Calculation of Rayleigh-wave phase velocities due to models with a high-velocity surface layer

Rayleigh-wave phase velocities have been utilized to determine shear (S)-wave velocities in near-surface geophysics since early 1980s. One of the key steps is to calculate theoretical dispersion curves of an earth model. When the S-wave velocity of the surface layer is higher than some of the layers below, however, the Rayleigh-wave phase velocity in a high-frequency range calculated by existing algorithms approaches the lowest S-wave velocity among the layers above the half-space, rather than a value related to the S-wave velocity of the surface layer. According to our numerical modeling results based on wave equation, trends of the Rayleigh-wave dispersive energy approach about a 91% of the S-wave velocity of the surface layer at a high-frequency range when its wavelength is much shorter than the thickness of the surface layer, which cannot be fitted by a dispersion curve calculated by existing algorithms. We propose a method to calculate Rayleigh-wave phase velocities of models with a high-velocity surface layer by considering its penetration depth. We build a substituted model that only contains the layer with the lowest S-wave velocity among the layers above the half-space and the layers above it. We use the substituted model to replace the original model to calculate phase velocities when the Rayleigh-wave wavelength is not long enough to penetrate the lowest S-wave velocity layer. Several synthetic models are used to verify fitness between the dispersion curve calculated by our proposed method and the trend of the highest dispersive energy. Examples of inversion also demonstrate high accuracy of using our method as the forward calculation method during the inversions.     

Determination of near-surface structures from multi-channel surface wave data using multi-layer perceptron neural network (MLPNN) algorithm

This study proposes the use of multi-layer perceptron neural networks (MLPNN) to invert dispersion curves obtained via multi-channel analysis of surface waves (MASW) for shear S-wave velocity profile. The dispersion curve used in inversion includes the fundamental-mode dispersion data. In order to investigate the applicability and performance of the proposed MLPNN algorithm, test studies were performed using both synthetic and field examples. Gaussian random noise with a standard deviation of 4 and 8% was added to the noise-free test data to make the synthetic test more realistic. The model parameters, such as S-wave velocities and thicknesses of the synthetic layered-earth model, were obtained for different S/N ratios and noise-free data. The field survey was performed over the natural gas pipeline, located in the Germencik district of Ayd?n city, western Turkey. The results show that depth, velocity, and location of the embedded natural gas pipe are successfully estimated with reasonably good approximation.     

声波测井中的相速度与群速度讨论(英文)

声波测井过程中获取的速度到底是相速度还是群速度,目前仍存在一些争议,本文从理论分析和数值模拟的角度,使用三种模型对这一问题进行了研究。首先,构造一个相速度与群速度可调的稳态声波传播模型——不同声速的两个平面波叠加模型,利用慢度时间相关(STC)方法提取声波波速,数值模拟结果表明,无论相速度较大或是群速度较大,STC方法提取出来的波速都是相速度;其次,通过频散分析和割线积分得到刚性壁圆柱流体模型中的频散曲线与分波波形,使用STC方法得到的速度与相速度的频散曲线吻合较好,而直接读取波至获得的速度与群速度的频散曲线趋势一致;最后,利用频散分析和实轴积分方法,获得偶极子在慢地层中激发的模式及全波波形,得到的结果再次验证了刚性壁圆柱流体模型中的结论。     

Determination of dispersive phase velocities for SASW method using harmonic wavelet transform

The spectral analysis of surface waves (SASW) method is an in situ, seismic method for determining the shear wave velocity (or maximum shear modulus) profile of a site. The SASW test consists of three steps: field testing, evaluation of dispersion curve by phase unwrapping method, and determination of shear modulus profile by inversion process. In general, field testing and dispersion curve evaluation are regarded as simple work. However, because of characteristic of Fourier transform used in the conventional phase unwrapping method, dispersion curve is sensitive to background noise and body waves in the low frequency range. Furthermore, under some field conditions such as pavement site, the usual phase unwrapping method can lead to erroneous dispersion curve. To overcome problem of the usual phase unwrapping method, in this paper, a new method of determining dispersion curve for SASW method was applied using time–frequency analysis based on harmonic wavelet transform as an alternative method of a current phase unwrapping method. To estimate the applicability of proposed method to SASW method, numerical simulations at various layered soil and pavement profiles were performed and the dispersion curves by proposed method are more reliable than those by the usual phase unwrapping method.     

