Waveform inversion of time-corrected refraction data

Abstract

SUMMARY Seismic refraction data collected in land or marine surveys are often complicated by small, near-random time shifts of the individual seismograms relative to one another. For the case of fixed-receiver geometry, these shifts arise primarily from basement topography, often masked by sediments, beneath each source. Although a topographic timing correction is normally applied to the seismograms, the effects of poorly-known topography produce residual shifts in the seismograms. The application of additional time corrections (statics) can bias solutions computed using iterative waveform inversion, because a suitable set of statics can make a poor starting velocity model appear to match the data. Without any correction, however, seismograms computed from even the best-fitting laterally homogeneous model may not agree with the data to within one-half period. In this paper I present a formalism for iterative waveform inversion of refraction data containing residual time shifts. In this method the statics are directly modelled in the synthetic seismograms, and new values estimated in the inversion together with new velocity model parameters. The method is similar to studies of statics in seismic reflection data, but in this case values for the statics are estimated simultaneously with the velocity model; with the use of suitable norms the new velocity model is required to be smooth and the statics required to be small. Convergence is achieved when the velocity profile's roughness, the RMS size of the statics, and the waveform misfit are in equilibrium. Because the starting synthetics need not match the data to within one-half period, a much larger set of velocity models used for an initial guess will converge on the family of solutions than for waveform inversions in which time shifts are not used. The original, arbitrary starting model loses its importance after the first iteration, and solutions meeting the convergence criterion appear to be independent of the particular choice of starting model. Numerical tests show the method to be robust: an inaccurate starting model that fits the data only through a biased set of statics is accurately corrected. The method is illustrated on a set of refraction data collected in the vicinity of the East Pacific Rise. In this application two quite different starting velocity models converge to a common family of solutions.