Seismic imaging and wave scattering in zones of random heterogeneity

Most current interpretations of lower crustal seismic reflectivity suggest the existence of fine-scale ({dollar}{bsol}approx{dollar}100 m thick) layered structures at depth. Typical common-midpoint (CMP) stacked images of deep structures are, however, noisy and show discontinuous reflections characterized by numerous subhorizontal segments. Present interpretation techniques cannot definitively resolve whether such a reflection response is attributable to heterogeneity at the target or whether the seismic image is distorted by propagation effects and contaminated by noise. The quantitative assessment of lateral heterogeneity in the deep crust is fundamental to understanding mechanisms of crustal formation and evolution.; Here, crustal heterogeneity is represented by velocity structures that vary randomly in two dimensions, with a correlation distance comparable to the dominant wavelength of the seismic source. Synthetic CMP seismic data are computed for various models using a fourth-order finite-difference solution to the acoustic wave equation. A conventional data processing sequence produces CMP stacked sections with greater lateral continuity than is present at the target and an overall appearance comparable to that of field-recorded data. Lateral coherence is quantified using the spectral coefficient of coherence, applied to trace pairs having various spatial separations. Increased continuity in the CMP stack is attributable to the dip-filtering action of stacking and can be compensated by the application of migration before stack or equivalent processes.; The reflection response observed in common-shot trace gathers shows amplitude and lateral coherence increasing with offset, an effect attributable to the source-receiver geometry. Observed wavefield coherence is related to the correlation properties of the target through a convolutional expression. A field data example from the Black Forest, Germany shows that enhanced coherence can be expected in wide-angle field experiments and that a model having two-dimensional heterogeneity matches field data previously interpreted in terms of extreme fine-scale layering. A densely-sampled field data set from the Basin and Range Province, Nevada shows increased coherence for P{dollar}{bsol}sb{lcub}{bsol}rm m{rcub}{dollar}P at large offsets. Observed lateral coherence values are lower than predicted for scattering purely in the Moho transition zone; coherence levels can be modeled by including scattered energy from inhomogeneities above the target zone.