起伏地表三维高频瑞雷面波传播特性研究
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摘要
瑞雷面波是P波和Sv波在自由界面处相长干涉而形成的沿自由界面传播,在垂直自由界面方向迅速衰减的特殊地震波,由英国数学家和物理学家Rayleigh爵士于1887年首次在理论上证明其存在。瑞雷波能量强,是天然地震中破坏性最大的波和反射地震勘探中的强干扰波。上世纪50年代,地震学家们发现瑞雷波在层状介质中的频散特性携带有地层参数的信息,可以利用其频散特性来研究地球内部结构,估计岩土力学参数。目前,利用瑞雷波的频散特性来研究各种尺度的地球物理问题已经成为热门领域,特别是基于完全弹性介质中瑞雷波传播特性的多道面波分析方法取得了长足的进步。
现有理论框架内,瑞雷面波的频散特性只在水平层状介质中有解析解。实际地球介质并非完全水平层状介质,如地表上广泛分布的山脉、海洋、沙漠、沼泽、湖泊等复杂地形,强烈地影响沿地表面传播的瑞雷波频散性质。因此,研究复杂地表条件下瑞雷面波的传播特性,对于拓展经典理论,开展地球内部结构的精细探测均具有重要作用。文献调研表明,已有的关于瑞雷波的研究工作多局限于一维和二维地球模型,对于实际三维地球模型中瑞雷波的传播特性了解甚少。因此,开展三维起伏地表条件下瑞雷面波传播特性的数值模拟研究是必要和迫切的任务。
本文采用交错网格有限差分方法,合理设计起伏地表边界条件,实现了起伏地表条件下的三维地震波场的高精度数值模拟。通过对几类典型三维起伏地形条件下瑞雷波传播的数值模拟试验,获得了三维起伏地表对瑞雷波传播的影响规律,为在复杂地区开展实际瑞雷波勘探奠定了基础。主要研究内容包括：
(1)起伏地表条件下三维高频瑞雷面波数值模拟方法研究,将处理自由界面条件的声学-弹性界面近似方案与经典“以折代曲”的起伏地表离散化方法相结合,给出了起伏地表条件下三维地震波场的高精度、高效率模拟方案。
(2)典型起伏地表条件下瑞雷面波传播特性研究。设计了包括三维单斜面、山脊、山谷、独立隆起地形、独立凹陷地形等简单常见起伏地表半空间模型,实现了高频瑞雷波在三维起伏地表模型中传播过程的数值模拟,并根据模拟结果分析了起伏地表对瑞雷波传播特性的影响。
(3)三维多道面波分析方法研究。设计了非线型阵列观测方式,对合成地震记录采用多道面波分析方法提取其瑞雷波频散曲线,并利用所提取面波相速度反演了一维横波速度结构,论证了新的观测和数据处理方法提取的频散曲线对应接收阵列所围区域重心点处的一维横波速度结构,并讨论了新的方法在面波勘探中压制局部地形起伏影响上的优越性。
通过对所设计的三维起伏地表模型进行瑞雷波传播的数值模拟与分析,笔者获得如下几点主要结论：
(1)通过自由界面倾斜角度从0°到90°以10°为增量的系列含倾斜自由界面半空间模型上瑞雷面波数值模拟结果,进一步分析了2D起伏地表AEA法自由界面边界条件处理方法的精度。其实验结果表明AEA法要明显优于SIM法,特别是在倾斜角度在45°附近时。模拟误差的大小与模型剖分的精细程度有关,为保证得到各角度情况下满足精度要求的模拟结果,采用AEA法模拟,依然需要对模型进行较精细的网格剖分,发现至少需要60ppw才能满足要求,与Bohlen和Saenger(2006)的结论一致。同时发现,采用AEA的交错网格有限差分法与采用旋转交错网格(RSG)法具有类似的模拟精度,而前者比RSG法更容易实现。
(2)二维含倾斜地表面层状介质模型的数值模拟试验表明,当瑞雷面波沿倾斜地表面传播时,其频散性质由地层的真厚度决定,而非铅垂厚度决定。因此,在多道面波勘探(MASW)中根据瑞雷面波频散曲线反演S波速度时,反演所得到的层厚度,应为层的真厚度而非铅垂厚度,仅当界面水平时二者才一致。据笔者文献调研,未见前人有相同结论。另外,数值实验结果再一次证明了多道面波分析(MASW)中排列中点假设的正确性,即多道面波分析所得频散曲线反映参与计算的多道记录中点处的地层性质。
(3)对三维含倾斜地表面两层模型的数值模拟结果表明,非线型观测阵列合成地震记录所提取的瑞雷波频散能量的峰值与水平地表两层介质瑞雷波理论频散曲线高度拟合,从而数值验证了三维多道面波分析方法的可行性。对比发现,非线型观测阵列比线型排列所提取的频散曲线具有更好的抗假频干扰能力,高阶模式频散曲线与理论高阶模式频散曲线拟合程度更佳。
