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.     

A joint inversion algorithm to process geoelectric and surface wave seismic data. Part II: applications

Seismic and geoelectric methods are often used in the exploration of near-surface structures. Generally, these two methods give, independently of one other, a sufficiently exact model of the geological structure. However, sometimes the inversion of the seismic or geoelectric data fails. These failures can be avoided by combining various methods in one joint inversion which leads to much better parameter estimations of the near-surface underground than the independent inversions. In the companion paper (Part I: basic ideas), it was demonstrated theoretically that a joint inversion, using dispersive Rayleigh and Love waves in combination with the well-known methods of DC resistivity sounding, such as Schlumberger, radial dipole-dipole and pole-pole arrays, provides a better parameter estimation. Two applications are shown: a five layer structure in Borsod County, Hungary, and a three-layer structure in Thüringen, Germany. Layer thicknesses, wave velocities and resistivities are determined. Of course, the field data sets obtained from the ‘real world’ are not as complete and as good as the synthetic data sets in the theoretical Part I. In both applications, relative model distances, in percentages, serve as quality control factors for the different inversions; the lower the relative distance, the better the inversion result. In the Borsod field case, Love wave group slowness data and Schlumberger, radial dipole-dipole and pole-pole (i.e two-electrode) data sets are processed. The independent inversion performed using the Love wave data leads to a relative model distance of 155%. An independent Schlumberger inversion results in 41%, a joint geoelectric inversion of all data sets in 15%, a joint inversion of Love wave data and all geoelectric data sets in 15% and the robust joint inversion of Love wave data and the three geoelectric data sets in 10%. In the Thüringen field case, only Rayleigh wave group slowness data and Schlumberger data were available. The independent inversion using Rayleigh wave data results in a relative model distance of 19%. The independent inversion performed using Schlumberger data leads to 34%, the joint and robust joint inversion of Rayleigh wave and Schlumberger data gave results of 18% and 20%, respectively.     

地震面波与重力联合反演方法研究回顾与展望

面波和重力都是研究地下介质的重要手段.面波数据对于地下介质的剪切波速度敏感,但是面波单独反演的非唯一性对反演结果的解释造成了困难.重力数据是地下密度体的综合反映,总体而言受浅部的密度变化影响较大.利用包括岩石物理中的经验关系在内的约束关系作为桥梁,可以通过联合反演充分发挥两种数据的优势,从而获得更合理的反演结果.本文回顾了面波与重力联合反演主要环节的基本方法和研究进展,并指出了两种数据的分辨率不同可能导致的问题,最后对该领域未来的发展方向进行了展望.     

2D surface topography boundary conditions in seismic wave modelling

New formulations of boundary conditions at an arbitrary two-dimensional (2D) free-surface topography are derived. The top of a curved grid represents the free-surface topography while the grid's interior represents the physical medium. The velocity–stress version of the viscoelastic wave equations is assumed to be valid in this grid. However, the rectangular grid version attained by grid transformation is used to model wave propagation in this work in order to achieve the numerical discretization. We show the detailed solution of the particle velocities at the free surface resulting from discretizing the boundary conditions by second-order finite-differences (FDs). The resulting system of equations is spatially unconditionally stable. The FD order is gradually increased with depth up to eighth order inside the medium. Staggered grids are used in both space and time, and the second-order leap-frog and Crank–Nicholson methods are used for time-stepping. We simulate point sources at the surface of a homogeneous medium with a plane free surface containing a hill and a trench. Applying parameters representing exploration surveys, we present examples with a randomly realized surface topography generated by a 1D von Kármán function of order 1. Viscoelastic simulations are presented using this surface with a homogeneous medium and with a layered, randomized medium realization, all generating significant scattering.     

