横向高分辨率瑞雷波数据处理技术研究
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摘要
1885年英国学者瑞雷首先发现并证明均匀半空间中瑞雷波的存在,为后人利用瑞雷波研究地球结构与组成揭开了新的一页。50年代初,Haskel用矩阵方法计算层状介质瑞雷面波频散曲线,奠定了利用天然地震面波信号研究地球内部、利用人工地震面波信号进行近地表地球物理研究的基础。半个世纪以来,许多学者对瑞雷波在多种介质中的传播理论进行了广泛研究。
瑞雷波是一种沿自由界面传播的表面波,它是纵波和横波的干涉波。质点在瑞雷面波传播方向上垂直平面振动,不同波长的瑞雷波是近地表不同深度岩土力学性质的响应。近地表介质(土壤、岩石、堆积物)的横波速度广泛应用于地下水探测、工程和环境勘查领域。由于横波速度在瑞雷波传播过程中起主导作用,所以从面波数据中可快速估计出横波速度。
为克服面波谱分析法(SASW,Spectral Analysis of Surface Waves)提取频散曲线精度低、不能得到高阶模式频散曲线等缺点,美国堪萨斯地质调查所(KGS,Kansas GeologicalSurvey)提出了多道面波分析法(MASW,Multichannel Analysis of Surface Waves)。该方法利用便携式并可重复使用的震源,采集宽频带(2～200 Hz)瑞雷面波;对多道纪录进行波场分析提取一维瑞雷波频散曲线;利用频散曲线反演一维近地表横波速度剖面;通过空间插值构建二维横波速度场。利用多道面波分析法(MASW)反演横波速度具有较高的精度,且野外操作方便和高效等优点,近年来成为瑞雷波勘探研究的热点之一。研究内容主要包括:场地实验可重复性、处理中的假象、模型参数的影响以及其它研究等。
近年来多道面波分析方法研究取得了较大进展,增强了其在实际中的应用能力。然而,提高多道面波分析方法的横向分辨率仍需要深入研究。采用短排列数据提取瑞雷波频散曲线是提高横向分辨率的最有效方法之一。但在实际勘探过程中,基阶瑞雷波数据容易被体波及高模式瑞雷波干扰,因此运用合适的数据处理技术将基阶瑞雷波从单炮数据中分离出来,是实现横向高分辨率瑞雷波勘探的基础和关键。主要体现在:(1)由于体波和多模式瑞雷波在t-x域互相干扰和重叠,因此必须利用先进的数据处理技术对单炮数据进行变换,提高变换后数据的分辨率,获取相应域中相互分离的多模式波及体波,便于在该域中选取基阶瑞雷波;(2)数据正、反变换必须保幅、保角;这样才能实现模式分离;(3)研究快速的数据处理方法技术,以便应用于实际工作。
本文在总结多道面波分析法(MASW)横向分辨率主要因素的基础上,分析瑞雷波数据在不同场域的分布特点,利用波场分离技术进行瑞雷波模式分离,提出横向高分辨率瑞雷波数据处理的方法技术,主要研究内容包括:
(1)定义了多道面波分析法(MASW)获取频散曲线的横向分辨率,它是二维瑞雷波勘探的基础,决定了提高横向分辨率的方法技术。
(2)在分析均匀半空间中利用两道瑞雷波数据计算频散曲线精度的基础上,提出了利用MASW约束和利用两道数据计算频散曲线的数据处理技术。
(3)综合分析目前四种获取频散曲线算法的优缺点,提出了利用高分辨率线性Radon变换求取频散曲线能量谱和分离瑞雷波各模式、利用分离后的单炮数据(仅含基阶瑞雷波)中的相邻道计算基阶瑞雷波频散曲线的计算思路。
(4)对多模式波联合反演进行了初步研究:讨论了六层层状介质模型的基阶和高模式波相速度对横波速度及深度的敏感性,利用阻尼最小二乘SVD算法对该模型进行联合反演,并通过实例数据检验联合反演效果。
本研究得出如下结论:
(1)在满足平面波传播条件下,多道面波分析法(MASW)获取的频散曲线横向分辨率主要由检波器排列长度决定,反演的横波速度是检波器排列下方地球物理模型的平均效应;反演的二维横波速度横向分辨率主要由检波器的排列长度和炮间距决定。因此,利用短检波器排列数据计算瑞雷波频散曲线是提高瑞雷波勘探横向分辨率的直接手段。
(2)利用均匀半空间两道数据计算瑞雷波相速度的精度与道间距(横向分辨率)的关系研究结果表明:道间距越小(横向分辨率越高),计算精度越低;瑞雷波相速度在低频部分的相对误差较高频部分大。在实际应用中,必须在频散曲线的横向分辨率和可靠性之间寻求折衷点;理论和实际数据计算结果表明,在选取合适的道间距后,利用互相关法结合相移法计算两道数据频散曲线,能够获取高横向分辨率并具有较高精度的二维横波速度。