(4)对三维含山脊、山谷、独立凸起、独立凹陷等起伏地表半空间模型的数值模拟试验表明,三维起伏地表对瑞雷面波传播影响较大,在起伏地表边缘处有瑞雷波能量的反射与散射现象发生,且负地形比正地形对产生反射和/或散射瑞雷波的作用更明显。由于反射和/或散射瑞雷波能量的存在,根据线型排列所计算的频散能量图中,瑞雷波频散能量产生分叉现象,而根据非线型阵列记录所计算的频散能量中的分叉现象得到压制。对于山谷地形和独立凹陷地形模型,瑞雷波通过山谷或独立凹陷时部分能量被反射,并且以山谷或凹陷为中心,产生地震波能量的相互干涉而形成共鸣震荡现象。对于独立凸起地形模型,当瑞雷面波经过独立凸起时,由于被山包四周的地表面多次反射,有较强的能量被圈闭在山包内部。
(5)通过对典型起伏地表模型的数值模拟试验,发现多道面波分析的平均效应虽然降低了横向分辨率,却改善了局部地形起伏对瑞雷波频散曲线的影响。二维起伏地表模型数值模拟结果表明,线型排列多道面波方法压制地形影响的效果取决于排列长度与起伏地形宽度之间的比值,在文中数值模拟记录的震源主频为20Hz的情形下,该比值大于或等于3时可基本消除正地形的影响,该比值需达到5以上才能较好地压制独立负地形的影响。当采用非线型阵列在三维起伏地表模型上观测时,阵列覆盖面积达到起伏区域面积的1.5倍可基本消除正地形的影响：阵列覆盖面积至少需达到起伏区域面积2倍以上,才能基本消除负地形的影响。
(6)二维多道面波分析中排列中点假设已在勘探实践和数值实验中得到验证。对三维含倾斜地表双层介质断层模型和起伏地层界面模型进行了数值模拟,利用高精度线性拉东变换算法计算了非线型阵列多道记录的频散曲线,然后采用阻尼最小二乘法和模拟退火法反演获得了一维横波速度模型。对比重建的横波速度模型和理论模型,证明了三维多道面波分析中重心假设是正确的,即非线型阵列多道分析的频散曲线对应的空间位置是该阵列覆盖区域的重心。该结论为三维面波多道分析方法提供了应用基础。
Rayleigh waves propagate along the free surface and vanish exponentially in vertical direction, which are formed under the constructive interference of P-and Sv-waves near the free surface, and were first discovered in theory by Lord Rayleigh in1887. Since they have strong energy, Rayleigh waves are the most damaging wave type during earthquakes, and regarded as strong noise in petroleum exploration. However, because the dispersive characteristic of Rayleigh waves in layered earth model was found in1950's, they have been used as effective waves in several geophysical problems, for example in deducing inner structure of earth and soil mechanic parameters, material composition researching of the crust and the mantle, near-surface structure survey and non-destructive engineering detecting. At present, there are some classical literatures in describing the propagation characteristics of Rayleigh waves in elastic media. And Rayleigh waves have been widely used in several multi-scale geophysical researches, and the dispersion characteristics study of Rayleigh waves becomes a hot issue of geophysical researches. In recent years, the surface wave method based on Rayleigh waves propagation characteristics in elastic media, has been considerable advancing.