Tutorial: unified 1D inversion of the acoustic reflection response

Acoustic inversion in one-dimension gives impedance as a function of travel time. Inverting the reflection response is a linear problem. Recursive methods, from top to bottom or vice versa, are known and use a fundamental wave field that is computed from the reflection response. An integral over the solution to the Marchenko equation, on the other hand, retrieves the impedance at any vertical travel time instant. It is a non-recursive method, but requires the zero-frequency value of the reflection response. These methods use the same fundamental wave field in different ways. Combining the two methods leads to a non-recursive scheme that works with finite-frequency bandwidth. This can be used for target-oriented inversion. When a reflection response is available along a line over a horizontally layered medium, the thickness and wave velocity of any layer can be obtained together with the velocity of an adjacent layer and the density ratio of the two layers. Statistical analysis over 1000 noise realizations shows that the forward recursive method and the Marchenko-type method perform well on computed noisy data.     

波阻抗反演在储层预测研究中的应用

随着勘探开发的不断深入, 对油气田的老区勘探开发及二次评价,在储层预测研究上,如何更有效地识别碎屑岩储层及变质岩储层,最大限度地降低波阻抗反演过程中某些不确定性因素造成的影响,以确保储层预测的精度,提高钻探的成功率. 波阻抗反演在以上两种储层反演预测的过程中,能够充分利用钻井、测井、试油、试采等动态、静态资料,更好的对地下地质体进行高精度反演预测,找出油气藏储层在纵向、横向上的分布规律,为井位部署及储量上报提供可靠的依据.     

A surface seismic approach to liquefaction

The liquefaction potential of soils is traditionally assessed through geotechnical approaches based on the calculation of the cyclical stress ratio (CSR) induced by the expected earthquake and the ‘resistance’ provided by the soil, which is quantified through standard penetration (SPT), cone penetration (CPT), or similar tests. In more recent years, attempts to assess the liquefaction potential have also been made through measurement of shear wave velocity (V_S) in boreholes or from the surface. The latter approach has the advantage of being non-invasive and low cost and of surveying lines rather than single points. However, the resolution of seismic surface techniques is lower than that of borehole techniques and it is still debated whether it is sufficient to assess the liquefaction potential.In this paper we focus our attention on surface seismic techniques (specifically the popular passive and active seismic techniques based on the correlation of surface waves such as ReMi^TM, MASW, ESAC, SSAP, etc.) and explore their performance in assessing the liquefaction susceptibility of soils. The experimental dataset is provided by the two main seismic events of M_L=5.9 and 5.8 (M_W=6.1, M_W=6.0) that struck the Emilia-Romagna region (Northern Italy) on May 20 and 29, 2012, after which extensive liquefaction phenomena were documented in an area of 1200 km².The CPT and drillings available in the area allow us to classify the soils into four classes: A) shallow liquefied sandy soils, B) shallow non-liquefied sandy soils, C) deep non-liquefied sandy soils, and D) clayey–silty soils, and to determine that on average class A soils presented a higher sand content at the depth of 5–8 m compared to class B soils, where sand was dominant in the upper 5 m. Surface wave active–passive surveys were performed at 84 sites, and it was found that they were capable of discriminating among only three soil classes, since class A and B soils showed exactly the same V_S distribution, and it is possible to show both experimentally and theoretically that they appear not to have sufficient resolution to address the seismic liquefaction issue.As a last step, we applied the state-of-the art CSR–V_S method to assess the liquefaction potential of sandy deposits and we found that it failed in the studied area. This might be due to the insufficient resolution of the surface wave methods in assessing the Vs of thin layers and to the fact that Vs scales with the square root of the shear modulus, which implies an intrinsic lower sensitivity of Vs to the shear resistance of the soil compared to parameters traditionally measured with the penetration tests. However, it also emerged that the pure observation of the surface wave dispersion curves at their simplest level (i.e. in the frequency domain, with no inversion) is still potentially informative and can be used to identify the sites where more detailed surveys to assess the liquefaction potential are recommended.     