The Selection of Field Acquisition Parameters for Dispersion Images from Multichannel Surface Wave Data

The accuracy and resolution of surface wave dispersion results depend on the parameters used for acquiring data in the field. The optimized field parameters for acquiring multichannel analysis of surface wave (MASW) dispersion images can be determined if preliminary information on the phase velocity range and interface depth is available. In a case study on a fill slope in Hong Kong, the optimal acquisition parameters were first determined from a preliminary seismic survey prior to a MASW survey. Field tests using different sets of receiver distances and array lengths showed that the most consistent and useful dispersion images were obtained from the optimal acquisition parameters predicted. The inverted S-wave velocities from the dispersion curve obtained at the optimal offset distance range also agreed with those obtained by using direct refraction survey.     

Structure of the crust in the Black Sea and adjoining regions from surface wave data

Group velocities of Rayleigh and Love waves along the paths across the Black Sea and partly Asia Minor and the Balkan Peninsula are used to estimate lateral variations of the crustal structure in the region. As a first step, lateral variations of group velocities for periods in the range 10–20 s are determined using a 2D tomography method. Since the paths are oriented predominantly in NE–SW or N–S direction, the resolution is estimated as a function of azimuth. The local dispersion curves are actually averaged over the extended areas stretched in the predominant direction of the paths. The size of the averaging area in the direction of the best resolution is approximately 200 km. As a second step, the local averaged dispersion curves are inverted to vertical sections of S-wave velocities. Since the dispersion curves in the 10–20 s period range are mostly affected by the upper crustal structure, the velocities are estimated to a depth of approximately 25 km. Velocity sections along 43° N latitude are determined separately from Rayleigh and Love wave data. It is shown that the crust under the sea contains a low-velocity sedimentary layer of 2–3 km thickness, localized in the eastern and western deeps, as found earlier from DSS data. Beneath the sedimentary layer, two layers are present with velocity values lying between those of granite and consolidated sediments. Velocities in these layers are slightly lower in the deeps, and the boundaries of the layers are lowered. S-wave velocities obtained from Love wave data are found to be larger than those from Rayleigh wave data, the difference being most pronounced in the basaltic layer. If this difference is attributed to anisotropy, the anisotropy coefficient = (SH - SV)/Smean is reasonable (2–3%) in the upper layers, and exceeds 9% in the basaltic layer.     

Dipping-interface Mapping Using Mode-separated Rayleigh Waves

Multichannel analysis of surface waves (MASW) method is a non-invasive geophysical technique that uses the dispersive characteristic of Rayleigh waves to estimate a vertical shear (S)-wave velocity profile. A pseudo-2D S-wave velocity section is constructed by aligning 1D S-wave velocity profiles at the midpoint of each receiver spread that are contoured using a spatial interpolation scheme. The horizontal resolution of the section is therefore most influenced by the receiver spread length and the source interval. Based on the assumption that a dipping-layer model can be regarded as stepped flat layers, high-resolution linear Radon transform (LRT) has been proposed to image Rayleigh-wave dispersive energy and separate modes of Rayleigh waves from a multichannel record. With the mode-separation technique, therefore, a dispersion curve that possesses satisfactory accuracy can be calculated using a pair of consecutive traces within a mode-separated shot gather. In this study, using synthetic models containing a dipping layer with a slope of 5, 10, 15, 20, or 30 degrees and a real-world example, we assess the ability of using high-resolution LRT to image and separate fundamental-mode Rayleigh waves from raw surface-wave data and accuracy of dispersion curves generated by a pair of consecutive traces within a mode-separated shot gather. Results of synthetic and real-world examples demonstrate that a dipping interface with a slope smaller than 15 degrees can be successfully mapped by separated fundamental waves using high-resolution LRT.     

Anisotropy in the Earth's crust and uppermost mantle in southeastern Europe obtained from Rayleigh and Love surface waves

Digital seismograms from 25 earthquakes located in the southeastern part of Europe, recorded by three-component very broadband seismometers at the stations Vitosha (Bulgaria) and Muntele Rosu (Romania), were processed to obtain the dispersion properties of Rayleigh and Love surface waves. Rayleigh and Love group-velocity dispersion curves were obtained by frequency–time analysis (FTAN). The path-averaged shear-wave velocity models were computed from the obtained dispersion curves. The inversion of the dispersion curves was performed using an approach based on the Backus–Gilbert inversion method. Finally, 70 path-averaged velocity models (35 R-models computed from Rayleigh dispersion curves and 35 L-models computed from Love dispersion curves) were obtained for southeastern Europe. For most of the paths, the comparison between each pair of models (R-model and L-models for the same path) shows that for almost all layers the shear-wave velocities in the L-models are higher than in the R-models. The upper sedimentary layers are the only exception. The analysis of both models shows that the depth of the Moho boundary in the L-models is shallower than its depth in the R-models. The existence of an anisotropic layer associated with the Moho boundary at depths of 30–45 km may explain this phenomenon. The anisotropy coefficient was calculated as the relative velocity difference between both R- and L-models at the same depths. The value of this coefficient varies between 0% and 20%. Generally, the anisotropy of the medium caused by the polarization anisotropy is up to 10–12%, so the maximum observed discrepancies between both types of models are also due to the lateral heterogeneity of the shear-wave velocity structure of the crust and the upper mantle in the region.     