At present, researches of Rayleigh-waves dispersive characteristics are focused on flat layered media. However, the actual earth is not completely flat layered media. Especially the earth surface is not wholly horizontal. There are extensive complex areas on the earth surface, such as mountains, seas, deserts, marshes, lakes. Hence, research of propagation of Rayleigh waves under complex topographic surface becomes significantly important in detecting the interior structure of the earth. In addition, many researches about the dispersive characteristics and numerical simulation technique of Rayleigh wave are carried out in two dimension (2D) media. However, the real earth is three-dimension (3D). To let the models approach the real underground media, our researches should be proposed in3D. Some complex wave fields can not be well explained by2D numerical simulation results. However, the3D numerical simulation results can be used to quantitatively explain a lot phenomenon of complex wave fields. Hence, the research of propagation of Rayleigh waves in3D media with topography is an imperative work.
To study the propagation of Rayleigh waves in3D media with topography, a reasonable free-surface condition approach for the staggered-grid finite-difference method is applied in numerical simulations. A series of typical topographic models are designed, and the propagations of Rayleigh waves in these models are numerical simulated. Some propagation regularities of Rayleigh waves on topographic surface are obtained. In our study, we focused on the following issues.
(1) Methods for simulation of high-frequency Rayleigh waves propagation in three-dimensional media with topography. We propose a feasible finite difference scheme incorporating the acoustic/elastic interface approach (AEA) into a 'stair-case' mesh for modeling surface wave propagation with the topographic free-surface.
(2) To study the propagation of Rayleigh waves under the topographic surface, a series of typical three-dimensional half-space models are designed, such as a slope free surface, a horst case free surface, valley case free surface, independent mountain case free surface, and independent pot case free surface. With the numerical results of Rayleigh waves on these models, we analyze the propagation characteristics of Rayleigh waves under topographic surfaces.
(3) To study the true3D surface-wave method, we design a fan-case arbitrary acquisition geometry to get the synthetic seismograms. High-resolution linear Radon transform method is used to obtain the dispersive energy curves from the synthetic seismograms. With the dispersive energy curves, we analyze the effects of the true3D surface-wave method in eliminating influences of small topographies for Rayleigh-wave dispersion. The one dimensional S-wave profiles for the orthocenter of the fan areas are got from the inversion of the dispersive curves.
By the analysis of the numerical simulation results of Rayleigh-wave propagation in the topographic surface models we designed, we conclude that:
(1) A series of half-space model with slope free surface are numerically investigated with the slope angles from0degree to90degree with10degree increment. By the analysis of the numerical results, we further check the modeling precision of our2D numerical simulation approach for the topographic models. The numerical results show that our AEA method is superior to stress image method (SIM) in numerical Rayleigh wave simulation on the slope free-surface models, especially for the half-space model with45degree dipping planar free surface. It is noted that the error increases, for the dip angel increases from0to90degree, more harsh for a coarser grid spacing. The error of the AEA decreases more rapidly with increasing grid pints than the SIM. However, to achieve good accuracy for all dip angles with a fine sampling for the wavefields, approximately more than60ppw is required (also see Bohlen and Saenger,2006). And we get similar accuracy as the rotated staggered grid (RSG) finite difference method when the same ppw is used. However, it is obviously that our method is much easier in implementation.
(2) Propagation and dispersion of Rayleigh waves in2D layered models with slope free surface are numerical analyzed. The results demonstrate that the Rayleigh-wave propagation along the slope free-surface is dominated by the real thickness of the layer. Therefore, the inverted1D S-wave velocity profile of the multichannel analysis of surface waves method (MASW) should be the S-wave velocity vs. depth in the direction perpendicular to the slope surface. To our knowledge, this conclusion points out the important characteristics of the Rayleigh-wave propagation along a slope free surface. The simulation results of a wedged layer underlying a half space model also demonstrate this important characteristics. And the numerical comparisons further prove the middle-of-receiver-spread assumption which is an implication to guide us in Rayleigh-wave exploration in practice.
