Refraction traveltime and amplitude corrections for very near- surface inhomogeneities

The 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 generation of artefacts, and facilitates the computation of detailed seismic velocities in the refractor at each receiver. These detailed seismic velocities, together with the GRM SSM‐corrected amplitude products, can facilitate the computation of the ratio of the density in the bedrock to that in the weathered layer. The accuracy of the computed density ratio improves where lateral variations in the seismic velocities in the weathered layer are known.     

Multi-refractor imaging with stacked refraction convolution section

Multi‐refractor imaging is a technique for constructing a single two‐dimensional image of a number of refractors by stacking multiple convolved and cross‐correlated reversed shot records. The method is most effective with high‐fold data that have been obtained with roll‐along acquisition programs because the stacking process significantly improves the signal‐to‐noise ratios. The major advantage of the multi‐refractor imaging method is that all the data can be stacked to maximize the signal‐to‐noise ratios before the measurement of any traveltimes. However, the signal‐to‐noise ratios can be further increased if only those traces that have arrivals from the same refractor are used, and if the correct reciprocal times or traces are employed. A field case study shows that multi‐refractor imaging can produce a cross‐section similar to the familiar reflection cross‐section with substantially higher signal‐to‐noise ratios for the equivalent interfaces.     

Non‐uniqueness with refraction inversion – the Mt Bulga shear zone

The tau‐p inversion algorithm is widely employed to generate starting models with many computer programs that implement refraction tomography. However, this algorithm can frequently fail to detect even major lateral variations in seismic velocities, such as a 50 m wide shear zone, which is the subject of this study. By contrast, the shear zone is successfully defined with the inversion algorithms of the generalized reciprocal method. The shear zone is confirmed with a 2D analysis of the head wave amplitudes, a spectral analysis of the refraction convolution section and with numerous closely spaced orthogonal seismic profiles recorded for a later 3D refraction investigation. Further improvements in resolution, which facilitate the recognition of additional zones with moderate reductions in seismic velocity, are achieved with a novel application of the Hilbert transform to the refractor velocity analysis algorithm. However, the improved resolution also requires the use of a lower average vertical seismic velocity, which accommodates a velocity reversal in the weathering. The lower seismic velocity is derived with the generalized reciprocal method, whereas most refraction tomography programs assume vertical velocity gradients as the default. Although all of the tomograms are consistent with the traveltime data, the resolution of each tomogram is comparable only with that of the starting model. Therefore, it is essential to employ inversion algorithms that can generate detailed starting models, where detailed lateral resolution is the objective. Non‐uniqueness can often be readily resolved with head wave amplitudes, attribute processing of the refraction convolution section and additional seismic traverses, prior to the acquisition of any borehole data. It is concluded that, unless specific measures are taken to address non‐uniqueness, the production of a single refraction tomogram that fits the traveltime data to sufficient accuracy does not necessarily demonstrate that the result is either correct, or even the most probable.     

Application of the virtual refraction to near‐surface characterization at the Boise Hydrogeophysical Research Site‡

Seismic interferometry is a relatively new technique to estimate the Green's function between receivers. Spurious energy, not part of the true Green's function, is produced because assumptions are commonly violated when applying seismic interferometry to field data. Instead of attempting to suppress all spurious energy, we show how spurious energy associated with refractions contains information about the subsurface in field data collected at the Boise Hydrogeophysical Research Site. By forming a virtual shot record we suppress uncorrelated noise and produce a virtual refraction that intercepts zero offset at zero time. These two features make the virtual refraction easy to pick, providing an estimate of refractor velocity. To obtain the physical parameters of the layer above the refractor we analyse the cross‐correlation of wavefields recorded at two receivers for all sources. A stationary‐phase point associated with the correlation between the reflected wave and refracted wave from the interface identifies the critical offset. By combining information from the virtual shot record, the correlation gather and the real shot record we determine the seismic velocities of the unsaturated and saturated sands, as well as the variable relative depth to the water‐table. Finally, we discuss how this method can be extended to more complex geologic models.     