输入界面对场地地表地震动参数的影响

本文以江淮地区典型场地资料为原型,选取不同深度的岩层位置作为地震动输入界面,构造多种场地土层模型,选择Taft、Kobe和E1centro 3条强震记录作为地震输入,采用一维频域等效线性化波动方法重点分析了地震动输入界面对场地地表地震动参数的影响。研究结果表明,随着输入界面深度的增加,场地地表的峰值加速度逐渐增加,且增加的幅度呈逐渐减小的趋势,但输入界面深度对地表加速度反应谱特征周期的影响较小;输入界面剪切波速值对反应谱特征周期影响有限,但对地表峰值加速度影响较为显著,地表峰值加速度随着输入界面剪切波速的增大而增大,且两者的增幅呈现近似的线性关系。     

基于混合波场地震动输入技术的近海场地地震反应分析方法

基于人工边界子结构模型,提出一种利用混合波场实现近海场地中地震P波和SV波垂直输入的方法.该方法中用于波动输入的混合波场由计算模型两侧截断边界的自由波场和底面边界的入射波场构成,避免了不规则近海场地的自由波场求解.同时采用基于声流体单元的流固耦合算法模拟场地-海水动力相互作用,利用流体介质人工边界和黏弹性人工边界单元模...     

Look-ahead vertical seismic profiling inversion approach for density and compressional wave velocity in Bayesian framework

To reduce drilling uncertainties, zero-offset vertical seismic profiles can be inverted to quantify acoustic properties ahead of the bit. In this work, we propose an approach to invert vertical seismic profile corridor stacks in Bayesian framework for look-ahead prediction. The implemented approach helps to successfully predict density and compressional wave velocity using prior knowledge from drilled interval. Hence, this information can be used to monitor reservoir depth as well as quantifying high-pressure zones, which enables taking the correct decision during drilling. The inversion algorithm uses Gauss–Newton as an optimization tool, which requires the calculation of the sensitivity matrix of trace samples with respect to model parameters. Gauss–Newton has quadratic rate of convergence, which can speed up the inversion process. Moreover, geo-statistical analysis has been used to efficiently utilize prior information supplied to the inversion process. The algorithm has been tested on synthetic and field cases. For the field case, a zero-offset vertical seismic profile data taken from an offshore well were used as input to the inversion algorithm. Well logs acquired after drilling the prediction section was used to validate the inversion results. The results from the synthetic case applications were encouraging to accurately predict compressional wave velocity and density from just a constant prior model. The field case application shows the strength of our proposed approach in inverting vertical seismic profile data to obtain density and compressional wave velocity ahead of a bit with reasonable accuracy. Unlike the commonly used vertical seismic profile inversion approach for acoustic impedance using simple error to represent the prior covariance matrix, this work shows the importance of inverting for both density and compressional wave velocity using geo-statistical knowledge of density and compressional wave velocity from the drilled section to quantify the prior covariance matrix required during Bayesian inversion.     

海南岛介质非弹性衰减及场地响应反演

利用海南数字地震台网18个地震台274条波形资料,运用遗传算法反演海南岛非弹性衰减系数及台站场地响应,计算得到海南岛非弹性衰减Q值随频率f的关系为Q（f）=343.7f^0.42,说明海南岛适中Q值区域,地壳相对稳定。18个地表台站的场地响应场与频率有关,其中：7个台站的场地响应接近1,平稳变化;2个台站在高频部分衰减;7个台站的场地响应小于1,变化平稳; 2个台站低频部分场地响应接近1,高频部分放大。     

地震波斜入射下层状场地中地下综合管廊地震响应分析

利用黏弹性人工边界和等效地震荷载时域波动输入方法,结合土层和半空间的精确动力刚度矩阵,实现了地震波斜入射下层状场地地下综合管廊地震反应分析,建立了不同场地条件下地下综合管廊分析模型。计算结果表明:地震波倾斜入射情况下,综合管廊结构地震响应与垂直入射时具有显著差异,一般SV波以30°临界角附近入射时结构地震反应最为剧烈;地下综合管廊动应力集中主要分布在管廊角部、中柱上下端;成层土波速结构变化对地下综合管廊地震反应亦具有显著影响。总体上看:当穿越软夹层时管廊结构地震反应更为剧烈,且覆盖层越厚,管廊结构内力幅值越大。因此地下综合管廊结构抗震设计宜考虑地震波倾斜入射及场地土层性质的影响。     

Implications of surface wave data measurement uncertainty on seismic ground response analysis

