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.     

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.     

时频域相位滤波在远震接收函数噪声压制中的应用

宽频带地震观测数据中有效信号和干扰噪声经常发生混频效应,常规的频率域滤波方法很难将二者分离.地震波信号属于时变非平稳信号,时频分析方法能够同时得到地震波信号随着时间和频率变化的振幅和相位特征,S变换是其中较为高效的时频分析工具之一.本文以S变换为例,提出了基于相位叠加的时频域相位滤波方法.与传统叠加方法相比,相位叠加方法对强振幅不敏感,对波形一致性相当敏感,更加利于有效弱信号信息的检测.时频域相位滤波方法滤除与有效信号不相干的背景噪声,保留了相位一致的有效信号成分,显著提高了信噪比.运用理论合成的远震接收函数数据和实际的宽频带地震观测数据检验结果显示该方法较传统的带通滤波方法相比,即使在信噪较低且混频严重条件下,时频域相位滤波方法的滤波效果依然很明显,有助于识别能量较弱的有效信号.     

Estimation of Seismic Velocities from Deep Reflections in the τ-p Domain

—In deep reflection seismics the estimation of seismic velocities is hampered in most cases due to the low signal level with respect to noise. In the τ-p domain, it is possible to perform the velocity analysis even under such unfavorable signal conditions. This is achieved by making use of special properties of the transform, which enhance the signal-to-noise ratio. Further noise suppression is realized by incorporating filter procedures into the transform algorithm. The velocity analysis itself is also done in the τ-p domain by calculating and evaluating constant velocity gathers. The results can be directly used in the time domain. A mute algorithm, implemented into the τ-p velocity analysis procedure, further reduces noise. This velocity estimation method is discussed with synthetic data and applied to DEKORP data.     

DETERMINATION OF LATERAL INHOMOGENEITIES IN REFLECTION SEISMICS BY INVERSION OF TRAVELTIME RESIDUALS*

Lateral inhomogeneities generate fluctuations in the traveltime of seismic waves. By evaluation of these traveltime fluctuations from different source and receiver positions, lateral inhomogeneities can be located using a pseudo inverse matrix method (Aki, Christoffersson and Husebye 1977). The formulation of the problem is possible for transmitted waves as well as for reflected and refracted waves. In reflection seismics this method is of importance, if no reflections from the inhomogeneities themselves, but only reflections from lower boundaries can be observed. The basic assumptions for the mathematical formulation are (1) the average velocities and depths of the reflecting horizons are known already from standard processing methods, and (2) the traveltime residuals are due to lateral velocity changes between different reflectors or between reflectors and the surface. The area of the earth to be considered is divided into layers and the layers into rectangular blocks. The parallel displacement of a ray after passing a disturbed block is neglected, only the traveltime residual is taken into account. In this paper the method and its application to data obtained with two-dimensional models are described.     

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.     

APPLICATION OF REFRACTION SEISMICS TO SUBSALT TECTONIC PROBLEMS IN A DEEP SALTDOME BASIN*

Despite the use of CDP and digital methods the Zechstein base is still the deepest horizon in the vast salt-dome basin of Central Europe for which continuous information can be obtained by reflection seismics. Thus in North-western Germany, in addition to reflection seismics, the refraction seismic method has been increasingly used for a reliable survey of deeper horizons. The first part of the paper deals with the investigation of the various possibilities and limitations of refraction seismics with regard to the investigation of Pre-Zechstein layers in a basin with a tectonically very complicated overburden. The recording techniques specially developed for continuous profiling of the desired refraction seismic arrivals and the data processing methods are described. The main problems of interpretation are then discussed, in particular with regard to depth representation. The advantages and disadvantages of the various methods, e.g. Gardner's, Hales' and Wyrobek's, and of the wave-front method, are compared. On account of the tectonically complicated overburden Thornburgh's wave-front method proved to be the most useful. In a further section the various possibilities for velocity determinations are mentioned, e.g. Wyrobek's determination of the overburden velocity, for which the wave-front method automatically furnishes the necessary corrections to a deep datum. Finally, some examples are given for the results obtained, including some incidental information on the deeper crust.     

