Derecke Palmer

An introduction to the generalized reciprocal method of seismic refraction interpretation

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.

Imaging refractors with the convolution section

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 sourc...

Resolving refractor ambiguities with amplitudes

Amplitudes are used to constrain refraction models. This study demonstrates that the refraction time section generated through the convolution of forward and reverse refraction traces together with a static shift facilitates the convenient recognition of amplitude variations related to changes in refractor wavespeed. For large contrasts in wavespeeds between the upper layer and the refractor, the head coefficient is approximately proportional to the ratio of the specific acoustic impedances. Since the convolution operation effectively multiplies the amplitudes of the forward and reverse arrivals, the convolved amplitudes are proportional to the square of this ratio. In general, the higher the contrast in the refractor wavespeed and/or density, the lower the amplitude. The regions recognized in the wavespeed analysis function correlate with those determined with amplitudes, thereby providing an additional constraint on inversion with model-based approaches.

Are refraction attributes more useful than refraction tomography

A seismic attribute is any measure that helps to better visualize or quantify features of interest in seismic data. Several refraction attributes, in addition to seismic velocity, can be readily computed from the first arrivals in seismic data. Refraction attributes can be usefully employed in the geotechnical characterization of the near surface. The major effect of tomography is largely cosmetic because it rarely improves resolution. Numerous refraction tomograms, which range from the geologically improbable to the very detailed, can satisfy the travel time data to sufficient accuracy. In the initial or reconnaissance stage, refraction attributes can be used to compute detailed starting models and to resolve non-uniqueness inherent in refraction tomography. Whereas refraction tomography non-uniquely models the single attribute of seismic velocity, this study demonstrates that the additional model parameters of scaled density ratio and P-wave modulus strength can be readily computed from combinations of refraction attributes. The spatially extensive refraction attributes can then be integrated with quantitative borehole and other geotechnical data using multivariate geostatistics. It is concluded that more useful quantitative geotechnical models of the near surface can be obtained by employing a wider range of attributes than the seismic velocity alone.

Maximising the lateral resolution of near-surface seismic refraction methods

The tau-p inversion algorithm is widely employed to generate starting models with most computer programs, which implement refraction tomography. This algorithm emphasises the vertical resolution of many layers, and as a result, it frequently fails to detect even large lateral variations in seismic velocities, such as the decreases which are indicative of shear zones. This study demonstrates the failure of the tau-p inversion algorithm to detect or define a major shear zone which is 50 m or 10 stations wide. Furthermore, the majority of refraction tomography programs parameterise the seismic velocities within each layer with vertical velocity gradients. By contrast, the Generalized Reciprocal Method (GRM) inversion algorithms emphasise the lateral resolution of individual layers. This study demonstrates the successful detection and definition of the 50 m wide shear zone with the GRM inversion algorithms. The existence of the shear zone is confirmed by a 2D analysis of the head wave amplitudes and by numerous closely spaced orthogonal seismic profiles carried out as part of a later 3D refraction investigation. Furthermore, an analysis of the shot record amplitudes indicates that a reversal in the seismic velocities, rather than vertical velocity gradients, occurs in the weathered layers. The major conclusion reached in this study is that while all seismic refraction operations should aim to provide as accurate depth estimates as is practical, those which emphasise the lateral resolution of individual layers generate more useful results for geotechnical and environmental applications. The advantages of the improved lateral resolution are obtained with 2D traverses in which the structural features can be recognised from the magnitudes of the variations in the seismic velocities. Furthermore, the spatial patterns obtained with 3D investigations facilitate the recognition of structural features such as faults which do not display any intrinsic variation or ‘signature’ in seismic velocities.