The extent of data uncertainty of surface-wave measurements may have significant consequences on 1D seismic response analysis and it may lead to inaccurate estimate of design ground motion. In this paper, an attempt has been made to quantify the data measurement uncertainty from a large repetition of the field data at two test sites and to determine bounds of data uncertainty. In the inversion with neighborhood algorithm, we generated profiles below the misfit value calculated from the uncertainty bound. Equivalent profiles have been selected covering the whole misfit value range and these profiles are subjected to equivalent linear 1D ground response analysis. The results of seismic response analysis are presented in the form of amplification spectra and response spectra which show remarkable variations. Significant variation is observed in peak frequency and peak amplification and it differs from one site to the other based on their measured data uncertainty bound. Peak Ground Acceleration (PGA) and peak spectral acceleration at both the sites reflect very high Coefficient of Variation (COV).     

A joint inversion algorithm to process geoelectric and sutface wave seismic data. Part I: basic ideas1

For the exploration of near-surface structures, seismic and geoelectric methods are often applied. Usually, these two types of method give, independently of each other, a sufficiently exact model of the geological structure. However, sometimes the inversion of the seismic or geoelectric data fails. These failures can be avoided by combining various methods in one joint inversion which feads to much better parameter estimations of the model than the independent inversions. A suitable seismic method for exploring near-surface structures is the use of dispersive surface waves: the dispersive characteristics of Rayleigh and Love surface waves depend strongly on the structural and petrophysical (seismic velocities) features of the near-surface Underground. Geoelectric exploration of the structure Underground may be carried out with the well-known methods of DC resistivity sounding, such as the Schlumberger, the radial-dipole and the two-electrode arrays. The joint inversion algorithm is tested by means of synthetic data. It is demonstrated that the geoelectric joint inversion of Schlumberger, radial-dipole and two-electrode sounding data yields more reliable results than the single inversion of a single set of these data. The same holds for the seismic joint inversion of Love and Rayleigh group slowness data. The best inversion result is achieved by performing a joint inversion of both geoelectric and surface-wave data. The effect of noise on the accuracy of the solution for both Gaussian and non-Gaussian (sparsely distributed large) errors is analysed. After a comparison between least-square (LSQ) and least absolute deviation (LAD) inversion results, the LAD joint inversion is found to be an accurate and robust method.     

基于波动方程三维表面多次波预测方法研究

与传统的二维表面多次波预测算法相比,基于波动方程的全三维表面多次波预测方法无需对地下介质做简单近似,其更符合地震波在地下介质中传播的真实状况,是地震资料处理中解决多次波预测问题的强有力工具.本文从三维多次波预测的基本理论出发,给出了全三维多次波预测算法的预测矩阵表示、计算方法以及实现条件,采用GPU(图形处理器)加速全三维表面多次波预测,较传统的CPU串行计算,GPU并行预测表面多次波的计算效率约提高165倍.文中分别利用二维和三维表面多次波预测算法对理论模拟的含表面多次波的三维地震数据进行多次波预测计算,对比分析结果表明,相比于二维算法,文中所述的基于波动方程的全三维表面多次波预测效果明显改善,其计算精度更高,辅以合理有效的自适应相减算法,可获得高精度的地震勘探资料表面多次波压制数据.     

Analysis of the magnetometer response to the passage of seismic wave

Results of synchronous recording magnetic variations and seismic vibrations caused by an earthquake with a magnitude M = 6.7 at a distance of 806 km from the observation site are considered. Measurements are carried out at the VLA observatory. Different patterns of seismic noise generation and their contributions to the magnetic variations recorded by torsion magnetometer are analyzed. As well, the correlation between the seismic and magnetic components is studied. The close correlation between the seismic accelerations of rocks and the magnetic variations is revealed, and its transfer coefficient is estimated. Such correlation in other types of magnetometers is supposed to hinder the measurement of seismomagnetic signals, which will require the seismic noise parameters to be known for different types of magnetometers.     