Improving modelling and inversion in refraction seismics with a first-order Eikonal solver

A first-order Eikonal solver is applied to modelling and inversion in refraction seismics. The method calculates the traveltime of the fastest wave at any point of a regular grid, including head waves as used in refraction. The efficiency, robustness and flexibility of the method give a very powerful modelling tool to find both traveltimes and raypaths. Comparisons with finite-difference data show the validity of the results. Any arbitrarily complex model can be studied, including the exact topography of the surface, thus avoiding static corrections. Later arrivals are also obtained by applying high-slowness masks over the high-velocity zones. Such an efficient modelling tool may be used interactively to invert for the model, but a better method is to apply the refractor-imaging principle of Hagedoorn to obtain the refractors from the picked traveltime curves. The application of this principle has already been tried successfully by previous authors, but they used a less well-adapted Eikonal solver. Some of their traveltimes were not correct in the presence of strong velocity variations, and the refractor-imaging principle was restricted to receiver lines along a plane surface. With the first-order Eikonal solver chosen, any topography of the receiving surface can be considered and there is no restriction on the velocity contrast. Based on synthetic examples, the Hagedoorn principle appears to be robust even in the case of first arrivals associated with waves diving under the refractor. The velocities below the refractor can also be easily estimated, parallel to the imaging process. In this way, the model can be built up successively layer by layer, the refractor-imaging and velocity-mapping processes being performed for each identified refractor at a time. The inverted model could then be used in tomographic inversions because the calculated traveltimes are very close to the observed traveltimes and the raypaths are available.     

Interpretation of shallow refraction seismic data by reflection/refraction tomography

A new algorithm for tomographic inversion of traveltimes of reflected and refracted seismic waves is developed. The inversion gives interface configurations and velocity distributions in layers. The important features of the algorithm are: (a) the inclusion of shot time delays in the list of unknown parameters; (b) the regularization is applied in such a way that the most probable model is characterized by the similarity of neighbouring interfaces. As the problem under consideration is non-linear, several iterations are necessary in order to obtain the final model. In the case of a very inexact initial model, a 'layer-by-layer' inversion strategy is recommended as a first inversion step. The inversion program is supplied with a user interface, thanks to which one can: (a) pick interactively and identify seismic traveltimes; (b) build and edit depth/velocity models; and (c) display calculated traveltime curves and compare them with picked traveltimes as well as with the original seismic sections. The efficiency of the inversion software developed is illustrated by a numerical example and a field example in which shallow seismic data are considered. Application to wide-aperture reflection/refraction profiling (WARRP) data is also possible.     

ON THE SIGNIFICANCE OF AMPLITUDE STUDIES IN SHALLOW REFRACTION SEISMICS*

An analysis of amplitudes of refraction records of some shallow refraction profiles shot primarily for detailing the near-surface structure in a granitic terrain has yielded information on refractor properties: reduced amplitudes are plotted on amplitude-distance graphs. The negative power n to which distance should be raised to represent (elastic) amplitude decay with respect to distance due to spreading of the critically refracted wave involved is examined. Computed values of this “spreading index”n are close to n = 2 as predicted by the theory. With this value of n, amplitude data are processed to determine residual attenuation attributable to elastic absorption in the bedrock. A graphical approach for this purpose from comparison of amplitude-distance graphs with the plots of amplitude decay due to spreading which is applicable to flat and horizontal refractor situations is suggested. Assuming residual attenuation to represent absorption in the granite bedrock, the computed coefficients of absorption, which vary from 0.5 to 3.90 km^?1 for a frequency of 50 Hz, are obtained. From amplitude graphs of reversed profiles it is shown that the amplitude differences plot bears a relation to lateral velocity changes in the refractor. From comparison of practical amplitude decay graphs with those computed for different subsurface models, it appears possible to detect fractured rock occurrences in the refractor.     

