Applications of Inverse Methods to the Analysis of Refraction and Wide-angle Seismic Data

The refraction inverse problem was initially investigated by Herglotz (1907), Bateman (1910), and Wiechert and Geiger (1910) who applied Abel transforms for the inversion of seismic travel-times in radially varying media. For smoothly varying media in the absence of low velocity zones, this formulation provides an inverse solution which includes ray bending. In the presence of low velocity zones, bounds on the solu­ tion can be obtained from discontinuities in the travel-time data. As an illustration of the inversion of refraction data in radially varying media, slant-stacked wavefield data are used to invert for velocity in the earth's upper mantle. The inversion of wavefield data avoids the picking of travel-times, but requires good quality refraction data which is well sampled in offset. In laterally varying media, an inversion formulation using seismic attributes has been developed. Examples of seismic attributes include envelope amplitudes, instantaneous frequencies, and phase times of selected arrivals. Ray per­ turbation theory is used to compute the sensitivity of different attributes to variations in the model. To illustrate the inversion of seismic attributes in laterally varying me­ dia, attributes extracted from observed refraction data are used to invert for shallow crustal structure. Iterative inversions from smooth to less smooth models are used to progressively incorporate the longer wavelength features of the model.