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.     

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.     

A new direction for shallow refraction seismology: integrating amplitudes and traveltimes with the refraction convolution section

The refraction convolution section (RCS) is a new method for imaging shallow seismic refraction data. It is a simple and efficient approach to full‐trace processing which generates a time cross‐section similar to the familiar reflection cross‐section. The RCS advances the interpretation of shallow seismic refraction data through the inclusion of time structure and amplitudes within a single presentation. The RCS is generated by the convolution of forward and reverse shot records. The convolution operation effectively adds the first‐arrival traveltimes of each pair of forward and reverse traces and produces a measure of the depth to the refracting interface in units of time which is equivalent to the time‐depth function of the generalized reciprocal method (GRM). Convolution also multiplies the amplitudes of first‐arrival signals. To a good approximation, this operation compensates for the large effects of geometrical spreading, with the result that the convolved amplitude is essentially proportional to the square of the head coefficient. The signal‐to‐noise (S/N) ratios of the RCS show much less variation than those on the original shot records. The head coefficient is approximately proportional to the ratio of the specific acoustic impedances in the upper layer and in the refractor. The convolved amplitudes or the equivalent shot amplitude products can be useful in resolving ambiguities in the determination of wave speeds. The RCS can also include a separation between each pair of forward and reverse traces in order to accommodate the offset distance in a manner similar to the XY spacing of the GRM. The use of finite XY values improves the resolution of lateral variations in both amplitudes and time‐depths. The use of amplitudes with 3D data effectively improves the spatial resolution of wave speeds by almost an order of magnitude. Amplitudes provide a measure of refractor wave speeds at each detector, whereas the analysis of traveltimes provides a measure over several detectors, commonly a minimum of six. The ratio of amplitudes obtained with different shot azimuths provides a detailed qualitative measure of azimuthal anisotropy and, in turn, of rock fabric. The RCS facilitates the stacking of refraction data in a manner similar to the common‐midpoint methods of reflection seismology. It can significantly improve S/N ratios.Most of the data processing with the RCS, as with the GRM, is carried out in the time domain, rather than in the depth domain. This is a significant advantage because the realities of undetected layers, incomplete sampling of the detected layers and inappropriate sampling in the horizontal rather than the vertical direction result in traveltime data that are neither a complete, an accurate nor a representative portrayal of the wave‐speed stratification. The RCS facilitates the advancement of shallow refraction seismology through the application of current seismic reflection acquisition, processing and interpretation technology.     

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.     

AN ANALYTICAL RAYPATH APPROACH TO THE REFRACTION WAVEFRONT METHOD1

Seismic refraction surveying is still an important tool for determining the geometries and elastic wave propagation velocities of near-surface layers. Many analytical and graphical methods have been developed over the years for refraction interpretation, and these can be classified into two basic groups. The first group visualizes critically refracted rays converging on a common surface position, while the second group, which includes the wavefront methods, makes use of the critical rays emerging from a common point on the refractor. The method described in this paper is an analytical approach to the wavefront methods. The reverse refracted ray received by a geophone is intersected by the forward refracted rays received by subsequent geophones and a common critical refraction point on the refractor is estimated after a series of comparisons. This process is repeated for each geophone to yield the geometry and the velocity of the refractor. Several interpolations are performed to achieve a better accuracy. Palmer's models are used to test the efficiency of the algorithm. The results are presented together with those of other methods applied to the same models.     

