Non-uniqueness in surface-wave inversion and consequences on seismic site response analyses

Surface-wave tests are based on the solution of an inverse problem for shear-wave velocity profile identification from the experimentally measured dispersion curve. The main criticisms for these testing methodologies are related to the inverse problem solution and arise from the possible equivalence of different shear-wave velocity profiles. In this paper, some implications of solution non-uniqueness for seismic response studies are investigated using both numerical simulations and experimental data. A Monte Carlo approach for the inversion problem has been used to obtain a set of equivalent shear-wave velocity models. This selection is based on a statistical test which takes into account both data uncertainty and model parameterization. This set of solutions (i.e., soil profiles) is then used to evaluate the seismic response with a conventional one-dimensional analysis. It is shown that equivalent profiles with respect to surface-wave testing are equivalent also with respect to site amplification, thus countering the criticism related to inversion uncertainty for the engineering use of surface-wave tests.     

改进的等效半空间法及瑞雷波频散曲线反演

层状模型的理论频散曲线表明,层状模型表面瑞雷波同一频率对应的相速度具有多值特点,这就是所谓的瑞雷波多阶性. 面波的多阶性导致了实测频散曲线的复杂性,当地层中存在软弱夹层时这一问题尤为突出,从而给实测频散曲线的解释带来了困难. 本文从工程实用的角度出发,根据等效半空间理论,提出了一种计算理论频散曲线的新算法——改进的等效半空间法,避开了面波多阶性这一复杂问题. 由此方法计算得到的面波相速度并不同于某个具体阶数的面波,而是对多阶面波的综合反映. 按照改进的等效半空间法编制了拟合反演程序,并在工程中进行了运用,取得较好的效果.     

中长周期数字化面波记录与中国东南地区地壳结构

本文使用适配滤波频时分析技术首次对中国数字地震台网的中长周期面波记录进行处理,获得穿过东南地区的82条勒夫波频散数据.使用随机反演理论,获得了东南沿海地区4°×4°网格的纯路径频散数据.这些频散的周期为1.95-68.27s,弥补了长周期面波所不能分辨的浅层结构.在网格反演的基础上,使用Harkrider的面波及演程序得出了中国东南地区的地壳和上地幔结构,浅部可分辨到1km,深部可达80km.在分辨率保证的前提下得出东南地区深至80km的三维剪切波速度结构.     

Global surface wave inversion with model constraints‡

Practical applications of surface wave inversion demand reliable inverted shear‐wave profiles and a rigorous assessment of the uncertainty associated to the inverted parameters. As a matter of fact, the surface wave inverse problem is severely affected by solution non‐uniqueness: the degree of non‐uniqueness is closely related to the complexity of the observed dispersion pattern and to the experimental inaccuracies in dispersion measurements. Moreover, inversion pitfalls may be connected to specific problems such as inadequate model parametrization and incorrect identification of the surface wave modes. Consequently, it is essential to tune the inversion problem to the specific dataset under examination to avoid unnecessary computations and possible misinterpretations. In the heuristic inversion algorithm presented in this paper, different types of model constraints can be easily introduced to bias constructively the solution towards realistic estimates of the 1D shear‐wave profile. This approach merges the advantages of global inversion, like the extended exploration of the parameter space and a theoretically rigorous assessment of the uncertainties on the inverted parameters, with the practical approach of Lagrange multipliers, which is often used in deterministic inversion, which helps inversion to converge towards models with desired properties (e.g., ‘smooth’ or ‘minimum norm' models). In addition, two different forward kernels can be alternatively selected for direct‐problem computations: either the conventional modal inversion or, instead, the direct minimization of the secular function, which allows the interpreter to avoid mode identification. A rigorous uncertainty assessment of the model parameters is performed by posterior covariance analysis on the accepted solutions and the modal superposition associated to the inverted models is investigated by full‐waveform modelling. This way, the interpreter has several tools to address the more probable sources of inversion pitfalls within the framework of a rigorous and well‐tested global inversion algorithm. The effectiveness and the versatility of this approach, as well as the impact of the interpreter's choices on the final solution and on its posterior uncertainty, are illustrated using both synthetic and real data. In the latter case, the inverted shear velocity profiles are blind compared with borehole data.     