(3) Three2D linear arrays and two fan-case acquisition geometries are designed in numerical simulations. Numerical results of the3D two layer model with flat and slope free surfaces demonstrate the feasibility of the true3D surface wave method. The dispersive energy images of synthetic seismograms of linear array and arbitrary fan acquisition geometries generated by high-resolution linear Radon transform. The coincidence of the dispersive energy images with the analytical dispersion curves of a layered model demonstrates the feasibility of the true3D surface wave method.
(4) Numerical results of3D half-space models with topographic surface as a horst case, a valley case, a single hill case and a single pit case show the influence of topographic surface for the propagation of Rayleigh waves. When Rayleigh waves pass the topographic areas, they are strongly influenced by the topographic surface, the wave form distorts, and the energy is reflected and scattered from the edge of the topographic surface. Numerical comparisons show that the influence of the valley case topography is more distinct than the horst case, and the influence of the single pit case topography is more distinct than the single hill case. Due to the existence of reflection and scattering of Rayleigh waves, energy bifurcations appear in the dispersive energy images generated from the synthetic seismograms of2D linear arrays. However, the energy bifurcations are suppressed obviously in the energy images of the true3D surface method. These results demonstrate the superiority of the true3D surface wave method. With the numerical results of Rayleigh wave propagation along the valley case topography and the single pit case topography, we find that the energy of Rayleigh waves is diffracted beside the valley or the single pit. And when Rayleigh waves pass the single hill topographic surface, a part of energy is trapped in the hill and reflected by the cliff again and again. This phenomenon can explain the fact when an earthquake occurs, the constructions in the mountaintop are damaged more seriously than the constructions on the bottom of the hill.
(5) The multichannel analysis of surface wave (MASW) method has been effectively used to determine near-surface S-wave velocity. The assumption of the dispersion curves determined by the geophysical structure within the geophone spread of MASW method has been demonstrated by Luo in2009with synthetic and real-world examples. These tests also show the fact that a dispersion curve generated from the MASW spread is an average effect of the underneath geophysical structure of the receiver spread. Therefore, the MASW method possesses an average effect for underneath structure. With the numerical results of a series of2D and3D models with typical topographic free surfaces, we find that the average effect of MASW method can eliminate the harmful influences of topographic surfaces in Rayleigh-wave dispersion energy images generating. The numerical results of two2D half-space models with a single hill or a pit topographic free surface reveal the effects of2D MASW method in eliminating the harmful influences of topographic surfaces for generating Rayleigh waves dispersive energy images. By the analysis, we find that for the single-hill-case topography, when spread length is3times of the width of the hill, the harmful influences of topography can be eliminated by the MASW method. However, for the single-pit-case topography the spread length should be more than5times of width of the pit. We also analyze the average effects of the true3D surface method in eliminating the harmful influences of a3D single hill or pit topography for generating the dispersive energy images. We conclude that for the single-hill-case topography, when the arbitrary acquisition area is1.5times of the hill area, the harmful influence can be eliminated. However, for the single-pit-case topography, the acquisition area should be more than twice of the pit area. All the results point out simple but important guidelines of the MASW method.
(6) The middle-of-receiver-spread assumption has been proved in the numerical and real-world examples by many researchers. Similar to the2D MASW method, we have an orthocenter assumption for the true3D surface wave method. The dispersion curves we get from the seismograms of an arbitrary acquisition geometry can be used to invert the underneath S-wave structure of the orthocenter of the arbitrary acquisition geometry area. The numerical results of a3D wedged layer model proved the orthocenter assumption. Based on the middle-of-receiver-spread assumption, a series of dispersion curves are generated from the numerical results of a2D two layer fault model and a3D two layer fault model with linear spread receivers. And by allying the inversion results of these dispersion curves, we get a pseudo-2D S-wave velocity profile and a pseudo-3D S-wave velocity body. As is shown on the pseudo-2D and pseudo-3D S-wave velocity results, the layer interface and the fault are reconstructed very well. Meanwhile, based on the orthocenter assumption, a series of dispersion curves are generated from numerical results of a3D two-layer topographic-layer-interface model with a series of arbitrary acquisition geometries. By allying the inversion results of these dispersion curves, we get a pseudo-3D S-wave velocity body. On the pseudo velocity body, the topographic-layer interface is reconstructed well. These inversion results prove the orthocenter assumption further and have an implication to guide us in performing Rayleigh-wave exploration in practice.
