A review on microtremor H/V spectral ratio method
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摘要: 微动H/V谱比，即地表记录的不同频率地震背景噪声的水平分量与垂直分量的比值. 在工程地震领域，通常用V表示微动记录的垂直分量，用H表示微动记录的水平分量，测得作为频率函数的H/V谱比曲线后，依据一定的关系（通常是经验的），建立H/V谱比曲线的峰值与地层结构基阶共振频率之间的关系，从而估计沉积层厚度或场地放大因子，有时也称为HVSR（Horizontal-to-Vertical Spectral Ratio）或QTS（Quasi Transfer Spectrum）方法. 由于微动中波型成分的物理来源模糊不清，其主导能量究竟是Rayleigh波、S波或者其它波型成分存在争议，因此，虽然在工程地震领域获得了广泛应用，微动H/V谱比法仍然缺乏严格的理论解释. 这导致该方法趋于两个方向发展：一是从地震记录中，识别出Rayleigh波能量，计算Rayleigh波的ZH幅度比，又称Rayleigh波椭率（ellipticity）. 之所以称为Rayleigh波ZH幅度比，是因为在地震层析成像领域，V常用来表示Rayleigh波水平分量的特征函数，多用Z表示Rayleigh波的垂直分量. 作为独立变量，Rayleigh波ZH幅度比对浅层速度结构更为敏感，在区域尺度地震层析成像领域获得广泛应用，用于弥补单独相（群）速度对浅层结构，尤其是沉积层结构约束不够的缺点. 这种方法意味着H/V谱比曲线中的主要能量是Rayleigh波，除了在区域尺度与Rayleigh波的频散和（或）接收函数联合反演地球结构之外，在工程物探领域，也利用Rayleigh波椭率反演近地表S波速度结构. 基于H/V谱比曲线的峰值推断场地响应的理论假设是SH波占据微动的主导能量，这与微动观测记录通常由Rayleigh波能量占据主导地位的情况不符，因此H/V谱比法的另一个研究方向是发展不同的背景噪声源模型，考虑可能贡献的背景噪声能量，解释H/V谱比曲线. 这样就避免了微动记录的主导成分是面波还是体波的争论，发展更适合或接近实际记录的微动模型解释H/V谱比曲线，该方向的发展是伴随地震干涉理论的发展而逐步发展起来的. 我们曾经对区域尺度的（地震事件或背景噪声）Rayleigh波ZH幅度比的研究和应用进行了评述. 本文主要评述微动H/V谱比法在工程地震领域和近地表S波速度结构反演中的应用及相应的理论解释. 包括基于SH波共振频率解释的微动H/V谱比法估计场地特征，基于Rayleigh波占据微动主导能量的Rayleigh波椭率在反演近地表速度结构中的应用，以及为解释实际微动H/V谱比曲线而发展的背景噪声源模型.
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关键词:
- 微动H/V谱比 /
- Rayleigh波椭率 /
- 卓越频率 /
- 场地响应 /
- 噪声源模型
Abstract: The microtremor H/V spectral ratio is the ratio of the horizontal component to the vertical component of the ambient seismic noise at different frequencies, recorded at the earth surface. In the field of engineering earthquake, V and H are usually used to denote the vertical and horizontal components of the microtremor, respectively. Based on the measured H/V curve, which is a function of frequency, the sedimentary thickness or site amplification factor can be estimated using the established relationship between the peak of the H/V curve and the fundamental resonance frequency of the formation structure. Although it has been widely used in the field of engineering earthquake, the theoretical explanation on the microtremor H/V method, which is also called HVSR (Horizontal-to-Vertical Spectral Ratio) or QTS (Quasi-Transfer Spectrum), is still under debate, since which is the dominant wave type of the microtremor (Rayleigh wave, S wave or the other types of waves) is unclear. This leads the microtremor H/V method to be developed in two directions. One is to identify the Rayleigh wave energy from the microtremor and calculate the ZH amplitude ratio of the Rayleigh wave (i.e.Rayleigh wave ellipticity), where Z represents the vertical component of the Rayleigh waveand V represents the eigenvalue of the horizontal component. As an independent variable, the Rayleigh wave ZH ratio is sensitive to shallow structure and it has been widely used to constrain the shallow structure combined with the phase or/and group velocity in regional-scale seismic tomography. This process assumes that the dominant energy in the H/V curve is from Rayleigh wave. Apart from being used in the joint inversion