Characterization of the shallow aquifers by high-resolution seismic data

We present the results obtained by processing high-resolution seismic data acquired along the spring line located in the Friuli-Venezia Giulia plain (NE of Italy), in order to characterize an important multilayered aquifer. This system is made of an unconfined layer and, at increasing depths, of several confined aquifers of variable thickness and hydraulic permeability, mainly consisting of sand and gravel material. The main targets of this study are two shallow aquifers located at about 30 m and 200 m depth respectively. The seismic method is not frequently used for this type of study but in this case, it was considered a good tool due to the depth of the targets. The detailed velocity model we obtained reveals lateral velocity variations with a maximum value of 600 m/s. The higher velocities could be associated to layers that are confined aquifers; in fact, sand and gravel are characterized by higher seismic velocity compared to clay layers. Pre-stack depth migration using this velocity model gives a clear picture of the multilayered aquifer, highlighting lateral changes of seismic amplitude along the main reflectors. Finally, vertical variations of Poisson's ratio, computed by amplitude versus offset analysis, provide useful information about the petrophysical properties, such as the fluid content of the subsoil and lithologic changes.     

基于波动方程的广义屏叠前深度偏移

地震波传播算子的计算效率和精度是制约三维叠前深度偏移的关键因素. 广义屏传播算子(GSP, Generalized Screen Propagator)是一种在双域中实现的广角单程波传播算子. 这一方法略去了在非均匀体之间发生的交混回响,但它可以正确处理包括聚焦、衍射、折射和干涉在内的各种多次前向散射现象. 通过背景速度下的相移和扰动速度下的陡倾角校正,广义屏算子能够适应地层速度的强烈横向变化. 这种算子可以直接应用于炮集叠前偏移,通过将广义屏算子作用于双平方根方程,还可以获得一种高效率、高精度的炮检距域叠前深度偏移方法,用于二维共炮检距道集和三维共方位角道集的深度域成像. 本文首先简述了炮检距域广义屏传播算子的理论,进而讨论了共照射角成像(CAI, Common Angle Imaging)条件,由此给出各个不同照射角(炮检距射线参数)下的成像结果,进而得到共照射角像集. 由于照射角和炮检距的对应关系,共照射角像集又为偏移速度分析和AVO(振幅随炮检距变化)分析等提供了有力工具.     

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.     

The seismic velocity distribution in the vicinity of a mine tunnel at Thabazimbi, South Africa

Analysis of the refracted arrivals on a seismic reflection profile recorded along the wall of a tunnel at an iron mine near Thabazimbi, South Africa, shows variations in P-wave velocity in dolomite away from the de-stressed zone that vary between 4.4 and 7.2 km/s, though values greater than 5.8 km/s predominate along most of the profile. The seismic velocities at the tunnel wall, however, vary between 4.2 and 5.2 km/s. Time–depth terms are in the range from 0.1 to 0.9 ms, and yield thicknesses of the zone disturbed by the tunnel excavations of between 2 and 9 m. The very low seismic velocities away from the tunnel wall in two regions are associated with alcoves or ‘cubbies’ involving offsets in the wall of up to 10 m. The large variations in seismic velocity resolved over distances less than 15 m with signals of wavelength around 6–9 m are attributed to variations in the sizes and concentrations of fracture systems and cracks, and in the degree of groundwater saturation of the fracture systems. The results suggest that seismic velocity variations from reflection surveys may also assist modelling studies of the stress regime in deep mines, particularly if both P and S wave velocity variations can be determined. The seismic velocity variations inferred also show that application of refraction static corrections in the processing of ‘in-mine’ seismic reflection profiles is as important as in surface surveys, because of the higher frequencies of the seismic energy recorded in the deep mine environment.     

AN INVESTIGATION OF THE RELATIVE ACCURACY OF THE MOST COMMON NORMAL-MOVEOUT EXPRESSIONS IN VELOCITY ANALYSES*

Three common expressions for the normal moveout of recorded seismic events are investigated by numerical simulation procedures for accuracy in predicting the root-mean-squared (RMS) or mean, as the case may be, subsurface velocity function from seismic data. The principal investigation, for which detailed error curves are shown, was derived for a stochastic subsurface model composed of strata with thicknesses ranging up to 91.4 m (300 ft) and boundary velocity contrasts ranging up to 45.7 m/sec (150 ft/sec); there was a 95 percent chance of velocity increase with increased depth. The effects of changes in the basic statistical subsurface model are discussed. The results appear to confirm the judiciousness of the choices of to and (x/z') as plotting parameters to be used with the respective percent errors in the three expressions, where are, respectively, the zero-offset arrival time of, the offset distance of, and the mean-squared velocity encountered by a seismic ray. Out of the three normal-moveout expressions examined, the “straight-raypath” expression with the RMS velocity substituted as its velocity term proved to be the most accurate in the determination of velocities.     