Determination of a shallow velocity–depth model from seismic refraction data by coherence inversion1

Seismic refractions have different applications in seismic prospecting. The travel- times of refracted waves can be observed as first breaks on shot records and used for field static calculation. A new method for constructing a near-surface model from refraction events is described. It does not require event picking on prestack records and is not based on any approximation of arrival times. It consists of the maximization of the semblance coherence measure computed using shot gathers in a time window along refraction traveltimes. Time curves are generated by ray tracing through the model. The initial model for the inversion was constructed by the intercept-time method. Apparent velocities and intercept times were taken from a refraction stacked section. Such a section can be obtained by appling linea moveout corrections to common-shot records. The technique is tested successfully on synthetic and real data. An important application of the proposed method for solving the statics problem is demonstrated.     

Parsimonious wave‐equation travel‐time inversion for refraction waves

We present a parsimonious wave‐equation travel‐time inversion technique for refraction waves. A dense virtual refraction dataset can be generated from just two reciprocal shot gathers for the sources at the endpoints of the survey line, with N geophones evenly deployed along the line. These two reciprocal shots contain approximately 2N refraction travel times, which can be spawned into refraction travel times by an interferometric transformation. Then, these virtual refraction travel times are used with a source wavelet to create N virtual refraction shot gathers, which are the input data for wave‐equation travel‐time inversion. Numerical results show that the parsimonious wave‐equation travel‐time tomogram has about the same accuracy as the tomogram computed by standard wave‐equation travel‐time inversion. The most significant benefit is that a reciprocal survey is far less time consuming than the standard refraction survey where a source is excited at each geophone location.     

THE RESOLUTION OF NARROW LOW-VELOCITY ZONES WITH THE GENERALIZED RECIPROCAL METHOD1

The depth to the surface of a refractor and the seismic velocity within the refractor are very often intimately related. In the shallow environment, increased thicknesses of weathering occur in areas of jointing, shearing or lithological variations, and these zones of deeper weathering can have lower subweathering refractor velocities. This association is important in geotechnical investigations and in the measurement of weathering thicknesses and sub-weathering velocities for statics corrections for reflection seismic surveys. Algorithms, which employ forward and reverse traveltime data and which explicitly accommodate the offset distance through the process known as refraction migration, are necessary if detailed structure on a refractor and rapid lateral variations of the seismic velocity within it are to be resolved. These requirements are satisfied with wavefront construction techniques, Hales’ method and the generalized reciprocal method (GRM). However, these methods employ refraction migration in fundamentally different manners. Most methods compute an offset distance with an often imprecise knowledge of the seismic velocities of the overlying layers. In contrast, the GRM uses a range of offset distances from less than to greater than the optimum value, with the optimum value being selected with a minimum-variance criterion. The approach of the GRM is essential where there are undetected layers and where there are rapid variations in the depth to a refractor and the seismic velocity within it. In the latter situations the offset distance necessary to define the seismic velocities can differ considerably from the value required to define depths. The efficacy of the GRM in resolving structure and seismic velocity is demonstrated with three model studies and two field examples.     