of the large scale earth structure with the Rayleigh wave dispersion and/or receiver function, Rayleigh wave ellipticity is also used to invert the near-surface S-wave velocity structure in engineering geophysical prospecting on a small scale. The peak of the H/V curve can be used to figure out the site characteristics under the assumption of that SH wave dominates the microtremor. This assumption is in consistent with the observation that the Rayleigh wave energy is usually dominated. Another direction of the microtremor H/V method development is to develop noise source model, with which all possible contributions of noise energy are considered. The H/V curve is then interpreted based on this model. The controversy on which type of wave dominates the microtremor is avoided. The model has been proved to be suitable for explaining the real microtremor record and the shape of H/V curve. This direction is developed with the develovement of seismic interference theory. We have reviewed the theory and application of Rayleigh wave ellipticity on the regional scale. This paper mainly reviews the theory and application of microtremor H/V method in the field of engineering earthquake and near-surface S-wave velocity structure inversions, including the theoretical interpretation of H/V curve based on SH wave resonance frequency, the application of microtremor H/V method in site estimation, and the noise source model developed to explain the H/V curve. -
图 1 不同的H/V谱比计算方法相对于H/V谱比数学期望的相对偏差[采用平均式（a）]. “o”表示算术平均值，（4）式；“×”代表取几何平均值，（5）式；“+”代表取矢量和，（6）式；“□”取均方根，（10）式；“*”代表取最大值，（12）式；
$m \equiv 2L$ 表示自由度，$L$ 为使用的窗口数（修改自Albarello and Lunedei, 2013）Figure 1. Relative deviations of different H/V ratio calculation methods relative to the mathematical expectation of H/V ratio [calculated using the average method (a)].“circle” represents arithmetic mean (Eq. 4); “cross” represents geometric mean (Eq. 5); “plus” represents vector summation (Eq. 6); “square” represents quadratic mean (Eq. 10) and “star” represents maximum value (Eq. 12).
$m \equiv 2L$ is the number of degrees of freedom and$L$ is the number of windows (modified from Albarello and Lunedei, 2013)
图 2 （a）在有损弹性情况（实线，沉积层的品质因子
${Q_1} = 10$ ，基岩品质因子${Q_2} = 50$ ，$Z = 0.3$ ）和无损弹性情况（虚线，品质因子${Q_1} = {Q_2} = \infty $ ，$Z = 0.3$ ）中，S波放大情况.（b）1/4波长与沉积层厚度之间关系示意图（修改自Ibs-von Seht and Wohlenberg, 1999; Carcione et al., 2017）Figure 2. (a) S-wave site amplification in the lossy-elastic case (solid line, quality factor of sediment layer
${Q_1} = 10$ , quality factor of bedrock${Q_2} = 50$ ,$Z = 0.3$ ) and lossless-elastic case (dashed line,${Q_1} = {Q_2} = \infty $ ,$Z = 0.3$ ). (b) Schematic diagram of the relationship between the quarter wavelength and the thickness of the sediment layer (modified from Ibs-von Seht and Wohlenberg, 1999; Carcione et al., 2017)
图 3 沉积盆地简单结构，其中
${H_f}$ 和${V_f}$ 为沉积层表面位移水平分量和垂直分量的频谱振幅，${H_b}$ 和${V_b}$ 为基岩体波位移水平分量和垂直分量的频谱振幅，${H_r}$ 和${V_r}$ 为基岩露头位移水平分量和垂直分量的频谱振幅（修改自Nakamura, 2000）Figure 3. Simple structure of sedimentary basin.
