We introduce here an integral two-dimensional (2-D) scheme for the processing of deep crustal reflection profiles. This approach, in which migration occurs before stacking, is tailored to the unique character of the data in which nonvertically propagating energy is as important as vertically propagating energy. Since reflector depths range beyond 30 km, the horizontal displacement of reflections which occurs in migration can be as large as reflector depths; under these circumstances, the common-midpoint (CMP) stack is inadequate.In our scheme, each common-source trace gather is transformed into a set of traces (beams) corresponding to a set of different incidence angles. A correction for wavefront curvature similar to the normal moveout (NMO) correction yields traces (focused beams) which are focused at image points along the direction of arrival. While the method is equivalent to the Kirchhoff integral migration method, and therefore to any complete continuation method, it gives rise to an intermediate data set which is characterized by the direction of arrival of the upward propagating energy. By a geometrical transformation of the beams and summation, we may synthesize images composed of a specified range of Fourier spatial components. Geologic examples suggest that complex structures in the basement may be most easily characterized by their local direction of layering, a quantity we may determine by this approach.Noise-free synthetic data examples illustrate the limits of horizontal and vertical resolving power at mid-crustal depths for any imaging method. Velocity determination is difficult at these depths due to the small NMO and may be possible only by evaluating the effects of velocity models on the imaged data. Examples of the imaged section from the COCORP test profile in Hardeman County, Texas, show a combination of horizontally continuous reflectors and an irregular pattern of scatterers with locally horizontal layering.

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