No abstract

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.

Although accurate depth-migration is essential for the correct geometrical interpretation of deep reflection data, migration by the standard numerical methods has generally not been satisfactory. The alternative method presented in this paper provides an efficient migration for deep reflection profiles in the form of a digitized line-drawing assuming a general, 2-D velocity structure. Migration of a digitized line-drawing reduces the effects of low signal/noise ratios. The calcutation is rapid allowing migrations to be calculated for a large number of alternative velocity structures and iterative improvement of the velocity structure. The migration has been applied to 3-D structures observed on intersecting profiles collected by BIRPS (British Institutes Reflection Profiling Syndicate).

S U M M A R YFor a geological feature to be resolved in a seismic reflection profile its size must be comparable with the dimensions of the Fresnel zone for its depth and the frequency-content of the seismic wavefield. Since the diameter of the Fresnel zone is over 5 km for lower-crustal reflections, the effects of variations of the crust on smaller length scales must be considered when interpreting deep reflection profiles.Modelling the seismic wavefield using first-order scattering theory shows how the reflections observed in a small-offset profile are affected by the statistical distribution of elastic vanations within the crust. Crustal heterogeneities on length-scales smaller than the seismic wavelength cause frequency-dependent attenuation which can be comparable with the losses due to anelastic absorption. Larger scale elastic variations cause rapid loss of coherence in the seismic field. The observation of deep seismic reflections can thus be used to constrain the degree to which the crustal elasticity varies on small length scales. Coherent seismic reflections from the lower crust limit the fractional variation of elasticity averaged over the entire crust to a few percent on a wide range of length-scales.