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 forwardmodel 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.iii 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 t...

Inversion methodology for determination of near-surface geology from seismic refraction amplitudes

“…Although ф has been reduced significantly, comparison between Figure 6 and Figures 2 and 4 suggests that this has come at the expense of geological certainty in the receiver domain. Because Meulenbroek (2010) showed that the receiver terms in Figure 2 are relatively consistent with the results obtained using Palmer's method, the fact that the receiver terms in Figure 6 differ suggests that while targeting the offset terms to reduce the residual error, the shot and offset terms have also been affected. Clearly a compromise must be reached whereby ф is reduced if possible, but with care taken to ensure the geological fidelity of the solution.…”

“…The reader is referred to Broyden (1965) and Doherty (2010) for further information. Figure 2 shows the result for the inverted shot, receiver and offset terms using a simple initial model and default control parameters generated by PEST (Meulenbroek, 2010). The runtime for this solution was 5 hours.…”

“…Palmer (2001aPalmer ( , 2001b attempted to do this using a novel approach called the refraction convolution section (RCS). Meulenbroek (2010) presented an alternative technique in which a surface-consistent, non-linear least-squares inversion scheme in employed. The formulation of this inverse problem has similarities to that of surface-consistent residual statics.…”

“…The formulation of this inverse problem has similarities to that of surface-consistent residual statics. This paper extends on Meulenbroek (2010), focussing more on the inversion methodology, namely the means of forcing the problem to a realistic solution as fast as, and with as little error, as possible.…”

Comparison of near-surface properties derived from non-linear inversion of refraction amplitudes versus the refraction convolution section

“…Palmer (2001aPalmer ( , 2001b published a method of doing this called the refraction convolution section (RCS). Meulenbroek (2010) presented an alternative technique where the problem is formulated as a formal, non-linear inverse problem. This paper presents a comparison of the two methods on a Vibroseis-scale dataset acquired for the Australian National Seismic Imaging Resource (ANSIR) in 1999.…”