${H_f}$ and${V_f}$ are the spectral amplitudes of the horizontal and vertical components of the displacement of the sediment layer surface.${H_b}$ and${V_b}$ are the spectral amplitudes of the horizontal and vertical components of the bedrock body wave displacement.${H_r}$ and${V_r}$ are the spectral amplitudes of the horizontal and vertical components of the bedrock outcrop displacement (modified from Nakamura, 2000)
图 4 地面剪切应变示意图，其中基岩S波的平均速度为
${V_{{\rm{S}}b}}$ ，基岩表面的S波地震动位移为$d$ ，沉积层厚度为$h$ ，沉积层的S波速度为${V_{\rm{S}}}$ ，其对S波的放大系数为${A_h}$ ，地面的S波地震动位移为${A_h} \cdot d$ （修改自Nakamura, 1997, 2009）Figure 4. Schematic of ground shear strain.
${V_{{\rm{S}}b}}$ is the average S-wave velocity of the bedrock;$d$ is S-wave ground motion displacement at the surface of the bedrock;$h$ is the thickness of sediment;${V_{\rm{S}}}$ is the S-wave velocity of the sediment. The amplification factor of the sediment for S-wave is${A_h}$ , so the S-wave ground motion displacement at the surface of sediment can be expressed as${A_h} \cdot d$ (modified from Nakamura, 1997, 2009)
图 5 慢度
$p = 1/c$ 、垂直慢度${\eta _\beta }$ 、S波速度$\,\beta $ 和入射角$\,\theta $ 之间的关系示意图Figure 5. The relationship between slowness
$p = 1/c$ , vertical slowness${\eta _\beta }$ , S-wave velocity$\,\beta $ and incident angle$\,\theta $ 
图 6 表2中（a）层状Rayleigh波的模型频散曲线；（b）自由表面椭率；（c）半空间界面椭率. 红色线表示基阶模式（Mode 0），绿色线表示一阶模式（Mode 1），蓝色线表示二阶模式（Mode 2）.（a）中实线表示相速度，虚线表示群速度.（b）中彩色虚线表示粒子顺进运动，实线表示粒子逆进运动，垂直的黑色虚线表示第一层的共振频率.（c）中水平的黑色虚线表示
$H/V = 1$ Figure 6. (a), (b), and (c)are dispersion curves, ellipticities at the free surface and the half-space interface of Rayleighwaves for the model shown in Table 2, respectively. Red line represents the parameters of fundamental mode (Model 0), green line represents the parameters of first-order mode (Model 1), and blue line represents the parameters of second-order mode (Model 2). In (a), solid line respresents phase velocity and dashed line respresents group velocity. In (b), color dashed line respresents clockwise motion; solid line respresents counterclockwise motion, vertical black dotted line represents the resonant frequency. Black dotted line in (c) denotes
$H/V = 1$ 
图 7 微动H/V曲线反演S波速度结构示意图，介质模型由N个均匀各向同性层组成，最下面一层为半空间. 每层的介质参数为厚度H、密度
$\rho $ 、P波速度${V_{\rm{P}}}$ 和S波速度${V_{\rm{S}}}$ . 示意图显示微动H / V频谱的非线性反演，重复该迭代过程，当误差$\varepsilon $ 收敛到可接受范围时可确定介质模型参数（修改自Arai and Tokimatsu, 2004）Figure 7. Schematic showing how the S-wave velocitystructure is inverted from microtremor H/V ratio.The model consists of N homogeneous layers with a half-space. The media parameters for each layer include: thickness H, density
$\rho $ , P-wave velocity${V_{\rm{P}}}$ and S-wave velocity${V_{\rm{S}}}$ . Schematic showing nonlinear inversion process based on microtremor H/V ratio. The iteration is repeated until the root mean of the sum of squares of the normalized misfit$\varepsilon $ is converged into an acceptable small value, and the media model is then determined (modified from Arai and Tokimatsu, 2004)