(3)利用高分辨率线性Radon变换计算瑞雷波频散曲线能量谱的结果表明:较倾斜叠加算法,高分辨率线性Radon变换将能量谱的分辨率提高50%以上,为此,可实现各模式波在频率—速度域彼此分离,有利于多模式波频散曲线的提取及分离;
(4)高分辨率线性Radon正、反变换保幅、保角并快速高效的特点,为各模式波的分离提供了基础。理论和实例数据计算结果表明:由于瑞雷波频散曲线能量谱分辨率的提高,各模式波可以准确地从单炮数据中分离出来,且延伸了高模式波的频率范围,有利于得到更深的横波速度信息与更准确地确定高模式波的截止频率;
(5)利用高分辨率线性Radon变换求取频散曲线能量谱、分离各模式瑞雷波、利用分离后的炮集数据(仅含基阶瑞雷波)中的相邻道计算基阶瑞雷波频散曲线。结果表明:较多道面波分析方法(MASW),高横向分辨率瑞雷波数据处理技术在提高频散曲线横向分辨率同时,极大地减少了野外数据采集工作量。例如:在实例中,多道面波分析方法(MASW)需要24炮数据确定一段基岩面,而横向高分辨率瑞雷波数据处理技术仅需要3炮(检波器排列的两个端点和中间各1炮)数据。
(6)六层层状介质模型基阶和高模式瑞雷波相速度对横波速度和深度敏感性研究结果表明:基阶波较高模式波对浅部地层的横波速度更敏感,敏感性频带窄,峰值频带集中;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瑞雷波反演,结果表明:联合反演提高了反演的稳定性和精度。
Rayleigh (1885) firstly described the theory of the motion of Rayleigh waves in a homogeneous elastic half-space, which opened a new page to study the structure and composition of the Earth using Rayleigh waves. Haskel (1953) used matrix method to carry out dispersion computation on a solid layered half-space, which provided the foundation for Earth interior and near-surface geophysics study using earthquake and seismic surface-wave signal. Many scientists have widely investigated on Rayleigh-wave propagation in varies materials over the last half century.
Rayleigh waves are surface waves that travel along a 'free' surface, such as the earth-air interface and are the result of interfering P- and S-waves. Particle motion is constrained to the vertical plane consistent with the direction of wave propagation. Different wavelengths carry geotechnical information at different depths. S-wave velocities of near-surface materials (soil, rocks, and pavement) and their effect on seismic-wave propagation are of fundamental interest in many groundwater, engineering, and environmental studies. Because of the S-wave velocity being the dominant property of the fundamental mode of Rayleigh wave phase velocities, S-wave velocities can be estimated quickly from inversion of Rayleigh-wave data.