利用深反射地震数据构建的多阶面波频散曲线反演近地表横波速度结构——以跨班公湖—怒江缝合带深反射地震资料为例

深反射地震剖面法为了获取深部结构特征常常采取大的偏移距采集数据.目前公开发表的相关资料中,鲜有利用深反射地震炮集数据获取近地表的结构特征.为此,本文通过正演测试了相关数据处理流程,即利用有限差分正演了起伏地表模型的大偏移距地震单炮弹性波场特征,通过共检波点域面波信号F-K频谱叠加构建新方法,从深反射地震数据集中提取了高品质的多阶面波频散曲线,再利用多阶面波联合反演获得了近地表的结构特征.在前述正演流程基础上,利用跨越班公湖—怒江缝合带的SinoProbe深反射地震剖面中的实际炮集数据,求取了基阶和一阶瑞利波频散曲线,联合反演后得到近地表横波速度结构.该结果与初至波走时反演获取的纵波速度结构具有较好的一致性,且在近地表的浅层分辨率较纵波速度结构特征更高,而更与已有地质认识相吻合.本文提供的相关数据处理流程表明利用深反射地震炮集数据,也能够获取近地表浅层的横波速度结构.

     

SH波地表散射的局域边界元模拟

本文提出了一种计算不规则起伏地形中SH波散射的有效方法——局域边界元法.本方法基于传统边界元法,为计算复杂地表散射问题提供了一种更加高效的解决方案.根据地震波满足的边界积分方程中牵引力格林函数的特性,我们将自由边界分解成水平部分和起伏部分.通过公式推导,可将水平部分的位移由起伏部分的位移通过格林函数线性叠加表示,因此只需对起伏部分的位移进行直接求解,从而极大地减少了待求解的未知数个数,显著提高了计算效率.通过与半圆形山谷SH波平面波入射的解析解比较,验证了方法的正确性.数值模型比较显示,局域边界元模拟结果与传统边界元数值解完全吻合,但是大幅提高了计算效率.因此,局域边界元法可以作为模拟不规则地形中地震波散射的有效工具.

     

利用深反射地震数据构建的多阶面波频散曲线反演近地表横波速度结构——以跨班公湖—怒江缝合带深反射地震资料为例

深反射地震剖面法为了获取深部结构特征常常采取大的偏移距采集数据.目前公开发表的相关资料中,鲜有利用深反射地震炮集数据获取近地表的结构特征.为此,本文通过正演测试了相关数据处理流程,即利用有限差分正演了起伏地表模型的大偏移距地震单炮弹性波场特征,通过共检波点域面波信号F-K频谱叠加构建新方法,从深反射地震数据集中提取了高品质的多阶面波频散曲线,再利用多阶面波联合反演获得了近地表的结构特征.在前述正演流程基础上,利用跨越班公湖—怒江缝合带的SinoProbe深反射地震剖面中的实际炮集数据,求取了基阶和一阶瑞利波频散曲线,联合反演后得到近地表横波速度结构.该结果与初至波走时反演获取的纵波速度结构具有较好的一致性,且在近地表的浅层分辨率较纵波速度结构特征更高,而更与已有地质认识相吻合.本文提供的相关数据处理流程表明利用深反射地震炮集数据,也能够获取近地表浅层的横波速度结构.     

Stepwise joint inversion of surface wave dispersion,Rayleigh wave ZH ratio,and receiver function data for 1D crustal shear wave velocity structure

Accurate determination of seismic velocity of the crust is important for understanding regional tectonics and crustal evolution of the Earth. We propose a stepwise joint linearized inversion method using surface wave dispersion, Rayleigh wave ZH ratio (i.e., ellipticity), and receiver function data to better resolve 1D crustal shear wave velocity (v _S) structure. Surface wave dispersion and Rayleigh wave ZH ratio data are more sensitive to absolute variations of shear wave speed at depths, but their sensitivity kernels to shear wave speeds are different and complimentary. However, receiver function data are more sensitive to sharp velocity contrast (e.g., due to the existence of crustal interfaces) and v _P/v _S ratios. The stepwise inversion method takes advantages of the complementary sensitivities of each dataset to better constrain the v _S model in the crust. We firstly invert surface wave dispersion and ZH ratio data to obtain a 1D smooth absolute v _S model and then incorporate receiver function data in the joint inversion to obtain a finer v _S model with better constraints on interface structures. Through synthetic tests, Monte Carlo error analyses, and application to real data, we demonstrate that the proposed joint inversion method can resolve robust crustal v _S structures and with little initial model dependency.