Velocity analysis based on data correlation

Several methods exist to automatically obtain a velocity model from seismic data via optimization. Migration velocity analysis relies on an imaging condition and seeks the velocity model that optimally focuses the migrated image. This approach has been proven to be very successful. However, most migration methods use simplified physics to make them computationally feasible and herein lies the restriction of migration velocity analysis. Waveform inversion methods use the full wave equation to model the observed data and more complicated physics can be incorporated. Unfortunately, due to the band‐limited nature of the data, the resulting inverse problem is highly nonlinear. Simply fitting the data in a least‐squares sense by using a gradient‐based optimization method is sometimes problematic. In this paper, we propose a novel method that measures the amount of focusing in the data domain rather than the image domain. As a first test of the method, we include some examples for 1D velocity models and the convolutional model.     

地震波频散效应与反Q滤波相位补偿

本文以Futterman提出的地震波振幅衰减和相速度频散表达式为基础,从井震匹配的角度出发,推导了不进行反Q滤波、仅反Q滤波振幅补偿、仅反Q滤波相位补偿,以及反Q滤波相位与振幅同时补偿四种情况下,地震波速度频散与相速度及地震记录振幅谱间的表达式,并从理论上说明了反Q滤波相位补偿的必要性.通过相同观测系统,炸药震源和可控震源分别激发采集的零偏移距VSP资料实例,验证了本文所推导的速度频散表达式的合理性;通过井震标定实例,进一步说明了反Q滤波相位补偿,可有效消除地震子波速度频散,提升地面地震资料与零偏移距VSP走廊叠加剖面的匹配度,最终提高地震资料成果的可信度.     

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.     

基于深度降噪自编码神经网络的中国大陆地壳厚度反演

本文采用基于数据驱动的深度降噪自编码网络构建了瑞雷面波群速度、相速度频散特性与地壳厚度的正反演函数关系,并利用最新频散模型反演了中国大陆的地壳厚度.对于神经网络架构体系的评价,除了考虑传统意义上的测试误差、训练误差之外,本文还用已知物理原理的正演结果与网络预测结果进行比较;在设计网络构架时,同时考虑地球模型和面波频散的...     

Addressing non-uniqueness in linearized multichannel surface wave inversion

The multichannel analysis of the surface waves method is based on the inversion of observed Rayleigh-wave phase-velocity dispersion curves to estimate the shear-wave velocity profile of the site under investigation. This inverse problem is nonlinear and it is often solved using 'local' or linearized inversion strategies. Among linearized inversion algorithms, least-squares methods are widely used in research and prevailing in commercial software; the main drawback of this class of methods is their limited capability to explore the model parameter space. The possibility for the estimated solution to be trapped in local minima of the objective function strongly depends on the degree of nonuniqueness of the problem, which can be reduced by an adequate model parameterization and/or imposing constraints on the solution.
In this article, a linearized algorithm based on inequality constraints is introduced for the inversion of observed dispersion curves; this provides a flexible way to insert a priori information as well as physical constraints into the inversion process. As linearized inversion methods are strongly dependent on the choice of the initial model and on the accuracy of partial derivative calculations, these factors are carefully reviewed. Attention is also focused on the appraisal of the inverted solution, using resolution analysis and uncertainty estimation together with a posteriori effective-velocity modelling. Efficiency and stability of the proposed approach are demonstrated using both synthetic and real data; in the latter case, cross-hole S-wave velocity measurements are blind-compared with the results of the inversion process.     

Discussion on “Implications of surface wave data measurement uncertainty on seismic ground response analysis” by Jakka et al.

The discussion deals with the effect of shear wave velocity uncertainties on 1D seismic ground response analysis. In particular, the paper refers to uncertainties deriving from the solution of the inverse problem in surface wave methods. We address some issues related to the evaluation of “equivalent” profiles from surface wave data, the inversion strategy and the numerical simulation of seismic site response. The pitfalls in the analyses point out the need for more refined studies to draw general conclusions on the subject.     