MULTICOVER MEASUREMENTS IN REFRACTION SHOOTING*

Multicover measurements in refraction shooting are comparable to long-spread reflection shooting. Of course, spread length, distance of traces and offset may be larger than in reflection shooting and depend on the, depth, the velocity and the dipping of the refractors to be detected. For later processing an equation for the refractor velocity is derived in case of flat and steep dipping refractors. The depth and the angle of dip will be computed from delay times. An outlook to digital processing is given.     

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     

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.     

SEISMIC REFRACTION AND SCREENING BY THIN HIGH-VELOCITY LAYERS *

The screening effect of thin, relatively shallow high-velocity layers often presents considerable problems in seismic exploration. Such layers prevent the greater part of the seismic energy from travelling to greater depths and introduce additional refraction arrivals, confusing the seismogram still further. In order to investigate both the screening and refractive properties of high-velocity layers, scale-model experiments have been made over a wide range of layer-thickness/ wavelength ratios (0.05 < d/λ < 2) for suitably chosen material contrasts. The results may be summarised as follows. Refraction arrivals from thin layers in the field may be recognised by their relatively rapid amplitude decay. Furthermore, the “echeloning”-effect observed for refraction first arrivals may be due to the presence of a (thin) layered structure. Since the apparent refraction velocity varies with d/λ when d/λ < 1, differences between vertical well-log velocities and velocities observed along the surface may be expected, making time/depth conversion using surface velocity data inaccurate. Transmission of elastic energy may be expected, if anywhere, only near the shotpoint, at small geophone offset, and for relatively thin screens (d/λ < 0.1). The transmitted signal shape is then independent of the layer thickness. This transmitted energy may be registered either in a reflection set-up with geophones near the shotpoint, or in long-distance refraction work. Three possibilities are offered for overcoming the screening effect of thin high-velocity layers: Use longer-wavelength signals Apply short-spread reflection shooting Apply long-distance refraction shooting The experimental results obtained in scale-model arrangements of such set-ups confirm the potentialities of these methods.     

COMMON OFFSET PLANE MIGRATION (COPMIG)*

The quality of results of migration before stack is sensitive to inaccuracies in the velocity field applied. This does not hold if only traces of similar sources-receiver distances (common offset traces) enter the migration process. In this case, velocity deviations generate minor shifts in travel times of migrated interfaces but no deterioration in quality. These time shifts are proportional to both the velocity error and the square of the source-receiver distance. The above observations suggest the following migration scheme: migrate separately the traces of the various common offset planes or groups of neighbouring common offset planes; for every common midpoint plane and as a function of travel-time perform a residual NMO search to find trajectories t) =t)_o+px)² of maximum coherency along which migrated events are aligned; correct for residual NMO and stack the migration results obtained in the various common offset planes to obtain the final migration result. This process not only takes care of inaccurate migration velocities but also corrects partly for effects of refraction. It is shown by means of an example that good migration results are generated even with a considerably deviating velocity field.     

川东北复杂山地三维静校正应用及实例分析

川东北复杂山地由于地表高程变化大、风化层厚度不均匀、低降速带速度横向变化大、高速层底界不稳定等因素,得到的地震资料具有严重的静校正问题,因此,如何解决山地静校正问题是后续地震资料处理的关键之一,本文首先分析高程静校正、折射静校正、层析静校正的基本原理和适用条件,结合实际复杂山地三维地震资料的特点,进行试验对比,提出了进行山地静校正的基本思路,即：首先进行高程静校正,这样可以利用高程静校正更容易拾取初至时间,然后利用折射静校正结合微测井等资料建立近地表速度-深度模型,以此速度-深度模型作为层析静校正的初始模型进行迭代处理,最后得到最终的近地表速度-深度模型和静校正值.根据以上处理流程,我们建立了适合于川东北山地三维复杂地表地震资料的静校处理正方法,并在实际生产过程中取得了良好的效果.     