横向非均匀介质多道瑞雷波频散曲线正演

作为近地表横波速度结构成像的主要手段之一,面波多道分析法的正问题研究对现场观测系统设计及后续反演计算具有重要意义.目前面波频散曲线的正演主要分为两类:一是对水平层状介质中面波的本征值问题进行求解,该类方法计算效率高但较难考虑地下介质在横向上的不均匀性;二是基于波动方程的全波场模拟,该类方法在理论上可考虑任意复杂的地质模型但计算成本相对较高.本文基于振幅归一化加权的聚束分析,提出了一种适用于横向非均匀介质模型的多道瑞雷波频散曲线正演方法.首先,基于聚束分析的计算公式推导得到了经振幅归一化加权后输出功率谱中相速度与局部相速度之间的关系,然后通过黄金分割极值搜索算法计算得到了多道瑞雷波数据的理论频散曲线.数值分析结果表明,该算法能够快速地实现横向非均匀介质中多道瑞雷波频散曲线的正演计算,所求取的频散曲线与采用二维弹性波时间域有限差分模拟分析得到的结果误差较小,这在一定程度上说明了该计算方法的可靠性,从而可为面波多道分析法中的观测系统快速优化设计以及横向非均匀介质中频散曲线的反演解释提供理论支撑.     

Seismic tomography of Yunnan region using short-period surface wave phase velocity

Introduction The Yunnan region is located on the east margin of the collision zone between the Indian and Eurasian plates; it belongs to the south section of the N-S Seismic Belt of China and is the junc-ture of the Yangtze metaplatform, Songpan-Garz?fold system, Sanjiang fold system and South China fold system. This region has complex tectonic movements, crisscross faults and frequently occurring strong earthquakes, and hence it is one of the regions with the strongest earthquake ac-tivi…     

Experimental determination of Rayleigh-wave mode velocities using the method of wave number analysis

A method is presented to determine experimentally phase and group velocity dispersion curves of propagating Rayleigh-wave modes. Through the application of the Fourier transform method wave number spectra of surface displacements due to wave propagation along a line are constructed. The dominant peaks in the wave number spectra together with their corresponding wave numbers are identified. From the latter the phase velocities, which correspond to the wave modes present, are calculated. The phase and group velocity dispersion curves of wave modes are determined from repeated experiments with different frequencies of excitation. This method to determine the frequency-dependent Rayleighwave velocities solves the problem of non-linear phase changes between surface points in contrast to the conventional phase difference methods which assume linear phase changes.     

Measurement of shallow shear wave velocities at a rock site using the ReMi technique

Shallow shear wave velocities beneath a rock site are characterized using the refraction microtremor (ReMi) technique developed by Louie [Faster, better: shear-wave velocity to 100 m depth from ReMi arrays. Bull Seism Soc Am 2001; 91: 347–64]. Ground motion from a passing train enabled capture of energy propagating parallel to the recording array. This allowed evaluation of the variation of the minimum phase-velocity of the dispersion curve envelope and better estimation of the true minimum velocity beneath the site. We use a new method to image and evaluate the dispersion curve envelope via power–slowness profiles through the slowness–frequency plots introduced by Louie [Faster, better: shear-wave velocity to 100 m depth from ReMi arrays. Bull Seism Soc Am 2001; 91: 347–64]. Data illustrated the frequency dependency of dispersion curve uncertainties, with greater uncertainty occurring at low frequencies. These uncertainties map directly into uncertainty of the inverted velocity–depth profile. Above 100 m depth velocities are well constrained with 10% variability. Variability is greatly reduced when the energy propagation is along the geophone array. Greater velocity variation is observed below 100 m depth.     