Contrasts in morphogenesis and tectonic setting during contemporaneous emplacement of S- and I-type granitoids in the Eastern Lachlan Fold Belt, southeastern Australia

Abstract Integrative gravity and structural modelling of Ordovician-Silurian granitoids in the Eastern Lachlan Fold Belt (southeastern Australia) revealed contrasts in emplacement mode and deformation style between coeval S- and I-type granites. The NNE-SSW directed contraction during the Benambran event of the Lachlan Orogen caused dextral movement along two major strike-slip faults (Carcoar Fault/Copperhannia Thrust) and simultaneous formation of both transtensional pull-apart and transpressional shear zones. The geometry and deformation style of the plutons and country rock, their spatial relationship at depth to adjacent faults and the structural history of both the granites and country rocks suggest a genetic linkage between magma emplacement and synmagmatic deformation. Synchronously, the Carcoar Granodiorite was emplaced into a transtensional pull-apart structure and the Barry Granodiorite and Sunset Hills Granite intruded transpressional shear zones. The I-type Carcoar and Barry granites are square to tabular, wedge-shaped bodies exhibiting a weak deformation; whereas the S-type Sunset Hills Granite is an elongated, tabular to sheet-like pluton showing a moderate deformation degree. The contrasts in 3D shape, emplacement mode and deformation style between the I- and S-type granites are due to differences in nearfield stress regime, geometry of the emplacement sites, intrusion level with respect to thermal and rheological conditions, and in their response to deformation. This response is in part controlled by the proportion of resistant/non-resistant minerals in the granite and host rock. This study demonstrates that distinctive emplacement modes can operate simultaneously in different parts of a fault system under contrasting deformation conditions.

Integrating long- and short-wavelength statics with the generalized reciprocal method and the refraction convolution section

Abstract Statics, the corrections for variations in the elevation of the ground surface and for the weathered layer, represent the major challenge to improving the resolution of land seismic reflection data. This study describes a simple approach to determining long- and short-wavelength refraction statics that are generally accurate to a few milliseconds with good quality data. The approach employs the generalized reciprocal method (GRM) and the refraction convolution section (RCS). The resolution achieved with the GRM and RCS is comparable to that achieved with the delay-time method (DTM) together with one application of residual statics. Furthermore, a comparison with a coincident set of data recorded with different acquisition parameters shows that there is a long-wavelength static error with the DTM but not the GRM. There is a limit in the lateral resolution of variations in the base of the weathering, which is demonstrated with triplications or ‘frowns’ in the shot records. However, the statics model also exhibits short-wavelength variations, which suggest a resolution considerably greater than that indicated to be possible by the ‘frowns’. This study proposes that the long-wavelength component represents the variations in the time model of the weathering, which are caused by gross variations in the thickness of the weathered layer, while the short-wavelength components represent the variations in the surface soil layers. With the data used in this study, variations of more than 10 ms in the time model of the weathering were observed over distances of 10 m. Such variations result in similar intra-array statics with receiver arrays over comparable distances. These intra-array statics are a major cause of reduced resolution of reflection data and poor signal-to-noise ratios with first-break refraction data, especially in arid regions. Poor quality refraction data are the major impediment to obtaining accurate refraction statics.