Multichannel analysis of surface waves (MASW) proposed by Kansas Geological Survey (KGS) tries to overcome the few weaknesses (such as low precision of dispersion curves, multimode data mixture, body wave energy contamination, and so on) of the Spectral Analysis of Surface Waves (SASW) method. This technique consists of: acquisition of wide band (2~200Hz), high frequency ground roll using portable, repeatable, seismic source; utilization of wave-field analysis algorithm to extract and analyze 1D Rayleigh wave dispersion curves; inversion of dispersion curves to obtain S-wave velocity profiles; and generation of a 2D shear-velocity section by aligning 1D models at the midpoint of each spread with a spatial interpolation scheme. Because the MASW can acquire data at a lower cost and estimate S-wave velocities with relatively high precision and high efficiency, it has been one of the research hotspot in Rayleigh-wave investigation in recent years, including field repeatability, artifacts of data process, affects of model parameters, and others.
Although the MASW has undergone significant development in recent years that has greatly enhanced its capabilities, great effort should be spent on increasing horizontal resolution of Rayleigh-wave data. One of the most effective ways improving the horizontal resolution of the MASW is to extract accurate dispersion curves from a record with a short geophone spread. The fundamental-mode Rayleigh waves, however, are easily contaminated by high modes or body wave energy in the real-world data, so it is most important to use proper seismic processing technique to separate the fundamental-mode Rayleigh waves from raw surface-wave data. The main aspects include: (1) because different high-frequency (≥5Hz) Rayleigh-wave modes and body waves interfere and overlap with each other in the t-x domain, it is necessary to apply advanced techniques to carry out shot-gather data transform and to separate different mode of Rayleigh waves and body waves in a corresponding domain. In other words, the data after transform should possess high resolution so that different-mode Rayleigh waves can be easily distinguished; (2) an algorithm should have the ability to preserve amplitude and phase, so mode separation could be feasible; and (3) the data processing technique should be efficient to real-world data.
Based on the summary of main facts affecting on the horizontal resolution of the MASW, I studied the characteristics of Rayleigh waves in different field domains, used wavefield separation technique to carry out Rayleigh-wave mode separation, and proposed and accomplished a Rayleigh-wave data processing technique with high horizontal resolution. In developing the technique, I focused following subjects.
(1) I investigated the horizontal resolution of dispersion curves of the MASW, which is the basic research for 2D Rayleigh-wave exploration.
(2) I analyzed the accuracy of Rayleigh-wave dispersion curves calculated by a pair of traces in a Poisson's solid homogenous half-space and propose to use a pair of traces to calculate dispersion curves constrained by the MASW.
(3) I analyzed the advantages and disadvantages of current four algorithms in calculating image of high-frequency Rayleigh-wave dispersive energy, I proposed to image Rayleigh-wave dispersive energy and carry out mode separation by high-resolution linear Radon transform (LRT) and used a pair of consecutive traces within the shot gather after mode separation to calculate a dispersion curve.
(4) I primarily researched on the joint inversion of high-frequency Rayleigh waves with fundamental and higher modes. I discussed the sensitivity of dispersion curves with different modes in different frequency ranges for a six-layer earth model and used the theoretical model and a real-world example to demonstrate the advantages of joint inversion of multimodes to estimate S-wave velocities using a damped least-square method and the singular value decomposition (SVD) technique.