2D inversion of refraction traveltime curves using homogeneous functions

A method using simple inversion of refraction traveltimes for the determination of 2D velocity and interface structure is presented. The method is applicable to data obtained from engineering seismics and from deep seismic investigations. The advantage of simple inversion, as opposed to ray‐tracing methods, is that it enables direct calculation of a 2D velocity distribution, including information about interfaces, thus eliminating the calculation of seismic rays at every step of the iteration process. The inversion method is based on a local approximation of the real velocity cross‐section by homogeneous functions of two coordinates. Homogeneous functions are very useful for the approximation of real geological media. Homogeneous velocity functions can include straight‐line seismic boundaries. The contour lines of homogeneous functions are arbitrary curves that are similar to one another. The traveltime curves recorded at the surface of media with homogeneous velocity functions are also similar to one another. This is true for both refraction and reflection traveltime curves. For two reverse traveltime curves, non‐linear transformations exist which continuously convert the direct traveltime curve to the reverse one and vice versa. This fact has enabled us to develop an automatic procedure for the identification of waves refracted at different seismic boundaries using reverse traveltime curves. Homogeneous functions of two coordinates can describe media where the velocity depends significantly on two coordinates. However, the rays and the traveltime fields corresponding to these velocity functions can be transformed to those for media where the velocity depends on one coordinate. The 2D inverse kinematic problem, i.e. the computation of an approximate homogeneous velocity function using the data from two reverse traveltime curves of the refracted first arrival, is thus resolved. Since the solution algorithm is stable, in the case of complex shooting geometry, the common‐velocity cross‐section can be constructed by applying a local approximation. This method enables the reconstruction of practically any arbitrary velocity function of two coordinates. The computer program, known as godograf , which is based on this theory, is a universal program for the interpretation of any system of refraction traveltime curves for any refraction method for both shallow and deep seismic studies of crust and mantle. Examples using synthetic data demonstrate the accuracy of the algorithm and its sensitivity to realistic noise levels. Inversions of the refraction traveltimes from the Salair ore deposit, the Moscow region and the Kamchatka volcano seismic profiles illustrate the methodology, practical considerations and capability of seismic imaging with the inversion method.     

NOUVELLE METHODE DE RESTITUTION D'UN HORIZON REFRAGTEUR PAR SISMIQUE REFRACTION*

The purpose of this report is to show a method of determining the top of a refractor departing from the times and slopes of the direct and inverse dromocrones. The method does not need topographical correction and can be applied without knowledge of the distance between the geophone and the shot point. These results having been obtained, the commonly accepted point of view is upset: instead of looking for two points on the surface corresponding to one point of the refractor, we try to etablish, starting with only one point from the surface, the two corresponding points from the top of the refractor. This method can be applied to isolated points and does not demand interpretative hypotheses of any kind, excluding the velocity evaluation of the overburden and of the refractor. The necessary calculations can be easily executed by means of a digital computer to which the dromocrone times and the distances between the geophones must be given. These calculations can also be executed by a person having no knowledge of refraction seismology. This report also examines the validity of the approximations involved in the method proposed.     

3D seismic residual statics solutions derived from refraction interferometry

We apply interferometric theory to solve a three‐dimensional seismic residual statics problem to improve reflection imaging. The approach calculates the static solutions without picking the first arrivals from the shot or receiver gathers. The static correction accuracy can be significantly improved by utilising stacked virtual refraction gathers in the calculations. Shots and receivers may be placed at any position in a three‐dimensional seismic land survey. Therefore, it is difficult to determine stationary shots and receivers to form the virtual refraction traces that have identical arrival times, as in a two‐dimensional scenario. To overcome this problem, we use a three‐dimensional super‐virtual interferometry method for residual static calculations. The virtual refraction for a stationary shot/receiver pair is obtained via an integral along the receiver/shot lines, which does not require knowledge of the stationary locations. We pick the maximum energy times on the interferometric stacks and solve a set of linear equations to derive reliable residual static solutions. We further apply the approach to both synthetic and real data.     

Combination of common-midpoint-refraction seismics with the generalized reciprocal method

A useful method for increasing the signal/noise ratio of refracted waves is Common-Midpoint (CMP)-refraction seismics. With this technique the shallow underground can be described in detail using all information (amplitude, frequency, phase characteristics) of the wavetrain following the first break (first-break phase). Thus, the layering can be determined and faults, weak zones, and clefts can be identified. This paper deals with the optimization of CMP-refraction seismics used in combination with the Generalized Reciprocal Method (GRM). Theoretical studies show a close relationship of both methods to the kinematics of wave propagation. Velocities and optimum offsets determined by the GRM can be used directly in the partial Radon transformation in CMP-refraction seismics. The integration of refracted waves leads to an increase in the signal/noise ratio but simultaneously the integration boundaries must be restricted to deal only with selective parts of the investigated refractor. The result of this process is an intercept-time section which can be converted directly to a depth section using standard refraction seismic techniques. Another possibility of depth conversion is the transformation of this intercept-time section to a `pseudo-zero-offset section', known from reflection seismics. Thus, zero-offset sections can be migrated using wave-equation techniques such as Kirchhoff migration.     