Is visual interactive ray trace an efficacious strategy for refraction inversion

Visual interactive ray trace (VIRT) inversion is a manual approach to refraction tomography. VIRT tomograms neither detect nor define a major 50 m wide zone with a low seismic velocity at Mt Bulga. This failure is attributed to the probable use of a low resolution starting model, specifically the smooth velocity gradient wavepath eikonal traveltime (WET) tomogram, for the VIRT inversion. In this case, the low resolution of the VIRT tomogram is another demonstration of the ubiquity of non-uniqueness. Alternatively, the conventional reciprocal method has been used to generate a starting model, in which the existence of the low velocity region is unequivocal. In this case, confirmation bias has been employed to remove any expression of the low velocity region in the VIRT tomogram. By contrast, WET refraction tomograms produced with smooth and detailed starting models generated with the generalised reciprocal method (GRM) clearly define the 50 m wide zone with the low seismic velocities. The low velocity zone is confirmed with a priori information, specifically the inverted head wave amplitudes and a spectral analysis of the refraction convolution section, and by a posteriori information, specifically numerous closely spaced orthogonal refraction profiles. Furthermore, the GRM tomograms have smaller misfit errors than the tomograms obtained with VIRT tomography and with WET tomograms generated with VIRT starting models. VIRT tomography generates complex velocity models of the weathering from relatively small numbers of traveltimes, indicating that VIRT is overfitting the data. The extensive use of vertical interfaces across which there are large contrasts in seismic velocities is not consistent with standard models of normal weathering profiles, nor is it indicated in the traveltime graphs. By contrast, VIRT generates simple velocity models in the sub-weathering from many traveltimes, indicating that VIRT is underfitting those traveltimes. VIRT neither improves the accuracy nor the geological verisimilitude of refraction tomography. Furthermore, VIRT is time consuming, subjective, and in the final analysis, simply outdated. Although technically, VIRT is efficacious, the alternatives of automatic refraction tomography are more practical, more accurate, and generate more useful tomograms.

Generating starting models for seismic refraction tomography with common offset stacks

Common offset refraction (COR) traveltime attributes are derived from multi-fold data with novel adaptations of the generalised reciprocal method (GRM). COR GRM stacks are generated from a refraction equivalent of common midpoint (CMP) gathers, which are computed at each CMP with the COR GRM algorithms. The COR GRM stacks, which generate detailed spatially varying attributes for each layer detected in the near surface region, provide useful starting models for automatic refraction tomography. The spatial resolution of the depth models of the wavepath eikonal traveltime (WET) refraction tomograms obtained with starting models derived with the COR GRM is similar to the WET tomogram obtained with the standard GRM, whereas the COR GRM seismic velocity model is a smoothed version of the standard GRM model. In all cases, the GRM-derived WET tomograms avoid the generation of undetectable artefacts with common implementations of automatic refraction tomography, which can occur with the use of default starting models consisting of smooth vertical velocity gradients and with the need to minimise misfit errors through over-processing. The COR GRM attributes demonstrate that the traveltime data are consistent with minimal penetration within the sub-weathering, representative of uniform seismic velocities, and that the spatial variations in the time model and seismic velocities are more significant than any variations caused by vertical velocity gradients in the sub-weathered zone. However, the occurrence of vertical velocity gradients in the sub-weathering largely remains unresolved because minimal penetration of the first arrivals can occur even with large vertical velocity gradients, such as the hyperbolic velocity function. The WET tomograms generated with the COR GRM time model and seismic velocity attributes are generally very similar visually to the starting models, even though the misfit errors may differ. It is concluded that COR GRM starting models can frequently be a useful alternative to refraction tomography. Common offset implementations of the generalised reciprocal method generate detailed spatially varying models of the near surface from multi-fold seismic refraction data. These models facilitate the elimination of undetectable artefacts with automatic refraction tomography, the validation of vertical velocity gradients and the convenient evaluation of large sets of traveltime data.

The measurement of weak anisotropy with the generalized reciprocal method

Anisotropy parameters can be determined from seismic refraction data using the generalized reciprocal method (GRM) for a layer in which the velocity can be described with the Crampin approximation for transverse isotropy. The parameters are the standard anisotropy factor, which is the horizontal velocity divided by the vertical velocity, and a second poorly determined parameter which, for weak anisotropy, is approximated by a linear relationship with the anisotropy factor. Although only one anisotropy parameter is effectively determined, the second parameter is essential to ensure that the anisotropy does not degenerate to the elliptical condition which is indeterminate using the approach described in this paper. The anisotropy factor is taken as the value for which the phase velocity at the critical angle given by the Crampin equation is equal to the average velocity computed with the optimum XY value obtained from a GRM analysis of the refraction data. The anisotropy parameters can be used to improve th...