I conclude that:
(1) Under the assumption of plane-wave propagation, the horizontal resolution of the extracted dispersion curve by the MASW is mainly determined by the geophone spread length, the inverted 1D S-wave velocity is an averaged geophysical model under the geophone spread, and the horizontal resolution of the inverted 2D section is most influenced by the receiver spread length and the acquisition interval. So, one of the most direct ways to improve the horizontal resolution of inverted S-wave velocity is to extract accurate dispersion curves from a record with a short geophone spread;
(2) Results of the calculated dispersion curve by a pair of traces and receiver spacing (horizontal resolution) in a Poisson's solid homogenous half-space show that: a pair of traces with a smaller receiver spacing achieve higher horizontal resolution but result in a larger relative error; the relative error of the phase velocity at a high frequency is smaller than at a low frequency, and the relative error of the phase velocity is strongly affected by the S/N ratio of data. For real-world applications, one should choose a trade-off between horizontal resolution and accuracy of the calculated dispersion curves. Results of both synthetic and real-world data demonstrate that, after choosing a proper receiver interval, inverting high-frequency surface-wave dispersion curves—by a pair of traces through cross-correlation with the phase shift scanning method developed in my study and with the damped least-square method and the singular-value decomposition technique—can feasibly achieve a reliable pseudo-2D S-wave velocity section with relatively high horizontal resolution;
(3) Results of imaging Rayleigh-wave dispersive energy by the high-resolution LRT show that, compared with the slant stacking algorithm, high-resolution LRT can improve the overall resolution of images of dispersion energy by more than 50% and dispersion energy of different modes generated by the high-resolution LRT can be easily distinguished, which are important in picking multi-mode data for joint inversion and mode separation;
(4) Because the high-resolution LRT effectively preserves amplitude and phase information and improves overall resolution of images of dispersion energy with high efficiency, it is successfully used in mode separation. Results of mode separation show that, images of dispersion energy of different modes generated by the high-resolution LRT possess distinguished trends, which are the foundation for mode separation. Further more, higher mode dispersive energy extends its frequency range at the low frequency end so it can not only 'see' deeper and possess higher resolution but also cut-off frequencies can be determined more accurately;;
(5) I image Rayleigh-wave dispersive energy and carry out mode separation by the high-resolution LRT and use a pair of consecutive traces within the shot gather after mode separation to calculate a dispersion curve. Results show that: compared with the MASW, the Rayleigh-wave data processing technique with high horizontal resolution greatly improves the horizontal resolution of dispersion curves. In addition, synthetic and real-world examples suggested, the number of shots required in data acquisition can be dramatically reduced with the process technique. For example, I may only need maximum three shots, one at each end and one at the middle of a geophone spread for a real-world application where 24 shots are normally required for the MASW method to map a portion of bedrock.