现有理论框架内,瑞雷面波的频散特性只在水平层状介质中有解析解。实际地球介质并非完全水平层状介质,如地表上广泛分布的山脉、海洋、沙漠、沼泽、湖泊等复杂地形,强烈地影响沿地表面传播的瑞雷波频散性质。因此,研究复杂地表条件下瑞雷面波的传播特性,对于拓展经典理论,开展地球内部结构的精细探测均具有重要作用。文献调研表明,已有的关于瑞雷波的研究工作多局限于一维和二维地球模型,对于实际三维地球模型中瑞雷波的传播特性了解甚少。因此,开展三维起伏地表条件下瑞雷面波传播特性的数值模拟研究是必要和迫切的任务。
本文采用交错网格有限差分方法,合理设计起伏地表边界条件,实现了起伏地表条件下的三维地震波场的高精度数值模拟。通过对几类典型三维起伏地形条件下瑞雷波传播的数值模拟试验,获得了三维起伏地表对瑞雷波传播的影响规律,为在复杂地区开展实际瑞雷波勘探奠定了基础。主要研究内容包括：
(1)起伏地表条件下三维高频瑞雷面波数值模拟方法研究,将处理自由界面条件的声学-弹性界面近似方案与经典“以折代曲”的起伏地表离散化方法相结合,给出了起伏地表条件下三维地震波场的高精度、高效率模拟方案。
(2)典型起伏地表条件下瑞雷面波传播特性研究。设计了包括三维单斜面、山脊、山谷、独立隆起地形、独立凹陷地形等简单常见起伏地表半空间模型,实现了高频瑞雷波在三维起伏地表模型中传播过程的数值模拟,并根据模拟结果分析了起伏地表对瑞雷波传播特性的影响。
(3)三维多道面波分析方法研究。设计了非线型阵列观测方式,对合成地震记录采用多道面波分析方法提取其瑞雷波频散曲线,并利用所提取面波相速度反演了一维横波速度结构,论证了新的观测和数据处理方法提取的频散曲线对应接收阵列所围区域重心点处的一维横波速度结构,并讨论了新的方法在面波勘探中压制局部地形起伏影响上的优越性。
通过对所设计的三维起伏地表模型进行瑞雷波传播的数值模拟与分析,笔者获得如下几点主要结论：
(1)通过自由界面倾斜角度从0°到90°以10°为增量的系列含倾斜自由界面半空间模型上瑞雷面波数值模拟结果,进一步分析了2D起伏地表AEA法自由界面边界条件处理方法的精度。其实验结果表明AEA法要明显优于SIM法,特别是在倾斜角度在45°附近时。模拟误差的大小与模型剖分的精细程度有关,为保证得到各角度情况下满足精度要求的模拟结果,采用AEA法模拟,依然需要对模型进行较精细的网格剖分,发现至少需要60ppw才能满足要求,与Bohlen和Saenger(2006)的结论一致。同时发现,采用AEA的交错网格有限差分法与采用旋转交错网格(RSG)法具有类似的模拟精度,而前者比RSG法更容易实现。
(2)二维含倾斜地表面层状介质模型的数值模拟试验表明,当瑞雷面波沿倾斜地表面传播时,其频散性质由地层的真厚度决定,而非铅垂厚度决定。因此,在多道面波勘探(MASW)中根据瑞雷面波频散曲线反演S波速度时,反演所得到的层厚度,应为层的真厚度而非铅垂厚度,仅当界面水平时二者才一致。据笔者文献调研,未见前人有相同结论。另外,数值实验结果再一次证明了多道面波分析(MASW)中排列中点假设的正确性,即多道面波分析所得频散曲线反映参与计算的多道记录中点处的地层性质。
(3)对三维含倾斜地表面两层模型的数值模拟结果表明,非线型观测阵列合成地震记录所提取的瑞雷波频散能量的峰值与水平地表两层介质瑞雷波理论频散曲线高度拟合,从而数值验证了三维多道面波分析方法的可行性。对比发现,非线型观测阵列比线型排列所提取的频散曲线具有更好的抗假频干扰能力,高阶模式频散曲线与理论高阶模式频散曲线拟合程度更佳。
(4)对三维含山脊、山谷、独立凸起、独立凹陷等起伏地表半空间模型的数值模拟试验表明,三维起伏地表对瑞雷面波传播影响较大,在起伏地表边缘处有瑞雷波能量的反射与散射现象发生,且负地形比正地形对产生反射和/或散射瑞雷波的作用更明显。由于反射和/或散射瑞雷波能量的存在,根据线型排列所计算的频散能量图中,瑞雷波频散能量产生分叉现象,而根据非线型阵列记录所计算的频散能量中的分叉现象得到压制。对于山谷地形和独立凹陷地形模型,瑞雷波通过山谷或独立凹陷时部分能量被反射,并且以山谷或凹陷为中心,产生地震波能量的相互干涉而形成共鸣震荡现象。对于独立凸起地形模型,当瑞雷面波经过独立凸起时,由于被山包四周的地表面多次反射,有较强的能量被圈闭在山包内部。