Non‐uniqueness with refraction inversion – a syncline model study

Non‐uniqueness occurs with the 1D parametrization of refraction traveltime graphs in the vertical dimension and with the 2D lateral resolution of individual layers in the horizontal dimension. The most common source of non‐uniqueness is the inversion algorithm used to generate the starting model. This study applies 1D, 1.5D and 2D inversion algorithms to traveltime data for a syncline (2D) model, in order to generate starting models for wave path eikonal traveltime tomography. The 1D tau‐p algorithm produced a tomogram with an anticline rather than a syncline and an artefact with a high seismic velocity. The 2D generalized reciprocal method generated tomograms that accurately reproduced the syncline, together with narrow regions at the thalweg with seismic velocities that are less than and greater than the true seismic velocities as well as the true values. It is concluded that 2D inversion algorithms, which explicitly identify forward and reverse traveltime data, are required to generate useful starting models in the near‐surface where irregular refractors are common. The most likely tomogram can be selected as either the simplest model or with a priori information, such as head wave amplitudes. The determination of vertical velocity functions within individual layers is also subject to non‐uniqueness. Depths computed with vertical velocity gradients, which are the default with many tomography programs, are generally 50% greater than those computed with constant velocities for the same traveltime data. The average vertical velocity provides a more accurate measure of depth estimates, where it can be derived. Non‐uniqueness is a fundamental reality with the inversion of all near‐surface seismic refraction data. Unless specific measures are taken to explicitly address non‐uniqueness, then the production of a single refraction tomogram, which fits the traveltime data to sufficient accuracy, does not necessarily demonstrate that the result is either ‘correct’ or the most probable.     

THE INTERPRETATION OF TRAVELTIME FIELDS IN REFRACTION SEISMOLOGY*

We consider multiply covered traveltimes of first or later arrivals which are gathered along a refraction seismic profile. The two-dimensional distribution of these traveltimes above a coordinate frame generated by the shotpoint axis and the geophone axis or by the common midpoint axis and the offset axis is named a traveltime field. The application of the principle of reciprocity to the traveltime field implies that for each traveltime value with a negative offset there is a corresponding equal value with positive offset. In appendix A procedures are demonstrated which minimize the observational errors of traveltimes inherent in particular traveltime branches or complete common shotpoint sections. The application of the principle of parallelism to an area of the traveltime field associated with a particular refractor can be formulated as a partial differential equation corresponding to the type of the vibrating string. The solution of this equation signifies that the two-dimensional distribution of these traveltimes may be generated by the sum of two one-dimensional functions which depend on the shotpoint coordinate and the geophone coordinate. Physically, these two functions may be interpreted as the mean traveltime branches of the reverse and the normal shot. In appendix B procedures are described which compute these two functions from real traveltime observations by a least-squares fit. The application of these regressed traveltime field data to known time-to-depth conversion methods is straightforward and more accurate and flexible than the use of individual traveltime branches. The wavefront method, the plus-minus method, the generalized reciprocal method and a ray tracing method are considered in detail. A field example demonstrates the adjustment of regressed traveltime fields to observed traveltime data. A time-to-depth conversion is also demonstrated applying a ray tracing method.     