(6) Sensitivity analysis of the six-layered model 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.
瑞雷波是一种沿自由界面传播的表面波,它是纵波和横波的干涉波。质点在瑞雷面波传播方向上垂直平面振动,不同波长的瑞雷波是近地表不同深度岩土力学性质的响应。近地表介质(土壤、岩石、堆积物)的横波速度广泛应用于地下水探测、工程和环境勘查领域。由于横波速度在瑞雷波传播过程中起主导作用,所以从面波数据中可快速估计出横波速度。
为克服面波谱分析法(SASW,Spectral Analysis of Surface Waves)提取频散曲线精度低、不能得到高阶模式频散曲线等缺点,美国堪萨斯地质调查所(KGS,Kansas GeologicalSurvey)提出了多道面波分析法(MASW,Multichannel Analysis of Surface Waves)。该方法利用便携式并可重复使用的震源,采集宽频带(2～200 Hz)瑞雷面波;对多道纪录进行波场分析提取一维瑞雷波频散曲线;利用频散曲线反演一维近地表横波速度剖面;通过空间插值构建二维横波速度场。利用多道面波分析法(MASW)反演横波速度具有较高的精度,且野外操作方便和高效等优点,近年来成为瑞雷波勘探研究的热点之一。研究内容主要包括:场地实验可重复性、处理中的假象、模型参数的影响以及其它研究等。
近年来多道面波分析方法研究取得了较大进展,增强了其在实际中的应用能力。然而,提高多道面波分析方法的横向分辨率仍需要深入研究。采用短排列数据提取瑞雷波频散曲线是提高横向分辨率的最有效方法之一。但在实际勘探过程中,基阶瑞雷波数据容易被体波及高模式瑞雷波干扰,因此运用合适的数据处理技术将基阶瑞雷波从单炮数据中分离出来,是实现横向高分辨率瑞雷波勘探的基础和关键。主要体现在:(1)由于体波和多模式瑞雷波在t-x域互相干扰和重叠,因此必须利用先进的数据处理技术对单炮数据进行变换,提高变换后数据的分辨率,获取相应域中相互分离的多模式波及体波,便于在该域中选取基阶瑞雷波;(2)数据正、反变换必须保幅、保角;这样才能实现模式分离;(3)研究快速的数据处理方法技术,以便应用于实际工作。
本文在总结多道面波分析法(MASW)横向分辨率主要因素的基础上,分析瑞雷波数据在不同场域的分布特点,利用波场分离技术进行瑞雷波模式分离,提出横向高分辨率瑞雷波数据处理的方法技术,主要研究内容包括:
(1)定义了多道面波分析法(MASW)获取频散曲线的横向分辨率,它是二维瑞雷波勘探的基础,决定了提高横向分辨率的方法技术。
(2)在分析均匀半空间中利用两道瑞雷波数据计算频散曲线精度的基础上,提出了利用MASW约束和利用两道数据计算频散曲线的数据处理技术。
(3)综合分析目前四种获取频散曲线算法的优缺点,提出了利用高分辨率线性Radon变换求取频散曲线能量谱和分离瑞雷波各模式、利用分离后的单炮数据(仅含基阶瑞雷波)中的相邻道计算基阶瑞雷波频散曲线的计算思路。
(4)对多模式波联合反演进行了初步研究:讨论了六层层状介质模型的基阶和高模式波相速度对横波速度及深度的敏感性,利用阻尼最小二乘SVD算法对该模型进行联合反演,并通过实例数据检验联合反演效果。
本研究得出如下结论:
(1)在满足平面波传播条件下,多道面波分析法(MASW)获取的频散曲线横向分辨率主要由检波器排列长度决定,反演的横波速度是检波器排列下方地球物理模型的平均效应;反演的二维横波速度横向分辨率主要由检波器的排列长度和炮间距决定。因此,利用短检波器排列数据计算瑞雷波频散曲线是提高瑞雷波勘探横向分辨率的直接手段。
(2)利用均匀半空间两道数据计算瑞雷波相速度的精度与道间距(横向分辨率)的关系研究结果表明:道间距越小(横向分辨率越高),计算精度越低;瑞雷波相速度在低频部分的相对误差较高频部分大。在实际应用中,必须在频散曲线的横向分辨率和可靠性之间寻求折衷点;理论和实际数据计算结果表明,在选取合适的道间距后,利用互相关法结合相移法计算两道数据频散曲线,能够获取高横向分辨率并具有较高精度的二维横波速度。
(3)利用高分辨率线性Radon变换计算瑞雷波频散曲线能量谱的结果表明:较倾斜叠加算法,高分辨率线性Radon变换将能量谱的分辨率提高50%以上,为此,可实现各模式波在频率—速度域彼此分离,有利于多模式波频散曲线的提取及分离;
(4)高分辨率线性Radon正、反变换保幅、保角并快速高效的特点,为各模式波的分离提供了基础。理论和实例数据计算结果表明:由于瑞雷波频散曲线能量谱分辨率的提高,各模式波可以准确地从单炮数据中分离出来,且延伸了高模式波的频率范围,有利于得到更深的横波速度信息与更准确地确定高模式波的截止频率;
(5)利用高分辨率线性Radon变换求取频散曲线能量谱、分离各模式瑞雷波、利用分离后的炮集数据(仅含基阶瑞雷波)中的相邻道计算基阶瑞雷波频散曲线。结果表明:较多道面波分析方法(MASW),高横向分辨率瑞雷波数据处理技术在提高频散曲线横向分辨率同时,极大地减少了野外数据采集工作量。例如:在实例中,多道面波分析方法(MASW)需要24炮数据确定一段基岩面,而横向高分辨率瑞雷波数据处理技术仅需要3炮(检波器排列的两个端点和中间各1炮)数据。
(6)六层层状介质模型基阶和高模式瑞雷波相速度对横波速度和深度敏感性研究结果表明:基阶波较高模式波对浅部地层的横波速度更敏感,敏感性频带窄,峰值频带集中;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瑞雷波反演,结果表明:联合反演提高了反演的稳定性和精度。
Rayleigh (1885) firstly described the theory of the motion of Rayleigh waves in a homogeneous elastic half-space, which opened a new page to study the structure and composition of the Earth using Rayleigh waves. Haskel (1953) used matrix method to carry out dispersion computation on a solid layered half-space, which provided the foundation for Earth interior and near-surface geophysics study using earthquake and seismic surface-wave signal. Many scientists have widely investigated on Rayleigh-wave propagation in varies materials over the last half century.
