Joint inversion of high-frequency surface waves with fundamental and higher modes

Joint inversion of multimode surface waves for estimating the shear (S)-wave velocity has received much attention in recent years. In this paper, we first analyze sensitivity of phase velocities of multimodes of surface waves for a six-layer earth model, and then we invert surface-wave dispersion curves of the theoretical model and a real-world example. Sensitivity analysis shows that fundamental mode data are more sensitive to the S-wave velocities of shallow layers and are concentrated on a very narrow frequency band, while higher mode data are more sensitive to the parameters of relatively deeper layers and are distributed over a wider frequency band. These properties provide a foundation of using a multimode joint inversion to define S-wave velocities. Inversion results of both synthetic data and a real-world example demonstrate that joint inversion with the damped least-square method and the singular-value decomposition technique to invert high-frequency surface waves with fundamental and higher mode data simultaneously can effectively reduce the ambiguity and improve the accuracy of S-wave velocities.     

基阶与高阶瑞利波联合反演研究

研究了六层层状介质模型瑞利波基阶和高模式波相速度对横波速度、深度的敏感性,结果表明：基阶波较高模式波对7 m以内浅部地层的横波速度更敏感,敏感性频带在10～25 Hz范围内,峰值频带集中在18 Hz左右;高模式波较基阶波对深部地层的横波速度更敏感,敏感性频带宽,峰值分散.基阶波对浅层的敏感性和高模式波穿透深度更深的特点为近地表岩土层二维横波速度结构的联合反演提供了前提条件.利用阻尼最小二乘SVD（Singular Value Decomposition）算法联合基阶与高模式波对理论模型和实例数据进行横波速度反演,反演结果表明联合反演增强了反演的稳定性,提高了反演的精度.     

基于EEMD分解的气压改正方法研究

利用超导重力仪观测数据精确测定低于1 mHz的地球自由振荡简正模式的分裂频率,是在不与任何弹性系数发生联系的情况下改善一维密度模型的有效方法.但在该频段台站局部气压变化对重力观测数据的影响成为主要干扰来源,且具有频率依赖特性,因此精细地开展气压改正成为利用超导重力数据检测低频自由振荡信号的必要手段.本文基于EEMD方法,提出了一种具有频率依赖特性的气压改正方法.该方法将重力观测和气压变化分解成处于不同频段的本征模态函数,并在相应频段上分别进行重力-气压变化的回归分析,计算得到具有频率依赖特性的气压导纳值,精细地消除气压变化对重力观测的影响,并以此对微弱低频地球自由振荡信号开展高分辨率分析.基于本文提出的气压改正方法,利用大地震后的超导重力数据检测了频率小于1.5 mHz的低频地球自由振荡及其频谱分裂现象.研究结果表明：利用该方法进行气压改正后检测得到的各简正模具有更高的信噪比,估计的本征频率误差水平明显降低,获得的基频球型振荡₀S₂和₀S₃以及一阶球型振荡₁S₂的分裂谱峰的估计精度更高,同时还检测到了部分环型振荡在重力观测中的耦合现象.对低频地球振荡的高分辨率检测结果验证了基于EEMD分解提出的气压改正方法的有效性,同时再次证明了超导重力仪观测数据在低频地球自由振荡检测中的优势.     

Higher modes in simplified inelastic seismic analysis of single column bent viaducts

The influence of the higher modes and their consideration in the pushover analysis of reinforced concrete single column bent viaducts with different degree of irregularity is discussed. Typical multimode pushover‐based methods (modal pushover analysis, modal adaptive non‐linear static procedure and incremental response spectrum analysis) are addressed and compared with a single mode procedure (N2) and inelastic time history analysis. If in the transverse direction the substructure of the viaduct is flexible in comparison with the superstructure, the influence of higher modes is small (the structure is regular) and single mode procedure works well. This typically occurs when the columns are high or considerably damaged. Conversely, for the analysis of irregular structures having short and slightly damaged columns, the multimode methods are needed. In most cases, all the analysed multimode pushover‐based methods have given the results comparable with time history analysis, with the exception of cases where torsional sensitivity is varying during the response. All the methods have limitations (discussed in detail in the paper), which should be fully recognized by the user. Copyright © 2005 John Wiley & Sons, Ltd.     