基于广义模式识别面波基模式频散曲线反演研究

面波多道分析方法(MASW)是获取垂向剪切波速度剖面的一种有效方法。频散曲线反演是MASW中关键的一步。由于瑞雷波频散曲线反演具有非线性、多参数和多极值的特征,这对于常规的局部线性化反演方法是极大的挑战。为此,本文采取确定性的全局优化算法,广义模式识别算法(GPS)对瑞雷波频散曲线进行反演。其原理可以简述为:算法首先通过模式以确定性的方式对目标函数进行采样来搜索一个点序列;然后使序列中每一个点到下一个点的目标函数值逐渐减少,从而使点序列逐渐逼近全局最优解,最后的解便为待求的最优模型参数。为验证GPS的有效性,首先利用设计的3种典型的6层地质模型通过快速矢量传递算法正演模拟产生基模式频散曲线(频率范围为5~101Hz,频率间隔为2Hz,频点数为49),并对理论频散曲线进行反演。反演结果表明,模型的真实值已经被高度精确地重建。说明GPS可以用于实际勘探中的基模式频散曲线反演。为进一步验证GPS的有效性,在吉林大学校园采集瑞雷波实测数据,并提取基模式频散曲线,应用GPS进行反演。反演重建的横波速度剖面与先验的地质信息吻合得很好。理论模型和真实数据的反演结果表明,GPS可以应用在瑞雷波频散曲线非线性反演中。      

Structure of the upper mantle in Asia from phase and group velocities of Rayleigh waves

Dispersion curves of phase velocities of Rayleigh waves are determined by the method of frequency-time analysis in a range of periods of 10–200 s from data of 43 interstation traces in Central Asia. Because the joint use of phase and group velocities significantly decreases the uncertainty in the determination of S wave velocity structures, the same traces were used for calculating group velocities from tomographic reconstructions obtained in [Yanovskaya and Kozhevnikov, 2003, 2006] and determining average velocity structures along these traces. The velocity structures were calculated by the Monte Carlo and linear inversion methods, which gave consistent results. Using velocity values obtained at fixed depths by the 2-D tomography method, lateral variations in velocities at these depths were estimated, which allowed us to construct smoothed vertical velocity structures at some points in the region. The resulting structures were used as initial approximations for constructing local velocity structures solely from previously obtained local dispersion curves of group velocities in the area (32°–56°N, 80°–120°E). Based on these structures, we mapped the lateral distribution of velocity variations at upper mantle depths of 75–400 km and along three vertical profiles. The inferred velocity variations are in good agreement with data on the tectonics of the region.     

Estimation of crustal structure from observed group velocities ofPL-waves in Japan

Forward modelling of the crustal structure of the eastern Honshu Island, Japan, was made based on the group velocities ofPL-waves in the period range of 20–30 s. The observed values of group velocity were obtained by appling the multiple filter technique to the seismograms for earthquakes with the epicentral distance ranging from 500 to 1000 km. The theoretical values were calculated using Oliver and Major's method to find the best fit dispersion curve in the least-squares sense. The obtained structural model has considerably high crustal velocities compared to other previous models. It was shown that thePL-wave group velocity in the period range of interest was most sensitive to seismic velocities of the center of the crust. Numerical experiments confirmed the applicability of the approximation methods employed to obtain both observed and theoretical group velocities.     

基于频率-贝塞尔变换法的关东盆地S波速度成像

将一种新的方法——频率-贝塞尔变换法（F-Jmethod）应用于日本NIED在关东盆地布设的MeSO-net台网的背景噪声数据中,证明频率-贝塞尔变换法可以有效地从背景噪声中提取高阶频散曲线.利用提取的基阶和高阶频散曲线反演关东盆地区域的沉积层和地震基岩层的S波速度结构,并将我们反演得到的S波速度结构与Koketsu等提出的日本综合速度结构模型进行对比讨论.我们的例子证明,在基阶面波的基础上,高阶面波能减少在反演中的非唯一性,得到更为准确的S波速度结构.     

Simple equations guide high-frequency surface-wave investigation techniques

We discuss five useful equations related to high-frequency surface-wave techniques and their implications in practice. These equations are theoretical results from published literature regarding source selection, data-acquisition parameters, resolution of a dispersion curve image in the frequency–velocity domain, and the cut-off frequency of high modes. The first equation suggests Rayleigh waves appear in the shortest offset when a source is located on the ground surface, which supports our observations that surface impact sources are the best source for surface-wave techniques. The second and third equations, based on the layered earth model, reveal a relationship between the optimal nearest offset in Rayleigh-wave data acquisition and seismic setting—the observed maximum and minimum phase velocities, and the maximum wavelength. Comparison among data acquired with different offsets at one test site confirms the better data were acquired with the suggested optimal nearest offset. The fourth equation illustrates that resolution of a dispersion curve image at a given frequency is directly proportional to the product of a length of a geophone array and the frequency. We used real-world data to verify the fourth equation. The last equation shows that the cut-off frequency of high modes of Love waves for a two-layer model is determined by shear-wave velocities and the thickness of the top layer. We applied this equation to Rayleigh waves and multi-layer models with the average velocity and obtained encouraging results. This equation not only endows with a criterion to distinguish high modes from numerical artifacts but also provides a straightforward means to resolve the depth to the half space of a layered earth model.     

