Is forward modelling as efficacious as minimum variance for refraction inversion?

Abstract

One aspect of the inversion of refraction data is the determination of the velocity stratification of the layers above the target refractor. This aspect is notoriously unreliable with the standard approach in which the travel-time graphs are used to determine the relevant model and compute its parameters, because of the common existence of undetected layers, velocity inversions, variable velocity media, and vertical seismic anisotropy. While forward modelling with ray tracing can ensure that any result is compatible with the travel-time data, it does not ensure that the model selected is appropriate or that its parameters are well determined. Furthermore, there can be a considerable range in the depths computed with the various models which honour the travel-time data. Therefore, forward modelling is of little value in resolving most ambiguities in the velocity stratification above the target refractor. The other aspect of refraction inversion is the resolution of structure and seismic velocity within the refractor. This can be achieved with the generalized reciprocal method (GRM) and the minimum variance criterion, while still honouring the traveltimes to the target refractor. The use of specific ray tracing routines is not essential. In addition, the optimum XY value is a function of the thicknesses and seismic velocities of all layers above the refractor. Depths computed with the GRM approach have smaller errors than with the standard approach, they are usually related to the accuracy in determining the optimum XY value, and they are largely independent of the model selected. Furthermore, the GRM is able to make reasonable depth estimates for models which include the velocity inversion and the vertical anisotropy problems, for which the standard approach has no recognised solutions. It is proposed that forward modelling with ray tracing is neither a necessary nor a sufficient condition in refraction inversion.