Dispersion Energy Analysis of Rayleigh and Love Waves in the Presence of Low-Velocity Layers in Near-Surface Seismic Surveys

High-frequency surface-wave analysis methods have been effectively and widely used to determine near-surface shear (S) wave velocity. To image the dispersion energy and identify different dispersive modes of surface waves accurately is one of key steps of using surface-wave methods. We analyzed the dispersion energy characteristics of Rayleigh and Love waves in near-surface layered models based on numerical simulations. It has been found that if there is a low-velocity layer (LVL) in the half-space, the dispersion energy of Rayleigh or Love waves is discontinuous and ‘‘jumping’’ appears from the fundamental mode to higher modes on dispersive images. We introduce the guided waves generated in an LVL (LVL-guided waves, a trapped wave mode) to clarify the complexity of the dispersion energy. We confirm the LVL-guided waves by analyzing the snapshots of SH and P–SV wavefield and comparing the dispersive energy with theoretical values of phase velocities. Results demonstrate that LVL-guided waves possess energy on dispersive images, which can interfere with the normal dispersion energy of Rayleigh or Love waves. Each mode of LVL-guided waves having lack of energy at the free surface in some high frequency range causes the discontinuity of dispersive energy on dispersive images, which is because shorter wavelengths (generally with lower phase velocities and higher frequencies) of LVL-guided waves cannot penetrate to the free surface. If the S wave velocity of the LVL is higher than that of the surface layer, the energy of LVL-guided waves only contaminates higher mode energy of surface waves and there is no interlacement with the fundamental mode of surface waves, while if the S wave velocity of the LVL is lower than that of the surface layer, the energy of LVL-guided waves may interlace with the fundamental mode of surface waves. Both of the interlacements with the fundamental mode or higher mode energy may cause misidentification for the dispersion curves of surface waves.     

基于瑞利波高阶模式反演的实验研究

通过超声实验研究了沿分层介质,特别是含有低速层的分层介质传播的瑞利波频散特征. 分别对有机玻璃/钢构成的两层速度递增的半空间和铝/有机玻璃/钢构成的含有低速层的三层半空间进行了超声探测实验,采用频率波数分析方法分析了多模式的瑞利波频散曲线,对于速度递增的两层半空间,得到了第一和第二个模式的频散曲线; 对于含有低速层的三层介质,实验得到的频散曲线在不同频段对应不同的模式,从而在模式之间产生跳跃, 分析表明模式跳跃是由各个模式在表面位移幅度的不同分布引起的. 文中明确指出了低速层存在时,反演研究不仅要考虑各模式的频散特性,同时还要考虑不同模式在表面的位移分布情况,给出了低速层存在时的反演方法,避免了模式的误判. 利用遗传算法对两种实验模型的介质参数进行了反演,得到了和实际参数吻合的反演结果.     

随钻四极源声波测井多模式采集测量TTI地层各向异性的研究

本文应用三维柱坐标时域有限差分方法模拟了多极子随钻声波测井的波场,提出了在横向各向同性（TI）慢速地层倾斜井中,使用四极源激发、多模式采集进行各向异性参数反演的方法.模拟结果表明：在强各向异性地层大角度倾斜井中使用四极源能够激发出多极模式波,并且井孔内的声场会随着声源方向角β（声源方向和快横波偏振方向的夹角）的改变而发生变化.使用四极子采集方式记录时,可以发现波形会分裂成快慢两种波;并且在声源方向与地层快横波偏振方向成45°时,分裂的两种波形的速度更趋近于地层快慢横波波速,用此可反演地层各向异性值大小.使用单极子采集方式记录时,其波形能量与声源方向角β大致成cos²2β的关系,在声源方向角为45°时,其波形幅度最小,用此可判断与快横波偏振方向成45°角的方向.使用AC方向（与声源同方向）偶极子采集方式记录时,当声源方向与快横波偏振方向一致时,采集到的波形幅度最小;而与快横波偏振方向垂直时,波形幅度最大,所以通过偶极子采集方式记录的波形可以判断快横波偏振方向.因此,在强各向异性倾斜井中进行随钻四极子测量时,可以使用多模式采集方式来进行地层各向异性的反演.     

面波频散谱多模式高分辨率成像的多道信号比较法

高分辨率的面波频散谱成像是浅层地震勘探领域基于频散性质反演横波速度结构中的一个关键步骤.在天然地震探测领域,仅利用两个台站记录的线性信号比较法(LSC),被广泛用来计算面波的频散谱,并用于大尺度的面波层析成像.然而互相关的成像方式会造成频散谱在低频端较低的分辨率.非线性信号比较法(NLSC)利用指数函数克服了这个问题,同时极大地提高了频散谱的成像分辨率.然而,在研究中我们发现,仅利用两个台站的地震记录,并不能将面波的频散特性完整地考虑在内,导致LSC和NLSC方法对高阶模式的成像存在较大的误差.由于主动源面波勘探多道采集的方式,基于信号比较理论的多道信号比较法(MSC)充分利用多道地震信号,可以获得准确的多模式成像,然而该方法需要计算任意两道的频散谱并叠加,存在冗余的计算,导致计算效率较低.因此,本研究对MSC方法进行了相应的改进,通过追踪炮集记录上的面波波组提高了原方法的计算效率,同时,利用理论频散曲线进行叠加分析,验证了改进的MSC方法的正确性和有效性.通过与相移法、LSC和NLSC方法的对比分析,展示了MSC方法是一种准确的、高分辨率的面波多模式频散谱成像方法.实际地震资料的应用,揭示了MSC方法在浅层地震勘探中用于提取面波多模式频散信息的巨大潜力.     

