules for deep reflection data are inferred. The simplified formula indicates the limitations of interpretations based on geometrical optics. It shows that although geometrical optics cannot explain the amplitudes of the reflected image, it does correctly predict the arrival-times of the major observed reflections. This justifies a depth migration method based on ray-tracing.