图 8 DSS模型中源与接收器示意图，其中接收器在圆心位置，源均匀分布在阴影部分
Figure 8. Schematic of sources and receiver of the Distributed Surface Sources model (DSS). Receiver islocated at the centre of the circle and the sources are evenly arranged in the shaded area
图 9 面波（SWM）相对全波场（FWM）对微动波场的相对贡献. 使用表3中的层状模型，假设无源区域的半径为
$r = 0$ ，面波能量与全波型能量之间的比例，（a）水平分量；（b）垂直分量；（c）面波H/V与全波型H/V谱比曲线的比值. 灰色垂直实线表示S波共振频率${f_{\rm{S}}}$ ，灰色垂直虚线表示P波共振频率${f_{\rm{P}}}$ （修改自Albarello and Lunedei, 2011）Figure 9. Relative contribution of surface waves to the full waves in the ambient vibration wavefield. Ratios of surface-wave model (SWM) to full wavefield model (FWM) powers are shown for horizontal (a) and vertical (b) ground-motion components for the subsoil configuration in Table 3, under the assumption that the radius of the source-free area is
$r = 0$ . (c) shows the ratio of the horizontal to vertical spectral ratio function given by surface waves only and full wavefield. Grey vertical lines denote${f_{\rm{S}}}$ (solid) and${f_{\rm{P}}}$ (dashed) (modified from Albarello and Lunedei, 2011)
图 10 通过扩散场法（DFA）计算地壳模型（表4）微动不同震相在（a）水平分量、（b）垂直分量和（c）H/V谱比的能量占比. 蓝色线表示全波场，黄色线表示面波，青色线表示体波，红色线表示基阶Rayleigh波，品红色线表示高阶Rayleigh波，绿色线表示Love波. 黑虚线表示了理论的高频渐近线（修改自García-Jerez et al., 2013）
Figure 10. The power proportion of the different phases of the microtremor (Table 4) in the horizontal component (a), vertical component (b) and H/V ratio (c) calculated by Diffuse Field Approach (DFA). Blue line represents full wavefield, yellow line represents surface waves, cyan line represents body waves, red line represents the fundamental Rayleigh mode, magenta line represents the higher Rayleigh modes, green line represents the Love waves,and black dashed line represents the high frequency theoretic asymptote (modified from García-Jerez et al., 2013)
图 11 利用微动H/V谱比等值线给出的沉积层厚度，上面覆盖了地震反射剖面，白线表示根据地震反射推断出的沉积层—基岩界面的位置. 箭头指示单台H/V谱比曲线的位置，每个H/V谱比曲线经过归一化处理，使用色标范围从0（蓝色）到1（红色）（修改自Sgattoni and Castellaro, 2020）
Figure 11. Microtremor H/V ratio contour, overlaid with the seismic reflection profile. The white line indicates the position of the sedimentbedrock interface inferred from seismic reflection. The arrows mark the positions of the single H/V curves. Every H/V curve was normalized, so the colour scale ranges from 0 (blue) to 1 (red) (modified from Sgattoni and Castellaro, 2020)
图 12 不同地区的共振频率—沉积层厚度的经验关系
$h = a{f^b}$ 图（对数—对数坐标系）Figure 12. Empirical relationships
$h = a{f^b}$ between resonance frequency and sediment thickness in different areas (log-log coordinate system)
图 13 式（66）所示的VS30与基阶共振频率