A METHOD TO DETERMINE THE VELOCITIES OF THE SEAFLOOR AND NEAR-SURFACE SEDIMENTS*

Shotpoint gathers from conventional reflection seismic surveys contain both reflected and refracted waves. In this study shot records were processed and analyzed, and the data were modeled with reflected, refracted, and reflected-refracted waves to fit the recorded data. The result is a detailed velocity model. The inverse problem for refracted waves was solved by using the Wiechert-Herglotz inversion. A 500-km-long 26-fold reflection seismic line from the Barents Sea, north of Norway, has been investigated. The data show high velocities, multiple reflections, and various types of noise. To test the method a total of 34 shot gathers were analyzed along this line. The aim of the interpretation was to determine the velocity in the seafloor and the near-surface sediments. It is possible to map the vertical as well as the lateral velocity distribution in detail. Depending on the length of the streamer and the velocity gradient in the sediments, the calculated depth varies between 300 and 500 m below the seafloor. These velocities were also compared to the stacking velocities obtained from the reflection seismic data to see how the velocities determined by different methods were related. The velocity distribution in the sediments is one of the key factors in seismic interpretation. The technique discussed in this paper can contribute to velocity information both in the processing and interpretation of seismic data.     

MSH法直接将地球勘探测线转化为深度,密度剖面

根据运动学中的动量守恒定律、分析地震勘探过程中地震波在地下介质中的传播过程,利用反射能量、透射能量与人射能量的计算公式和检波器转化的电信号与地下密度界面反射地震波波动能量的等效原理,推导出直接求层速度和层密度公式。利用某一反射界面直接测得的波速或依据钻孔资料求得的平均速度,在计算机上就可直接计算出各地震测线物性层的埋深和密度（速度、波阻抗）,由此地质工作人员依据已知地质柱状剖面（钻孔资料）可进一步     

Comparison of surface seismic sources at the CO2SINK site, Ketzin, Germany

In 2004 three seismic surface sources (VIBSIST, accelerated weight drop and MiniVib) were tested in a pilot study at the Ketzin test site, Germany, a study site for geological storage of CO₂ (EU project CO₂SINK). The main objectives of this pilot study were to 1) evaluate the response of the Ketzin site to reflection seismics, especially at the planned injection depth, 2) test different acquisition parameters and 3) use the results to guide the planning of the 3D survey. As part of these objectives, we emphasize the source performance comparison in this study. The sources were tested along two perpendicular lines of 2.4 km length each. Data were acquired by shooting at all stations (source and receiver spacing of 20 m) on both lines, allowing common‐midpoint stacked sections to be produced. The sources' signal characteristics based on signal‐to‐noise ratio, signal penetration and frequency content of raw shot records were analysed and stacked sections were compared. The results show that all three surface sources are suitable for reflection seismic studies down to a depth of about 1 km and provide enough bandwidth for resolving the geological targets at the site, i.e., the Weser and Stuttgart Formations. Near surface conditions, especially a thick weathering layer present in this particular area, strongly influence the data quality, as indicated by the difference in reflectivity and signal‐to‐noise ratio of the two common‐midpoint lines. The stacked sections of the MiniVib source show the highest frequency signals down to about 500 ms traveltime (approximately 500 m depth) but also the shallowest signal penetration depth. The VIBSIST source generates signals with the highest signal‐to‐noise ratio and greatest signal penetration depth of the tested sources. In particular, reflections below 900 ms (approximately 1 km depth) are best imaged by the VIBSIST source. The weight drop performance lies in between these two sources and might be recommended as an appropriate source for a 3D survey at this site because of the shorter production time compared to the VIBSIST and MiniVib sources.     

