Can Linear Inversion Achieve Detailed Refraction Statics?

Abstract

In recent years, generalised linear inversion or GLI, has been used to process seismic refraction data in order to determine the long wavelength statics correction not adequately addressed by residual statics routines. With GLI, a model of the subsurface is refined after comparing the traveltimes of the model with the field data. This approach of constructing a model which agrees with the data is known as Backus-Gilbert construction. Unfortunately, it does not produce a unique solution. Furthermore, the forward modelling aspect using ray tracing is of questionable efficacy because of incomplete knowledge of the surface layer velocities as a function of depth and direction, the widespread occurrence of diffractions with irregular refractors, and inadequate spatial sampling. Furthermore, the accuracy of the inversion can be poor with complex weathering problems. An alternative approach is the formation of linear combinations of the data to generate unique averages of the model. This is known as Backus-Gilbert appraisal, and includes the GRM. However, the spatial sampling employed with most CMP acquisition programs precludes the use of any detailed refraction method, such as a fully optimised GRM approach. Instead a migration distance of a single station separation is used to compensate for the effect of the extended receiver array, to produce an effective CRM model. The CRM linear averages, also known as time-depths, are converted to a weathering replacement correction, using a ratio which is a function of the ratio of the weathering and sub-weathering seismic velocities. These CRM corrections are within a few milliseconds of the values computed with a fully optimised GRM approach.