偏离大圆路径传播对四川西部面波相速度成像的影响

面波成像是研究地壳上地幔横波速度结构的一种重要方法．通常,面波相速度或群速度成像假设面波沿大圆路径传播．但是,在地下介质速度结构变化较大时,面波会偏离大圆路径传播,从而导致基于大圆路径假设下的面波成像结果存在一定的误差. 我们采用基于射线追踪的面波成像方法,研究了面波的偏离大圆路径传播对四川西部地区面波相速度成像结果的影响．使用快速行进法(fast marching method)进行面波传播路径的射线追踪,采用子空间反演法(subspace inversion)进行迭代反演,对理论模型合成数据和川西台阵的短周期背景噪声相速度频散数据进行成像分析,并与使用大圆路径传播的成像结果进行对比．对理论模型的测试结果表明,当速度结构变化较大时,基于偏离大圆路径传播的面波成像能够更好地恢复模型异常．对川西台阵的真实数据反演结果显示:在短周期为6 s时,基于偏离大圆路径传播的反演方法较基于大圆路径传播的反演方法所获得的相速度异常的幅度更大些,在四川盆地区域两者的差异接近0.2 km/s;在周期为10 s时,两种反演方法的差异显著减小,基本都在0.1 km/s以内．这主要是因为6 s周期的面波相速度对复杂的上地壳浅层结构更为敏感,从而使得面波的偏离大圆路径传播效应对反演结果的影响更为显著．本文结果表明,当某一周期不同路径的面波相速度测量值变化较大,例如相对于平均相速度的异常超过10％时,则需考虑采用基于偏离大圆路径传播的面波成像方法,否则速度异常较大区域的反演结果可能会造成较大的偏差．      

The use of MASW method in the assessment of soil liquefaction potential

The multi-channel analysis of surface wave (MASW) method is a non-invasive method recently developed to estimate shear wave velocity profile from surface wave energy. Unlike conventional SASW method, multi-station recording permits a single survey of a broad depth range and high levels of redundancy with a single field configuration. An efficient and unified wavefield transform technique is introduced for dispersion analysis and on site data quality control. The technique was demonstrated in the assessment of soil liquefaction potential at a site in Yuan Lin, Taiwan. The shear wave velocity and liquefaction potential assessments based on MASW method compares favorable to that based on SCPT shear wave measurements. Two-dimensional shear wave velocity profiles were estimated by occupying successive geophone spreads at several sites in central western Taiwan, at some of which sand boils or ground cracks occurred during 1999 Chi Chi earthquake. Liquefaction potential analysis based on MASW imaging was shown to be effective for estimating the extent of potential liquefaction hazard.     

瑞雷波多阶模式频散曲线稀疏正则化反演方法研究

目前瑞雷波多阶模式频散曲线反演中仅考虑数据的拟合,缺乏对模型的约束,不能很好地刻画地层间断面的问题,针对此问题,研究了瑞雷波多阶模式频散曲线稀疏正则化反演方法.正演模拟基于广义反射-透射系数法,数值计算上采用一种快速求根方法,与二等分方法相比,能够在很短的时间内达到最优的收敛效果;反演建模时采用L1范数正则化方法对模型...     

中国西北地区岩石层瑞利波三维速度结构与沉积盆地

研究了中、新生界沉积层所覆盖的我国西北各沉积盆地：准噶尔盆地、塔里木盆地、柴达木盆地，以及一系列中小型盆地和其邻近地域的深部岩石层三维速度结构，探讨其和造山带与油气田的关系．使用了适配滤波频时分析方法，分析了我国数字台网的中长周期瑞利面波资料，计算得到２５７条混合路径的面波群速度频散．利用改进的分格随机反演理论与方法，从混合路径中提取了１００条频散突出路径的４°×４°网格单元的纯路径频散，并反演研究区的三维Ｓ波速度结构．频散的周期从１．９５ｓ到１５１．７ｓ，浅部分辨率可达１ｋｍ，得出了该区深达２００ｋｍ范围内三维瑞利波群速度的分布与特征．所得结果表明：塔里木盆地、哈密－吐鲁番盆地、伊宁盆地以及藏北地区的羌塘盆地具有较好的油气前景．我国西北邻国接壤地带，也均为良好的油气盆地潜在地带．     

Migration velocity analysis by depth image-wave remigration: first results

The image‐wave equation for depth remigration is a partial differential equation that is similar to the acoustic wave equation. In this work, we study its finite‐difference solution and possible applications. The conditions for stability, dispersion and dissipation exhibit a strong wavenumber dependence. Where higher horizontal than vertical wavenumbers are present in the data to be remigrated, stability may be difficult to achieve. Grid dispersion and dissipation can only be reduced to acceptable levels by the choice of very small grid intervals. Numerical tests demonstrate that, upon reaching the true medium velocity, remigrated images of curved reflectors propagate to the correct depth and those of diffractions collapse to single points. The latter property points towards the method's potential for use as a tool for migration velocity analysis. A first application to inhomogeneous media shows that in a horizontally layered medium, the reflector images reach their true depth when the remigration velocity equals the inverse of the mean medium slowness.     