A brief study of applications of the generalized reciprocal method and of some limitations of the method

An analysis of the generalized reciprocal method (GRM), developed by Palmer for the interpretation of seismic refraction investigations, has been carried out. The aim of the present study is to evaluate the usefulness of the method for geotechnical investigations in connection with engineering projects. Practical application of the GRM is the main object of this study rather than the theoretical/mathematical aspects of the method. The studies are partly based on the models and field examples presented by Palmer. For comparison, some other refraction interpretation methods and techniques have been employed, namely the ABC method, the ABEM correction method, the mean‐minus‐T method and Hales' method. The comparisons showed that the results, i.e. the depths and velocities determined by Palmer, are partly incorrect due to some errors and misinterpretations when analysing the data from field examples. Due to the limitations of the GRM, some of which are mentioned here, stated by Palmer in his various publications, and other shortcomings of the method (e.g. the erasing of valuable information), the GRM must be regarded as being of limited use for detailed and accurate interpretations of refraction seismics for engineering purposes.     

小波变换的过零点特性与地震勘探信号的信噪比和分辨率

利用小波变换研究地震勘探信号小波变换的过零点特性，本文提出了用小波变换的过零点特性和地震勘探信号相邻道的横向相关性提高信号分辨率和信噪比的新方法．该方法包括两个主要步骤：①利用相邻地震道信号具有很好相关性，而噪音相关性差的特点以及小波变换的过零点特性得到有效反射波同相轴随空间坐标的变化信息．②利用奇异值分解和最小二乘（SVD-TLS）方法沿同相轴对振幅进行多项式拟合去噪并增加信号高频提高信号分辨率．     

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.     

GUIDED LOW-FREQUENCY NOISE FROM AIRGUN SOURCES*

The presence of the water layer in marine seismic prospecting provides an effective waveguide for acoustic energy trapped between the sea-bed and the sea-surface. This energy persists to large ranges and can be the dominant early feature on far-offset traces. On airgun records, there is commonly a lower frequency set of arrivals following the water-trapped waves. These arrivals are not as obvious with higher frequency watergun sources. By using a combination of intercept-time/slowness (τ—p) mapping on observational data and theoretical modelling, we are able to identify the origin of the events. If a very rapid increase in a seismic wavespeed occurs beneath the sea-bed sediments, a new waveguide is formed bounded by the sea surface and this transition zone. The low frequency waves are principally guided within this thicker waveguide. Numerical filtering in the τ—p domain followed by trace reconstruction is very effective in removing the low frequency noise.     

Ray path of head waves with irregular interfaces

Head waves are usually considered to be the refracted waves propagating along flat interfaces with an underlying higher velocity. However, the path that the rays travel along in media with irregular interfaces is not clear. Here we study the problem by simulation using a new approach of the spectral-element method with some overlapped elements (SEMO) that can accurately evaluate waves traveling along an irregular interface. Consequently, the head waves are separated from interface waves by a time window. Thus, their energy and arrival time changes can be analyzed independently. These analyses demonstrate that, contrary to the case for head waves propagating along a flat interface, there are two mechanisms for head waves traveling along an irregular interface: a refraction mechanism and transmission mechanism. That is, the head waves may be refracted waves propagating along the interface or transmitted waves induced by the waves propagating in the higher-velocity media. Such knowledge will be helpful in constructing a more accurate inversion method, such as head wave travel-time tomography, and in obtaining a more accurate model of subsurface structure which is very important for understanding the formation mechanism of some special areas, such as the Tibetan Plateau.     

HOW DO SHEAR WAVE EVENTS AFFECT NORMAL P-WAVE RECORDS?*

It has been known since the beginning of reflection seismics that several disturbing events seen in seismic records are caused by waves with S-wave velocities instead of P-wave velocity. When using dynamite and recording with vertical geophones these events are primarily caused by converted waves. On the basis of known P- and S-wave velocities in a certain area a theoretical seismogram is calculated, displaying traveltime as well as energy relation for different wave configurations. By comparison with seismograms recorded in the same area it can be shown that converted wave events can be clearly recognized. These events can be described theoretically. Thus, either more effective computer programs can be applied to eliminate these disturbing events, or these events can be evaluated to get additional information about specific strata.     

