No abstract

The generalized reciprocal method (GRM) is a technique for delineating undulating refractors at any depth from in‐line seismic refraction data consisting of forward and reverse traveltimes. The traveltimes at two geophones, separated by a variable distance XY, are used in refractor velocity analysis and time‐depth calculations. At the optimum XY spacing, the upward traveling segments of the rays to each geophone emerge from near the same point on the refractor. This results in the refractor velocity analysis being the simplest and the time‐depths showing the most detail. In contrast, the conventional reciprocal method which has XY equal to zero is especially prone to produce numerous fictitious refractor velocity changes, as well as producing gross smoothing of irregular refractor topography. The depth conversion factor is relatively insensitive to dip angles up to about 20 degrees, because both forward and reverse data are used. As a result, depth calculations to an undulating refractor are particularly convenient even when the overlying strata have velocity gradients. The GRM provides a means of recognizing and accommodating undetected layers, provided an optimum XY value can be recovered from the traveltime data, the refractor velocity analysis, and/or the time‐depths. The presence of undetected layers can be inferred when the observed optimum XY value differs from the XY value calculated from the computed depth section. The undetected layers can be accommodated by using an average velocity based on the optimum XY value. This average velocity permits accurate depth calculations with commonly encountered velocity contrasts.

A B S T R A C TThe performance of refraction inversion methods that employ the principle of refraction migration, whereby traveltimes are laterally migrated by the offset distance (which is the horizontal separation between the point of refraction and the point of detection on the surface), can be adversely affected by very near-surface inhomogeneities. Even inhomogeneities at single receivers can limit the lateral resolution of detailed seismic velocities in the refractor.The generalized reciprocal method 'statics' smoothing method (GRM SSM) is a smoothing rather than a deterministic method for correcting very near-surface inhomogeneities of limited lateral extent. It is based on the observation that there are only relatively minor differences in the time-depths to the target refractor computed for a range of XY distances, which is the separation between the reverse and forward traveltimes used to compute the time-depth. However, any traveltime anomalies, which originate in the near-surface, migrate laterally with increasing XY distance. Therefore, an average of the time-depths over a range of XY values preserves the architecture of the refractor, but significantly minimizes the traveltime anomalies originating in the near-surface. The GRM statics smoothing corrections are obtained by subtracting the average time-depth values from those computed with a zero XY value. In turn, the corrections are subtracted from the traveltimes, and the GRM algorithms are then re-applied to the corrected data. Although a single application is generally adequate for most sets of field data, model studies have indicated that several applications of the GRM SSM can be required with severe topographic features, such as escarpments.In addition, very near-surface inhomogeneities produce anomalous head-wave amplitudes. An analogous process, using geometric means, can largely correct amplitude anomalies. Furthermore, the coincidence of traveltime and amplitude anomalies indicates that variations in the near-surface geology, rather than variations in the coupling of the receivers, are a more likely source of the anomalies.The application of the GRM SSM, together with the averaging of the refractor velocity analysis function over a range of XY values, significantly minimizes the *

Seismic refraction data are characterized by large moveouts between adjacent traces and large amplitude variations across the refraction spread. The moveouts are the result of the predominantly horizontally traveling trajectories of refraction signals, whereas the amplitude variations are the result of the rapid geometric spreading factor, which is at least the reciprocal of the distance squared. The large range of refraction amplitudes produces considerable variation in signal‐to‐noise (S/N) ratios. Inversion methods which use traveltimes only, employ data with a wide range of accuracies, which are related to the variations in the S/N ratios. The time section, generated by convolving forward and reverse seismic traces, addresses both issues of large moveouts and large amplitude variations. The addition of the phase spectra with convolution effectively adds the forward and reverse traveltimes. The convolution section shows the structural features of the refractor, without the moveouts related to the source‐to‐detector distances. Unlike the application of a linear moveout correction or reduction, a measure of the refractor wavespeed is not required beforehand. The multiplication of the amplitude spectra with convolution, compensates for the effects of geometric spreading and dipping interfaces to a good first approximation, and it is sufficient to facilitate recognition of amplitude variations related to geologic causes. These amplitude effects are not as easily recognized in the shot records. The convolution section can be generated very rapidly from shot records without a detailed knowledge of the wavespeeds in either the refractor or the overburden.