Rayleigh waves are surface waves that travel along a 'free' surface, such as the earth-air interface and are the result of interfering P- and S-waves. Particle motion is constrained to the vertical plane consistent with the direction of wave propagation. Different wavelengths carry geotechnical information at different depths. S-wave velocities of near-surface materials (soil, rocks, and pavement) and their effect on seismic-wave propagation are of fundamental interest in many groundwater, engineering, and environmental studies. Because of the S-wave velocity being the dominant property of the fundamental mode of Rayleigh wave phase velocities, S-wave velocities can be estimated quickly from inversion of Rayleigh-wave data.
Multichannel analysis of surface waves (MASW) proposed by Kansas Geological Survey (KGS) tries to overcome the few weaknesses (such as low precision of dispersion curves, multimode data mixture, body wave energy contamination, and so on) of the Spectral Analysis of Surface Waves (SASW) method. This technique consists of: acquisition of wide band (2~200Hz), high frequency ground roll using portable, repeatable, seismic source; utilization of wave-field analysis algorithm to extract and analyze 1D Rayleigh wave dispersion curves; inversion of dispersion curves to obtain S-wave velocity profiles; and generation of a 2D shear-velocity section by aligning 1D models at the midpoint of each spread with a spatial interpolation scheme. Because the MASW can acquire data at a lower cost and estimate S-wave velocities with relatively high precision and high efficiency, it has been one of the research hotspot in Rayleigh-wave investigation in recent years, including field repeatability, artifacts of data process, affects of model parameters, and others.
Although the MASW has undergone significant development in recent years that has greatly enhanced its capabilities, great effort should be spent on increasing horizontal resolution of Rayleigh-wave data. One of the most effective ways improving the horizontal resolution of the MASW is to extract accurate dispersion curves from a record with a short geophone spread. The fundamental-mode Rayleigh waves, however, are easily contaminated by high modes or body wave energy in the real-world data, so it is most important to use proper seismic processing technique to separate the fundamental-mode Rayleigh waves from raw surface-wave data. The main aspects include: (1) because different high-frequency (≥5Hz) Rayleigh-wave modes and body waves interfere and overlap with each other in the t-x domain, it is necessary to apply advanced techniques to carry out shot-gather data transform and to separate different mode of Rayleigh waves and body waves in a corresponding domain. In other words, the data after transform should possess high resolution so that different-mode Rayleigh waves can be easily distinguished; (2) an algorithm should have the ability to preserve amplitude and phase, so mode separation could be feasible; and (3) the data processing technique should be efficient to real-world data.
Based on the summary of main facts affecting on the horizontal resolution of the MASW, I studied the characteristics of Rayleigh waves in different field domains, used wavefield separation technique to carry out Rayleigh-wave mode separation, and proposed and accomplished a Rayleigh-wave data processing technique with high horizontal resolution. In developing the technique, I focused following subjects.