奇异值分解(SVD)实现地震波场分离与去噪新思路

依据不同性质的地震信号（反射波、折射波、直达波、面波、VSP上\下行波、多次波、随机干扰等）之间在运动学、视速度和相干性上的差异,借助某种数学变换、SVD分解与重构联合、时域与频域结合的方式,通过这些间接的处理手段,把要提取的目标信号或要剔除的干扰信号转换到一种相干性更好的空间域中,再进行SVD分解与重构,最充分利用SVD滤波技术特点,实现地震波场分离与去噪,而不是直接对信号进行SVD分解与重构来实现地震波场分离与去噪,这样做可有效地避免以往对SVD波场分离与去噪技术应用空间狭窄、有效信号损失严重等缺陷性.     

基于逆虚折射干涉法有效提取近地表弱地震信号

在地震勘探中,地形起伏和近地表速度的剧烈变化会导致地震波旅行时的扰动,通常会通过折射波信息来估算和消除这些扰动.本文在虚折射的基础上提出了逆虚折射干涉法,通过虚折射波场和原始折射波场的互相关,并对所有位于固定相位点上的检波点进行叠加,重构出逆虚折射波场.通过逆虚折射与超级虚折射的叠加,保证了不同偏移距下折射波振幅恢复的一致性,显著提高折射波的信噪比,有效提取弱信号.同时,本文采用反褶积干涉法来压制由于互相关和褶积产生的子波旁瓣的影响,弥补低频和高频能量的损失,改善恢复的折射波场的稳定性和分辨率.该新方法不需要知道近地表复杂速度模型的信息,可以将虚折射的勘探孔径恢复到原始地震记录的最大孔径.合成资料和实际资料的计算结果表明,基于反褶积的逆虚折射干涉法能够从低信噪比的资料中,有效恢复出折射波信息.     

不同深度布设台站的噪声及信号幅值特征分析

为探究地震观测中地震计检测到的噪声和信号强度均受其布设深度的影响,本文首先对CPUP和LPAZ两台站布设的不同深度地震计所得到的数据进行噪声水平和地震信号对比;其次采用对比功率谱密度的方法对两台站不同通道采集到的不同时段的噪声数据进行分析;最后比较两台站不同通道采集到的整月数据的噪声幅值、信号幅值、信噪比特征。结果显示:深度较大的通道,其噪声功率均值较小;当事件信号到来时,较深通道的地震计检测到的信号和噪声幅值比较浅通道均有所减小,在信号和噪声幅值均减小的共同影响下,信噪比有一定程度的变化,其中LPAZ台站的信噪比提高较为明显。      

Noise transfer in variable‐depth streamer deghosting

Single‐component towed‐streamer marine data acquisition records the pressure variations of the upgoing compressional waves followed by the polarity‐reversed pressure variations of downgoing waves, creating sea‐surface ghost events in the data. The sea‐surface ghost for constant‐depth towed‐streamer marine data acquisition is usually characterised by a ghost operator acting on the upgoing waves, which can be formulated as a filtering process in the frequency–wavenumber domain. The deghosting operation, usually via the application of the inverse Wiener filter related to the ghost operator, acts on the signal as well as the noise. The noise power transfer into the deghosted data is proportional to the power spectrum of the inverse Wiener filter and is amplifying the noise strongly at the notch wavenumbers and frequencies of the ghost operator. For variable‐depth streamer acquisition, the sea‐surface ghost cannot be described any longer as a wavenumber–frequency operator but as a linear relationship between the wavenumber–frequency representation of the upgoing waves at the sea surface and the data in the space–frequency domain. In this article, we investigate how the application of the inverse process acts on noise. It turns out that the noise magnification is less severe with variable‐depth streamer data, as opposed to constant depth, and is inversely proportional to the local slant of the streamer. We support this statement via application of the deghosting process to real and numerical random noise. We also propose a more general concept of a wavenumber–frequency ghost power transfer function, applicable for variable‐depth streamer acquisition, and demonstrate that the inverse of the proposed variable‐depth ghost power transfer function can be used to approximately quantify the action of the variable‐depth streamer deghosting process on noise.