(5)通过对典型起伏地表模型的数值模拟试验,发现多道面波分析的平均效应虽然降低了横向分辨率,却改善了局部地形起伏对瑞雷波频散曲线的影响。二维起伏地表模型数值模拟结果表明,线型排列多道面波方法压制地形影响的效果取决于排列长度与起伏地形宽度之间的比值,在文中数值模拟记录的震源主频为20Hz的情形下,该比值大于或等于3时可基本消除正地形的影响,该比值需达到5以上才能较好地压制独立负地形的影响。当采用非线型阵列在三维起伏地表模型上观测时,阵列覆盖面积达到起伏区域面积的1.5倍可基本消除正地形的影响：阵列覆盖面积至少需达到起伏区域面积2倍以上,才能基本消除负地形的影响。
(6)二维多道面波分析中排列中点假设已在勘探实践和数值实验中得到验证。对三维含倾斜地表双层介质断层模型和起伏地层界面模型进行了数值模拟,利用高精度线性拉东变换算法计算了非线型阵列多道记录的频散曲线,然后采用阻尼最小二乘法和模拟退火法反演获得了一维横波速度模型。对比重建的横波速度模型和理论模型,证明了三维多道面波分析中重心假设是正确的,即非线型阵列多道分析的频散曲线对应的空间位置是该阵列覆盖区域的重心。该结论为三维面波多道分析方法提供了应用基础。
Rayleigh waves propagate along the free surface and vanish exponentially in vertical direction, which are formed under the constructive interference of P-and Sv-waves near the free surface, and were first discovered in theory by Lord Rayleigh in1887. Since they have strong energy, Rayleigh waves are the most damaging wave type during earthquakes, and regarded as strong noise in petroleum exploration. However, because the dispersive characteristic of Rayleigh waves in layered earth model was found in1950's, they have been used as effective waves in several geophysical problems, for example in deducing inner structure of earth and soil mechanic parameters, material composition researching of the crust and the mantle, near-surface structure survey and non-destructive engineering detecting. At present, there are some classical literatures in describing the propagation characteristics of Rayleigh waves in elastic media. And Rayleigh waves have been widely used in several multi-scale geophysical researches, and the dispersion characteristics study of Rayleigh waves becomes a hot issue of geophysical researches. In recent years, the surface wave method based on Rayleigh waves propagation characteristics in elastic media, has been considerable advancing.