Signal reconstruction of surface waves on SASW measurement using Gaussian Derivative wavelet transform

Surface wave method consists of measurement and processing of the dispersive Rayleigh waves recorded from two or more vertical transducers. The dispersive phase data are inverted and the shear wave velocity versus depth is obtained. However, in case of residual soil, the reliable phase spectrum curve is difficult to be produced. Noises from nature and other human-made sources disturb the generated surface wave data. In this paper, a continuous wavelet transform based on mother wavelet of Gaussian Derivative was used to analyze seismic waves in different frequency and time. Time-frequency wavelet spectrum was employed to localize the interested seismic response spectrum of generated surface waves. It can also distinguish the fundamental mode of the surface wave from the higher modes of reflected body waves. The results presented in this paper showed that the wavelet analysis is able to determine reliable surface wave spectrum of sandy clayey residual soil.     

Effect of topography and subsurface inhomogeneity on seismic rayleigh waves

The effect of topography and subsurface inhomogeneity on surface motion is investigated in the case of Rayleigh waves. In the previous paper, the same effect was investigated in the case of SV waves. Several types of topography, such as cliffs both with and without a soft layer at the foot of the slope, are considered. Computations are made using a new hybrid method combining a particle model with a finite element method. In cases of harmonic Rayleigh waves, surface motions with amplitudes as large as 1.5 to 5 times the horizontal surface displacement of the incident Rayleigh waves are produced near the slope and the sloping interface. When a Rayleigh wave propagating through a hard single-layered ground encounters a sloping interface where hard ground and soft ground make contact with each other, Rayleigh waves having two different, phase velocities are produced and they correspond to the fundamental mode, and the first mode determined by Haskell's method. In addition, the transient response when Rayleigh waves propagate through the cliff is also simulated. Assuming the vertical component of the Tokachi-oki Earthquake (1968) measured on the surface to be a Rayleigh wave, the incident Rayleigh wave can be obtained by a Fourier synthesis of eigenfunctions of Rayleigh waves.     

基于矢量预测的SIMO系统混合相位地震子波提取方法研究

针对高阶统计量混合相位地震子波提取方法的局限性, 提出一种基于矢量预测的单输入多输出系统(SIMO)的混合相位地震子波提取方法. 该方法利用二阶循环平稳统计量包含的系统相位信息, 将CMP道集视为一个单输入多输出系统的输出, 利用道集中相邻两道或多道数据通过矢量预测来构建反子波计算的方程式, 进一步进行混合相位子波提取. 利用提取出的子波相位信息对CMP道集进行纯相位滤波, 能够替代相位校正技术, 并且利用获取的反褶积算子对CMP道集进行反褶积处理, 使提高分辨率后的不同道子波振幅、 频率、 波形相一致, 提高叠加的质量. 模型试算和实际资料处理结果表明, 文中方法适用于任意相位的子波提取及反褶积处理, 且处理精度较高, 具有较高的实际应用价值.      

IDENTIFICATION OF SEISMIC REFLECTIONS USING SINGULAR VALUE DECOMPOSITION*

Singular value decomposition (SVD) is applied to the identification of seismic reflections by using two different models: the impulse response model, where a seismic trace is assumed to consist of a known signal pulse convolved with a reflection coefficient series plus noise, and the delayed pulse model, where the seismic signal is assumed to consist of a small number of delayed pulses of known shape and with unknown amplitudes and arrival times. SVD clearly shows how least-squares estimation of the reflection coefficients may become unstable, since a division by the singular values is required. Two methods for stabilizing this procedure are investigated. The inverse of the singular values may be replaced by zeros when they are less than a given threshold. This is called the SVD cut-off method. Alternatively, we may use ridge regression which in filter design corresponds to assuming white noise. Statistical methods are used to compute an optimal SVD cut-off level and also to compute an optimal weighting parameter in ridge regression. Numerical studies indicate that the use of SVD cut-off or ridge regression stabilizes the least-squares procedure, but that the results are inferior to maximum-likelihood estimation where the noise is assumed to be filtered white noise. For the delayed pulse model, we use a linearization procedure to iteratively update the estimates of both the reflection amplitudes and the arrival times. In each step, the optimal SVD cut-off method is used. Confidence regions for the estimated reflection amplitudes and arrival times are also computed. Synthetic data examples demonstrate the effectiveness of this method. In a real data example, the maximum-likelihood method assuming an impulse response model is first used to obtain initial estimates of the number of reflections and their amplitudes and traveltimes. Then the iterative procedure is used to obtain improved estimates of the reflection amplitudes and traveltimes.     