Multichannel analysis of surface wave method with the autojuggie

The shear (S)-wave velocity of near-surface materials and its effect on seismic-wave propagation are of fundamental interest in many engineering, environmental, and groundwater studies. The multichannel analysis of surface wave (MASW) method provides a robust, efficient, and accurate tool to observe near-surface S-wave velocity. A recently developed device used to place large numbers of closely spaced geophones simultaneously and automatically (the ‘autojuggie’) is shown here to be applicable to the collection of MASW data. In order to demonstrate the use of the autojuggie in the MASW method, we compared high-frequency surface-wave data acquired from conventionally planted geophones (control line) to data collected in parallel with the automatically planted geophones attached to steel bars (test line). The results demonstrate that the autojuggie can be applied in the MASW method. Implementation of the autojuggie in very shallow MASW surveys could drastically reduce the time required and costs incurred in such surveys.     

一种基于层析成像技术提高浅地表面波勘探水平分辨率的方法

在高频面波方法中,水平分辨率是指水平方向上分辨异常体的能力.异常体在水平方向上的长度可用水平方向上横波速度的异常尺度来确定.面波多道分析（MASW）方法被广泛应用于浅地表横波速度结构的探测,然而该方法确定的横波速度是整个检波器排列的平均计算结果,因此水平分辨率较差.另外,采用共中心点（CMP）多次覆盖的方式采集数据亦增加了野外的工作量.我们在MASW方法的基础上,应用面波层析成像方法,提出一套提高面波勘探水平分辨率的完整方法的技术流程.首先,利用波场分离技术获得准确的基阶或高阶模式面波,采用相位扫描的互相关方法测量多道面波记录中任意两道之间的面波走时;然后根据面波层析成像方法,获得高分辨率的各目标网格内的纯路径相速度频散曲线;最后反演所有目标网格内的纯路径相速度频散曲线,得到研究区域的拟二维横波速度结构.这套方法具有一定的抗噪能力,理论上它可以准确地提取相邻两道之间面波的相速度频散曲线;同时由于该方法最少只需要1个排列就可以获得拟二维横波速度结构,因此它显著减小了野外工作量.理论模型和实际资料都证实了这套方法可有效提高面波勘探的水平分辨率.     

Rayleigh wave phase velocities of South China block and its adjacent areas

Using records of continuous seismic waveforms from 609 broadband seismic stations in the South China Block and its adjacent areas in 2010–2012, empirical Green's functions of surface waves were obtained from cross-correlation functions of ambient noise data between these stations. High quality phase velocity dispersion curves of Rayleigh waves were obtained using time-frequency analysis. These interstation dispersion curves were then inverted to build Rayleigh wave phase velocity maps at periods of 6–50 s. The results of phase velocity maps indicate that phase velocities at 6–10 s periods are correlated with the geological features in the upper crust. Major basins and small-scale grabens and basins display slow velocity anomalies; while most of the orogenic belts and the fold belts display high velocity anomalies. With the gravity gradient zone along Taihang Mountain to Wuling Mountain as the boundary for the phase velocity maps at period of 20–30 s, the western area mainly displays low velocity anomalies, while the eastern side shows high velocity anomalies. Phase velocities in the eastern South China Block south to the Qinling-Dabie orogenic belt is higher than that in the eastern North China Block to the north, which is possibly due to the differences of tectonic mechanisms between the North China Craton and the South China Block. The phase velocities at periods of40–50 s are possibly related to the lateral variations of the velocity structure in the lower crust and upper mantle: The low-velocity anomalies in the eastern part of the Tibetan Plateau are caused by the thick crust; while the Sichuan Basin and the southern part of the Ordos Basin display distinct high-velocity anomalies, reflecting the stable features of the lithosphere in these blocks. The lateral variation pattern of phase velocities in the southern part of the South China Block is not consistent with the surface trace of the block boundary in the eastern Yunnan Province and its vicinities. The phase velocities in the Sichuan Basin are overall slow at short periods and gradually increase with period from the central part to the edge of the basin, indicating the features of shallower basement in the center and overall stable lithospheric mantle of the basin. The middle and upper crust of the southern Ordos Basin in the North China Block is heterogeneous, while in lower crust and the uppermost mantle the phase velocities mainly exhibit high anomalies. High-velocity anomalies are widespread at the middle of the Qinling-Dabie orogenic belt, as well as the areas in southeastern Guangxi with Caledonian granite explosion, but its detailed mechanism is still unclear.