(1) I investigated the horizontal resolution of dispersion curves of the MASW, which is the basic research for 2D Rayleigh-wave exploration.
(2) I analyzed the accuracy of Rayleigh-wave dispersion curves calculated by a pair of traces in a Poisson's solid homogenous half-space and propose to use a pair of traces to calculate dispersion curves constrained by the MASW.
(3) I analyzed the advantages and disadvantages of current four algorithms in calculating image of high-frequency Rayleigh-wave dispersive energy, I proposed to image Rayleigh-wave dispersive energy and carry out mode separation by high-resolution linear Radon transform (LRT) and used a pair of consecutive traces within the shot gather after mode separation to calculate a dispersion curve.
(4) I primarily researched on the joint inversion of high-frequency Rayleigh waves with fundamental and higher modes. I discussed the sensitivity of dispersion curves with different modes in different frequency ranges for a six-layer earth model and used the theoretical model and a real-world example to demonstrate the advantages of joint inversion of multimodes to estimate S-wave velocities using a damped least-square method and the singular value decomposition (SVD) technique.
I conclude that:
(1) Under the assumption of plane-wave propagation, the horizontal resolution of the extracted dispersion curve by the MASW is mainly determined by the geophone spread length, the inverted 1D S-wave velocity is an averaged geophysical model under the geophone spread, and the horizontal resolution of the inverted 2D section is most influenced by the receiver spread length and the acquisition interval. So, one of the most direct ways to improve the horizontal resolution of inverted S-wave velocity is to extract accurate dispersion curves from a record with a short geophone spread;
(2) Results of the calculated dispersion curve by a pair of traces and receiver spacing (horizontal resolution) in a Poisson's solid homogenous half-space show that: a pair of traces with a smaller receiver spacing achieve higher horizontal resolution but result in a larger relative error; the relative error of the phase velocity at a high frequency is smaller than at a low frequency, and the relative error of the phase velocity is strongly affected by the S/N ratio of data. For real-world applications, one should choose a trade-off between horizontal resolution and accuracy of the calculated dispersion curves. Results of both synthetic and real-world data demonstrate that, after choosing a proper receiver interval, inverting high-frequency surface-wave dispersion curves—by a pair of traces through cross-correlation with the phase shift scanning method developed in my study and with the damped least-square method and the singular-value decomposition technique—can feasibly achieve a reliable pseudo-2D S-wave velocity section with relatively high horizontal resolution;
(3) Results of imaging Rayleigh-wave dispersive energy by the high-resolution LRT show that, compared with the slant stacking algorithm, high-resolution LRT can improve the overall resolution of images of dispersion energy by more than 50% and dispersion energy of different modes generated by the high-resolution LRT can be easily distinguished, which are important in picking multi-mode data for joint inversion and mode separation;
(4) Because the high-resolution LRT effectively preserves amplitude and phase information and improves overall resolution of images of dispersion energy with high efficiency, it is successfully used in mode separation. Results of mode separation show that, images of dispersion energy of different modes generated by the high-resolution LRT possess distinguished trends, which are the foundation for mode separation. Further more, higher mode dispersive energy extends its frequency range at the low frequency end so it can not only 'see' deeper and possess higher resolution but also cut-off frequencies can be determined more accurately;;
(5) I image Rayleigh-wave dispersive energy and carry out mode separation by the high-resolution LRT and use a pair of consecutive traces within the shot gather after mode separation to calculate a dispersion curve. Results show that: compared with the MASW, the Rayleigh-wave data processing technique with high horizontal resolution greatly improves the horizontal resolution of dispersion curves. In addition, synthetic and real-world examples suggested, the number of shots required in data acquisition can be dramatically reduced with the process technique. For example, I may only need maximum three shots, one at each end and one at the middle of a geophone spread for a real-world application where 24 shots are normally required for the MASW method to map a portion of bedrock.
(6) Sensitivity analysis of the six-layered model 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.
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