Statistical modelling of lower-crustal reflections

For 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. Key words: deep seismic reflection, lower-crustal reflection, statistical crustal model, first-order scattering, Born scatterin