At present, researches of Rayleigh-waves dispersive characteristics are focused on flat layered media. However, the actual earth is not completely flat layered media. Especially the earth surface is not wholly horizontal. There are extensive complex areas on the earth surface, such as mountains, seas, deserts, marshes, lakes. Hence, research of propagation of Rayleigh waves under complex topographic surface becomes significantly important in detecting the interior structure of the earth. In addition, many researches about the dispersive characteristics and numerical simulation technique of Rayleigh wave are carried out in two dimension (2D) media. However, the real earth is three-dimension (3D). To let the models approach the real underground media, our researches should be proposed in3D. Some complex wave fields can not be well explained by2D numerical simulation results. However, the3D numerical simulation results can be used to quantitatively explain a lot phenomenon of complex wave fields. Hence, the research of propagation of Rayleigh waves in3D media with topography is an imperative work.
To study the propagation of Rayleigh waves in3D media with topography, a reasonable free-surface condition approach for the staggered-grid finite-difference method is applied in numerical simulations. A series of typical topographic models are designed, and the propagations of Rayleigh waves in these models are numerical simulated. Some propagation regularities of Rayleigh waves on topographic surface are obtained. In our study, we focused on the following issues.
(1) Methods for simulation of high-frequency Rayleigh waves propagation in three-dimensional media with topography. We propose a feasible finite difference scheme incorporating the acoustic/elastic interface approach (AEA) into a 'stair-case' mesh for modeling surface wave propagation with the topographic free-surface.
(2) To study the propagation of Rayleigh waves under the topographic surface, a series of typical three-dimensional half-space models are designed, such as a slope free surface, a horst case free surface, valley case free surface, independent mountain case free surface, and independent pot case free surface. With the numerical results of Rayleigh waves on these models, we analyze the propagation characteristics of Rayleigh waves under topographic surfaces.
(3) To study the true3D surface-wave method, we design a fan-case arbitrary acquisition geometry to get the synthetic seismograms. High-resolution linear Radon transform method is used to obtain the dispersive energy curves from the synthetic seismograms. With the dispersive energy curves, we analyze the effects of the true3D surface-wave method in eliminating influences of small topographies for Rayleigh-wave dispersion. The one dimensional S-wave profiles for the orthocenter of the fan areas are got from the inversion of the dispersive curves.
By the analysis of the numerical simulation results of Rayleigh-wave propagation in the topographic surface models we designed, we conclude that:
(1) A series of half-space model with slope free surface are numerically investigated with the slope angles from0degree to90degree with10degree increment. By the analysis of the numerical results, we further check the modeling precision of our2D numerical simulation approach for the topographic models. The numerical results show that our AEA method is superior to stress image method (SIM) in numerical Rayleigh wave simulation on the slope free-surface models, especially for the half-space model with45degree dipping planar free surface. It is noted that the error increases, for the dip angel increases from0to90degree, more harsh for a coarser grid spacing. The error of the AEA decreases more rapidly with increasing grid pints than the SIM. However, to achieve good accuracy for all dip angles with a fine sampling for the wavefields, approximately more than60ppw is required (also see Bohlen and Saenger,2006). And we get similar accuracy as the rotated staggered grid (RSG) finite difference method when the same ppw is used. However, it is obviously that our method is much easier in implementation.
(2) Propagation and dispersion of Rayleigh waves in2D layered models with slope free surface are numerical analyzed. The results demonstrate that the Rayleigh-wave propagation along the slope free-surface is dominated by the real thickness of the layer. Therefore, the inverted1D S-wave velocity profile of the multichannel analysis of surface waves method (MASW) should be the S-wave velocity vs. depth in the direction perpendicular to the slope surface. To our knowledge, this conclusion points out the important characteristics of the Rayleigh-wave propagation along a slope free surface. The simulation results of a wedged layer underlying a half space model also demonstrate this important characteristics. And the numerical comparisons further prove the middle-of-receiver-spread assumption which is an implication to guide us in Rayleigh-wave exploration in practice.
(3) Three2D linear arrays and two fan-case acquisition geometries are designed in numerical simulations. Numerical results of the3D two layer model with flat and slope free surfaces demonstrate the feasibility of the true3D surface wave method. The dispersive energy images of synthetic seismograms of linear array and arbitrary fan acquisition geometries generated by high-resolution linear Radon transform. The coincidence of the dispersive energy images with the analytical dispersion curves of a layered model demonstrates the feasibility of the true3D surface wave method.