Retrieval of super‐virtual refraction by cross‐correlation

Topography and severe variations of near‐surface layers lead to travel‐time perturbations for the events in seismic exploration. Usually, these perturbations could be estimated and eliminated by refraction technology. The virtual refraction method is a relatively new technique for retrieval of refraction information from seismic records contaminated by noise. Based on the virtual refraction, this paper proposes super‐virtual refraction interferometry by cross‐correlation to retrieve refraction wavefields by summing the cross‐correlation of raw refraction wavefields and virtual refraction wavefields over all receivers located outside the retrieved source and receiver pair. This method can enhance refraction signal gradually as the source–receiver offset decreases. For further enhancement of refracted waves, a scheme of hybrid virtual refraction wavefields is applied by stacking of correlation‐type and convolution‐type super‐virtual refractions. Our new method does not need any information about the near‐surface velocity model, which can solve the problem of directly unmeasured virtual refraction energy from the virtual source at the surface, and extend the acquisition aperture to its maximum extent in raw seismic records. It can also reduce random noise influence in raw seismic records effectively and improve refracted waves’ signal‐to‐noise ratio by a factor proportional to the square root of the number of receivers positioned at stationary‐phase points, based on the improvement of virtual refraction's signal‐to‐noise ratio. Using results from synthetic and field data, we show that our new method is effective to retrieve refraction information from raw seismic records and improve the accuracy of first‐arrival picks.     

The problem of velocity inversion in refraction seismics: some observations from modelling results

The applicability of seismic refraction profiling for the detection of velocity inversion, which is also known as a low-velocity layer (LVL), is investigated with the aid of synthetic seismogram computations for a range of models. Our computational models focus on the inherent ambiguities in the interpretation of first-arrival time delays or 'skips' in terms of LVL model parameters. The present modelling results reveal that neither the measure nor even the existence of a shadow zone and/or a time shift (skip) in first arrivals is necessarily indicative of an LVL. Besides attenuation effects, the cap-layer velocity gradient is a critical parameter, determining the termination point of the cap-layer diving wave and thus the time skip.
We suggest that shallow LVLs can be delineated more reliably by traveltime and amplitude modelling of coherent phases reflected from their top and bottom boundaries, often clearly observed in the pre- and near-critical ranges in seismogram sections of refraction profiling experiments with a close receiver spacing. We demonstrate the applicability of this approach for a field data set of a refraction profile in the West Bengal Basin, India. The inferred LVL corresponds to the Gondwana sediments underlying the higher-velocity layer of the Rajmahal Traps. This interpretation is consistent with the data from a nearby well in the region.     

Simple inversion procedure for shallow seismic refraction in continuously nonhomogeneous soils

Seismic refraction analysis is presented for uniformly deposited shallow soil strata with wave velocity increasing continuously with depth due to differential compaction effects. Closed form solutions of the surface-to-surface travel time as well as for the depth to maximum penetration are derived for realistic velocity-depth functions. An inversion procedure based on simple formulas is presented and its applicability is demonstrated and discussed. The method takes into account the information along the entire refraction line in one step, in contrast to the discrete ray-tracing technique and is, therefore, less sensitive to the natural scatter of the data.     

复杂介质结构中折射界面的哈格多恩原理波前成像

在城市活断层探测中 ,浅层结构常常表现为强烈的非均匀性 ,界面横向强烈起伏 ,层内速度变化较大 ,传统的基于平界面均匀层模型的折射资料处理方法不能适用。研究开发能应用于复杂介质结构中折射资料处理的方法就显得十分必要。文中基于惠更斯原理 ,用波前扩张法对波场作正演计算 ,根据哈格多恩折射波前成像原理 ,在lecomte算法和Hole有限差分计算程序的基础上 ,开发出 1种复杂介质结构中折射资料的处理方法与软件 ,并用此方法处理了福州城市活断层折射探测试验中在义序完成的 2条折射剖面资料。结果表明 :探测区浅层为 3层结构 ,分别为盖层、强风化层和基岩。基岩顶界面的埋深约为 5 8～ 5 2m ,盖层P波速度变化较大