Inversion of seismic refraction amplitudes for near-surface velocity control

Abstract

Analysis of seismic refraction amplitudes has the potential to produce a richer geological interpretation than if only travel-times are considered. In theory, the amplitude of a seismic head-wave is dependent on the strength of the shot and the offset at which it is measured. A constant of proportionality, called the head-wave coefficient, is a function of the elastic properties either side of the refracting interface. As the velocity contrast between the two media decreases, the head-wave coefficient increases. A detailed examination of refraction amplitude theory reveals that the head-wave coefficient is a product of two Zoeppritz transmission coefficients, a downgoing one at the source end and an upgoing one at the receiver end. The bulk amplitude of the head-wave coefficient is mainly due to the transmission coefficient at the receiver end. However, the receiver component is relatively insensitive to lateral changes. On the other hand, the transmission coefficient at the source end is sensitive to lateral changes. Theoretical models, which simulate laterally inhomogeneous geologies, are used to forward-model refraction amplitudes. The head-wave coefficient is then estimated via non-linear inversion of refraction amplitudes. Inverted shot and receiver terms are shown to be related to the transmission coefficients at the shot and receiver ends. The product of the inverted shot and receiver terms are related to the full head-wave coefficient. The inversion cannot separate the effect of velocity contrast from short-wavelength shot/geophone coupling effects. Smoothing of the inverted solution is suggested as a means of reducing coupling effects. For laterally inhomogeneous models, offset limiting is required prior to inversion in order to achieve successful separation of constituent amplitude components. For offset-limited model data, the estimated model parameters exhibit consistency with the true model parameters in a relative sense. Non-uniqueness between parameter groups prohibits successful estimation of model parameters in an absolute sense. Calibration is therefore required to adjust the relative results obtained from inversion to results which are consistent with geology. This calibration uses independent estimates of weathering-layer velocity at several points along the seismic line. Calibration can be performed on the inverted shot terms alone, or the product of the inverted shot and receiver terms. The inversion methodology is evaluated on three real data sets. For the first Vibroseis dataset, the relative head-wave coefficient profile is consistent with that derived using an alternative approach (the Refraction Convolution Section). However, the implied weathering-layer velocity profile differs from that estimated by analysis of direct arrivals. For the second Vibroseis dataset, the derived weathering-layer velocity is reasonably consistent with the long-wavelength velocity profile derived from analysis of hammer shot records, acquired as part of the original survey. The CMP stack, incorporating the velocity profile from refraction amplitudes, shows subtle structural differences when compared to the conventional stack. The third dataset, which uses dynamite as a source, exhibits large variations in source strength. A velocity profile is not derived because these large source effects swamp any amplitude changes related to velocity changes at the refractor. For these real-data tests, offset limiting does not assist separation of the shot and receiver terms (as was the case for the model data). Independent statistical analysis of average shot and receiver amplitudes suggests that the inversion process itself is working correctly. However, it appears that in practice, observed refraction amplitudes are strongly influenced by factors not included in theoretical models. Further work is required before this technique can provide a reliable tool for near-surface characterisation.