(4) Numerical results of3D half-space models with topographic surface as a horst case, a valley case, a single hill case and a single pit case show the influence of topographic surface for the propagation of Rayleigh waves. When Rayleigh waves pass the topographic areas, they are strongly influenced by the topographic surface, the wave form distorts, and the energy is reflected and scattered from the edge of the topographic surface. Numerical comparisons show that the influence of the valley case topography is more distinct than the horst case, and the influence of the single pit case topography is more distinct than the single hill case. Due to the existence of reflection and scattering of Rayleigh waves, energy bifurcations appear in the dispersive energy images generated from the synthetic seismograms of2D linear arrays. However, the energy bifurcations are suppressed obviously in the energy images of the true3D surface method. These results demonstrate the superiority of the true3D surface wave method. With the numerical results of Rayleigh wave propagation along the valley case topography and the single pit case topography, we find that the energy of Rayleigh waves is diffracted beside the valley or the single pit. And when Rayleigh waves pass the single hill topographic surface, a part of energy is trapped in the hill and reflected by the cliff again and again. This phenomenon can explain the fact when an earthquake occurs, the constructions in the mountaintop are damaged more seriously than the constructions on the bottom of the hill.
(5) The multichannel analysis of surface wave (MASW) method has been effectively used to determine near-surface S-wave velocity. The assumption of the dispersion curves determined by the geophysical structure within the geophone spread of MASW method has been demonstrated by Luo in2009with synthetic and real-world examples. These tests also show the fact that a dispersion curve generated from the MASW spread is an average effect of the underneath geophysical structure of the receiver spread. Therefore, the MASW method possesses an average effect for underneath structure. With the numerical results of a series of2D and3D models with typical topographic free surfaces, we find that the average effect of MASW method can eliminate the harmful influences of topographic surfaces in Rayleigh-wave dispersion energy images generating. The numerical results of two2D half-space models with a single hill or a pit topographic free surface reveal the effects of2D MASW method in eliminating the harmful influences of topographic surfaces for generating Rayleigh waves dispersive energy images. By the analysis, we find that for the single-hill-case topography, when spread length is3times of the width of the hill, the harmful influences of topography can be eliminated by the MASW method. However, for the single-pit-case topography the spread length should be more than5times of width of the pit. We also analyze the average effects of the true3D surface method in eliminating the harmful influences of a3D single hill or pit topography for generating the dispersive energy images. We conclude that for the single-hill-case topography, when the arbitrary acquisition area is1.5times of the hill area, the harmful influence can be eliminated. However, for the single-pit-case topography, the acquisition area should be more than twice of the pit area. All the results point out simple but important guidelines of the MASW method.
(6) The middle-of-receiver-spread assumption has been proved in the numerical and real-world examples by many researchers. Similar to the2D MASW method, we have an orthocenter assumption for the true3D surface wave method. The dispersion curves we get from the seismograms of an arbitrary acquisition geometry can be used to invert the underneath S-wave structure of the orthocenter of the arbitrary acquisition geometry area. The numerical results of a3D wedged layer model proved the orthocenter assumption. Based on the middle-of-receiver-spread assumption, a series of dispersion curves are generated from the numerical results of a2D two layer fault model and a3D two layer fault model with linear spread receivers. And by allying the inversion results of these dispersion curves, we get a pseudo-2D S-wave velocity profile and a pseudo-3D S-wave velocity body. As is shown on the pseudo-2D and pseudo-3D S-wave velocity results, the layer interface and the fault are reconstructed very well. Meanwhile, based on the orthocenter assumption, a series of dispersion curves are generated from numerical results of a3D two-layer topographic-layer-interface model with a series of arbitrary acquisition geometries. By allying the inversion results of these dispersion curves, we get a pseudo-3D S-wave velocity body. On the pseudo velocity body, the topographic-layer interface is reconstructed well. These inversion results prove the orthocenter assumption further and have an implication to guide us in performing Rayleigh-wave exploration in practice.
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