Simulation of the seismic response of sedimentary basins with constant-gradient velocity along arbitrary direction using boundary element method:SH case

We presented a boundary element method using the approximate analytical Green's function given by Sánchez-Sesma et al.Coordinate transform is introduced to extend the method to deal with the model with constant-gradient velocity along oblique direction.The method is validated by comparing the numerical results with other independent methods.This method provides a useful tool for analyzing local site effects.We computed seismic response for two series of models.The results in both frequency and time domains are analyzed and show complex amplification patterns.The fundamental mode of resonance is dependent not only on the velocity at the free surface but also on the velocity distribution of the whole basin.For the higher modes of vibration the heterogeneous basin also has its own characteristic.     

体应变潮汐观测资料信息提取与映震效果

根据体应变观测资料的特点, 研究了体应变观测资料的处理方法, 提出了在时间域分析的数学模型。在数学模型中, 将潮汐因子、气压系数、非潮汐应变速率和加速度一并考虑, 在资料处理结果中, 这些参数可同时取得。分别用时间域分析方法和频率域分析方法对观测数据进行了处理, 发现潮汐因子、气压系数、应变速率和加速度等参数在大同地震前均有大小不同、持续时间不等的异常, 这些参数可作为物理意义明确的地震中短期预测的指标。     

Apparent phase velocities and fundamental-mode phase velocities of Rayleigh waves

Rayleigh wave dispersion data usually appear in the form of multimodal spectra for a layered model structure. The number of dispersion modal curves depends on the number of layers in the model. The measured dispersion velocities from the frequency–wavenumber (F–K) space, however, may not represent the true phase velocities of the fundamental-mode dispersion curve, but apparent phase velocities. The present study discusses how multimode curves are generated in the multichannel analysis of surface waves (MASW) method and the cause of the apparent velocity produced by the F–K method. Results from a field trial demonstrate that apparent phase velocities fail to reveal thin layers with low velocities. A better agreement of the inverted model with the geotechnical record is obtained by using the data points extracted from the fundamental-mode curve of the MASW spectral image.     

我国境内瑞利波的相速度

本文利用新不列颠岛两个地震在十二个基本台站所记录到的瑞利波,计算了我国不同地区的相速度.着重讨论鉴别和对比不同台站记录中同一震相的方法.在大部分台站的记录中,见到有周期约为35秒的相位,和后面的位相比较,它的周期较大,振幅较小.波形的对比对初步鉴别震相有很大的帮助.详细的震相对比是根据周期随距离变化的规律和各震相到时的规律.两个地震所得的相速度很符合.计算的结果表明:利用三台计算相速度时,如果射线的路程差别较大,海洋路程的校正是不能忽略的.因为有关我国地壳构造的资料还很少,我们所得的瑞利波相速度只能与普瑞司修正后非洲大陆的相速度理论相比较,由此得到我国不同地区的地壳厚度.这样所得的厚度,虽然不能视为最后的结果,但是它们仍然表现与主要地质单元之间有密切的联系.     

Constituents of Vertical-component Coda Waves at Long Periods

Aki (1969) first modeled coda waves of a local earthquake as a superposition of scattered surface waves. This paper attempts to clarify the constituents of surface-wave coda at long periods at very long lapse times. For a large earthquake of magnitude 7 or larger, vertical component oscillation in periods from 90 to 180 s persists for more than 20 hours from the earthquake origin time. Although the early portion of the coda envelope is successfully modeled by assuming incoherent scattered Rayleigh waves by heterogeneities distributed all over the Earth, the later potion of the observed coda envelope (roughly later than 35,000 s) has systematically larger amplitude than theoretical prediction. To clarify the cause of this discrepancy, we studied the constituents of vertical-component seismograms of three large earthquakes recorded by the F-net in Japan using the f-k power spectral analysis. We found that the direct and scattered fundamental-mode Rayleigh waves of velocity about 3.7 km/s are dominant in the earlier part of each envelope. It justifies the use of a scattering model of the fundamental Rayleigh waves for synthesizing the envelope. At lapse times later than 20,000 s–35,000 s, higher modes with phase velocities around 20 km/s become dominant. The transition time to the dominance of higher modes is found to become earlier for a deeper focus earthquake. The small coda attenuation factor from (1.90±0.23) × 10⁻³ to (2.38±0.32) × 10⁻³ estimated from later coda envelopes recorded at IRIS stations distributed worldwide also agrees with the attenuation factor of spheroidal modes according to PREM. We may interpret that higher mode waves are uniformly distributed at large lapse time due to large velocity dispersion and/or scattering and they dominate over the fundamental mode waves because of smaller attenuation in the lower mantle. The coda attenuation measurement proposed by Aki is found to be useful even for long periods and at very large lapse times.     