Spatial behaviour of Rayleigh waves in layered half‐spaces under active surface sources

In the free state, Rayleigh waves are assumed to travel in the form of planar wavefronts. Under such an assumption, the propagation behaviour of the modes of Rayleigh waves in layered half‐spaces is only frequency dependent. The frequency behaviour, which is often termed as dispersion, is determined by the shear wave velocity profile of layered soils within the depth related to wavelength (or frequency). According to this characteristic, the shear wave velocity profile can be back‐analysed from the dispersion. The technique is widely used in the surface wave testing. However, the wavefronts of Rayleigh waves activated by the surface sources are non‐planar. The geometric discrepancy could result in Rayleigh waves manifesting distance‐dependent behaviour, which is referred to as spatial behaviour in this paper. Conventional analysis ignoring this spatial behaviour could introduce unexpected errors. In order to take the effects of sources on the propagation behaviour into account, a new mathematical model is established for Rayleigh waves in layered elastic media under vertical disc‐like surface sources using the thin‐layer method. The spatial behaviour of the activated modes and the apparent phase velocity, which is the propagation velocity of Rayleigh waves superposed by the multiple modes, are then analysed. Aspects of the spatial behaviour investigated in this paper include the equilibrium path, the particle orbit, and the geometric attenuation of the activated Rayleigh waves. The results presented in this paper can provide some guidelines for developing new inverse mathematical models and algorithms.     

利用面波和接收函数联合反演滇西地区壳幔速度结构

考虑到面波频散对介质S波速度、接收函数对界面深度的各自敏感性优势,综合利用面波和接收函数资料实现联合反演,求取滇西地区壳幔速度结构. 本文利用适配滤波频时分析技术处理覆盖滇西地区的长周期面波资料,获得105～1050s周期范围内的面波群速度频散,进而利用分格反演方法提取研究区内1°×1°网格纯路径频散;基于滇西地区宽频带三分量远震记录,经反褶积后得到台站下方的远震P波接收函数. 联立面波纯路径频散信息和接收函数资料建立系统方程,利用阻尼最小二乘法实现联合反演,从而获得滇西地区壳幔S波速度结构. 结果表明,滇西地区以红河断裂为界,东西两侧壳幔结构存在明显差异,断裂西侧约20km深度处存在一厚度为10km左右的低速层,而东侧并不明显;滇缅泰块体上的畹町、沧源一带属于上地幔低速区,而另一个地幔低速区则位于滇中块体上的康滇古隆起上,两处地幔低速区与大地高热流分布、强震活动具有较好的对应关系.     

频率多尺度全波形速度反演

以二维声波方程为模型,在时间域深入研究了全波形速度反演.全波形反演要解一个非线性的最小二乘问题,是一个极小化模拟数据与已知数据之间残量的过程.针对全波形反演易陷入局部极值的困难,本文提出了基于不同尺度的频率数据的"逐级反演"策略,即先基于低频尺度的波场信息进行反演,得出一个合理的初始模型,然后再利用其他不同尺度频率的波场进行反演,并且用前一尺度的迭代反演结果作为下一尺度反演的初始模型,这样逐级进行反演.文中详细阐述和推导了理论方法及公式,包括有限差分正演模拟、速度模型修正、梯度计算和算法描述,并以Marmousi复杂构造模型为例,进行了MPI并行全波形反演数值计算,得到了较好的反演结果,验证了方法的有效性和稳健性.     

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.     

Scattering and attenuation of elastic waves in random media

In seismic exploration, elastic waves are sent to investigate subsurface geology. However, the transmission and interpretation of the elastic wave propagation is complicated by various factors. One major reason is that the earth can be a very complex medium. Nevertheless, in this paper, we model some terrestrial material as an elastic medium consisting of randomly distributed inclusions with a considerable concentration. The waves incident on such an inhomogeneous medium undergo multiple scattering due to the presence of inclusions. Consequently, the wave energy is redistributed thereby reducing the amplitude of the coherent wave.The coherent or average wave is assumed to be propagating in a homogeneous continuum characterized by a bulk complex wavenumber. This wavenumber depends on the frequency of the probing waves; and on the physical properties and the concentration of discrete scatterers, causing the effective medium to be dispersive. With the help of multiple scattering theory, we are able to analytically predict the attenuation of the transmitted wave intensity as well as the dispersion of the phase velocity. These two sets of data are valuable to the study of the inverse scattering problems in seismology. Some numerical results are presented and also compared, if possible, with experimental measurements.