NON-LINEAR AVO INVERSION FOR A STACK OF ANELASTIC LAYERS1

Parameters in a stack of homogeneous anelastic layers are estimated from seismic data, using the amplitude versus offset (AVO) variations and the travel-times. The unknown parameters in each layer are the layer thickness, the P-wave velocity, the S-wave velocity, the density and the quality factor. Dynamic ray tracing is used to solve the forward problem. Multiple reflections are included, but wave-mode conversions are not considered. The S-wave velocities are estimated from the PP reflection and transmission coefficients. The inverse problem is solved using a stabilized least-squares procedure. The Gauss-Newton approximation to the Hessian matrix is used, and the derivatives of the dynamic ray-tracing equation are calculated analytically for each iteration. A conventional velocity analysis, the common mid-point (CMP) stack and a set of CMP gathers are used to identify the number of layers and to establish initial estimates for the P-wave velocities and the layer thicknesses. The inversion is carried out globally for all parameters simultaneously or by a stepwise approach where a smaller number of parameters is considered in each step. We discuss several practical problems related to inversion of real data. The performance of the algorithm is tested on one synthetic and two real data sets. For the real data inversion, we explained up to 90% of the energy in the data. However, the reliability of the parameter estimates must at this stage be considered as uncertain.     

Geophysical constraints on deep weathering and water storage potential in the Southern Sierra Critical Zone Observatory

The conversion of bedrock to regolith marks the inception of critical zone processes, but the factors that regulate it remain poorly understood. Although the thickness and degree of weathering of regolith are widely thought to be important regulators of the development of regolith and its water‐storage potential, the functional relationships between regolith properties and the processes that generate it remain poorly documented. This is due in part to the fact that regolith is difficult to characterize by direct observations over the broad scales needed for process‐based understanding of the critical zone. Here we use seismic refraction and resistivity imaging techniques to estimate variations in regolith thickness and porosity across a forested slope and swampy meadow in the Southern Sierra Critical Zone Observatory (SSCZO). Inferred seismic velocities and electrical resistivities image a weathering zone ranging in thickness from 10 to 35 m (average = 23 m) along one intensively studied transect. The inferred weathering zone consists of roughly equal thicknesses of saprolite (P‐velocity < 2 km s^?1) and moderately weathered bedrock (P‐velocity = 2–4 km s^?1). A minimum‐porosity model assuming dry pore space shows porosities as high as 50% near the surface, decreasing to near zero at the base of weathered rock. Physical properties of saprolite samples from hand augering and push cores are consistent with our rock physics model when variations in pore saturation are taken into account. Our results indicate that saprolite is a crucial reservoir of water, potentially storing an average of 3 m³ m^?2 of water along a forested slope in the headwaters of the SSCZO. When coupled with published erosion rates from cosmogenic nuclides, our geophysical estimates of weathering zone thickness imply regolith residence times on the order of 10⁵ years. Thus, soils at the surface today may integrate weathering over glacial–interglacial fluctuations in climate. Copyright © 2013 John Wiley & Sons, Ltd.     

水平层状介质中多次叠加的某些理论问题

本文讨论了由具有垂向不均匀性的介质层构成的水平层状介质中反射波法的数学模型及其一般特性;研究了多道地震信号的最佳估计以及因之而提出的反射波时距曲线段的拟合问题;分析了水平迭加速度和视t₀时间的特性,并指出射线均方根速度是一种极限的水平叠加速度;阐明了偏移距太小时,多次叠加效果不好的原因,并论证了最佳反射叠加段的存在;用理论计算进行了验证.最后,一般地讨论了介质层的垂向不均匀性的识别和确定.