Multipole borehole acoustic theory: Source imbalances and the effects of an elastic logging tool

In recent years the emphasis in acoustic logging has been shifting from the wireline to the Logging While Drilling (LWD) environment, the latter being far different from the former in that both tool rigidity and tool radius are considerably greater. In this paper we present a generic mathematical formulation for the multipole borehole acoustic measurement (alternate and equal polarity case), including a detailed analysis on the effects of multipole source amplitude imbalances. It is shown that source imbalance induced mode contaminants have excitation amplitudes that are scaled by the sum of the relative source imbalances between diametrically opposed sources. Furthermore it is shown that for mode contaminants with odd modal number there can be a significant offset in the associated directivity pattern, even at low levels of source imbalance. However, it is also shown that source imbalance induced mode contaminants can be completely eliminated if the multipole source is accompanied with a ‘vertically’ (but not azimuthally) offset multipole receiver. Mathematically, it is demonstrated (for a centered tool) that a polarity weighted stack of these multipole receivers completely eliminates the source imbalance induced mode contaminants. Excitation amplitudes and phase slowness of borehole guided modes are presented for the most common excitation regimes, i.e., monopole, dipole, quadrupole and the hexapole excitation, the latter one showing to have the advantage of a higher formation shear cut-off frequency than the quadrupole mode. Special emphasis will be on the analysis of the dipole excitation and the differences that occur due to variations in tool rigidity, tool diameter and (isotropic) formation properties with the resulting conclusion that a formation flexural mode is not observable as a result of a LWD dipole excitation (this opposed to its dipole wireline counterpart). The guided mode excitation amplitudes are calculated as residues using a Laurent series expansion. This (unconventional) way of calculating the residue has the advantage that it is independent of the pole order, does not require the numerical evaluation of derivatives with respect to the vertical wavenumber and allows for an accurate and efficient FFT implementation.     

Data-resolution Matrix and Model-resolution Matrix for Rayleigh-wave Inversion Using a Damped Least-squares Method

Inversion of multimode surface-wave data is of increasing interest in the near-surface geophysics community. For a given near-surface geophysical problem, it is essential to understand how well the data, calculated according to a layered-earth model, might match the observed data. A data-resolution matrix is a function of the data kernel (determined by a geophysical model and a priori information applied to the problem), not the data. A data-resolution matrix of high-frequency (≥2 Hz) Rayleigh-wave phase velocities, therefore, offers a quantitative tool for designing field surveys and predicting the match between calculated and observed data. We employed a data-resolution matrix to select data that would be well predicted and we find that there are advantages of incorporating higher modes in inversion. The resulting discussion using the data-resolution matrix provides insight into the process of inverting Rayleigh-wave phase velocities with higher-mode data to estimate S-wave velocity structure. Discussion also suggested that each near-surface geophysical target can only be resolved using Rayleigh-wave phase velocities within specific frequency ranges, and higher-mode data are normally more accurately predicted than fundamental-mode data because of restrictions on the data kernel for the inversion system. We used synthetic and real-world examples to demonstrate that selected data with the data-resolution matrix can provide better inversion results and to explain with the data-resolution matrix why incorporating higher-mode data in inversion can provide better results. We also calculated model-resolution matrices in these examples to show the potential of increasing model resolution with selected surface-wave data.     

Variations of the lunar geomagnetic tide in the Indian region

The seasonal variations of the lunar geomagnetic tide are analysed at a group of stations around the longitude of India. The position of the focus of the lunar ionospheric current system is found to move with season and to disappear in northern winter. A year-to-year variability of the phases is also demonstrated. The phase relationships indicate the presence of antisymmetric atmospheric tidal modes of various strengths in different seasons. The different lunar Hough mode amplitudes, derived earlier, may also explain the observed September maximum in the lunar horizontal magnetic component at the equator.