${f_0} = {f_{{\rm{peak}}}}$ 、半空间剪切波速度${V_{{\rm{S}}b}} = {V_R}$ ，及沉积层与基岩的阻抗比IR的关系（修改自Hassani and Atkinson, 2016）Figure 13. Expected relationship (Eq. 66) between VS30 and site fundamental resonance frequency (
${f_0} = {f_{{\rm{peak}}}}$ ) under different circumstances of half-space shear wave velocity (${V_{{\rm{S}}b}} = {V_R}$ ) and impedance ratio (IR) between the sedimentary layer and the bedrock (modified from Hassani and Atkinson, 2016)
图 14 不同研究区域的VS30随H/V曲线得到的基阶共振频率
${f_0} = {f_{{\rm{peak}}}}$ 和对应幅度${A_0}$ 的变化，及其拟合曲线. 黄色区域表示黑色实线模型95%的置信区间. 虚线表示相对平均值1倍的标准偏差，不同颜色表示不同的研究区域（修改自Ghofrani and Atkinson, 2014）Figure 14. The variation and fitting curves showing how fundamental resonance frequency (
${f_0} = {f_{{\rm{peak}}}}$ ) and corresponding amplitude (${A_0}$ ) of VS30 vary with H/V curve in different research areas. Yellow area is the confidence intervals of 95% of the models (black solid lines). The dashed line represents the standard deviation of 1 time relative to the mean. Symbols are color-coded based on the locations of study areas (modified from Ghofrani and Atkinson, 2014)表 1 微动H/V谱比法的应用和理论解释
Table 1. The application and theoretical explanation of microtremor H/V ratio method
假设 理论解释 应用 估算方法 备注 微动H/V谱比法（Microtremor horizontal-to-vertical spectral ratio, MHVSR） 在共振频率处：
1.基岩处体波$H_b^{\rm{body}}/V_b^{\rm{body}}({f_{h0}}) \approx 1$
2.垂直分量不被放大
3.沉积层表面的面波垂直分量可以忽略
4.表示Rayleigh波的能量部分$\beta \cdot {{H_f^{\rm{Rayleigh}}} / {V_f^{\rm{Rayleigh}}}} \approx 0$基于体波的理论解释：H/V谱比曲线的峰值对应SH波基阶共振频率（Nakamura方法，或QTS） 1.推断工程场地放大倍数${A_h}(f)$
2.推断沉积层厚度$h$
3.估计场地的易损因子${K_g}$
4.估计平均剪切波速度VS30${A_h}({f_0}) = {H / V}({f_0})$
$h = \dfrac{{{V_{\rm{S}}}}}{{4{f_0}}} \cong \dfrac{{{V_{{\rm{S}}b}}}}{{4{A_h}{f_0}}}{K_g} = \dfrac{{A_h^2({f_0})}}{{{f_0}}}$
$\log [{V_{{\rm{S}}30}}] = a + b\log [{f_0}] + c\log [{A_0}]$${f_n} = (2n + 1)\dfrac{{{V_{\rm{S}}}}}{{4h}}$，$n$是自然振动的模式，${f_n}$是水平分量的共振频率，${f_0}$是基阶共振频率，$h$是沉积层厚度，${V_{\rm{S}}}$和${V_{{\rm{S}}b}}$分别为沉积层和基岩的剪切波速度. 有些研究者推广至所有频率，利用H/V谱比曲线估算所有频率的放大倍数，${A_h}(f) = {H / {V(f)}}$ 微动记录的主导成分是Rayleigh面波 基于面波的理论解释：H/V谱比曲线对应基阶Rayleigh波椭率（Rayleigh波椭率或Rayleigh波HVSR） 基于Rayleigh波椭率曲线反演介质S波速度剖面 拟合理论和观测的H/V曲线 Nakamura（2000）坚持认为不管Rayleigh波的程度影响如何，H/V谱比曲线总是可以基于共振频率推断场地响应和沉积层厚度 微动波场包括体波、面波、高阶面波等震相 微动震源模型 DSS模型 一般假设微动波场由Rayleigh波或Rayleigh波和Love波（约定其能量比R/L）反演层状S波速度结构 数值模拟H/V曲线，反演 在微动波场震相组成及占比未知的情况下，通常利用DSS模型模拟真实微动源位置，并利用层状介质格林函数模拟微动波场 微动波场为扩散状态下的波场，即P波与S波的能量比达到平衡而与散射的具体细节无关（扩散状态下可精确重建系统格林函数） DFA模型 利用重建的格林函数虚部与H/V谱比的关系，在一定频段（如峰值频率和谷值频率之间的频段）反演层状S波速度结构 数值模拟H/V曲线，反演 扩散状态下体波的衰减远大于面波，所以在DFA模型中隐含着面波能量占主导 地震记录HVSR 地震记录的HVSR反演，可延申至接收函数理论，本文主要关注微动H/V 
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表 2 两层介质模型
Table 2. The model of a layer over half-space
层 $h/{\rm{km}}$ $\alpha /\left({{\rm{km}} \cdot {{\rm{s}}^{ - 1}}} \right)$ $\beta /\left({{\rm{km}} \cdot {{\rm{s}}^{ - 1}}} \right)$ $\rho /\left({{\rm{g}} \cdot {\rm{c}}{{\rm{m}}^{{\rm{ - 3}}}}} \right)$ 1 0.024 1.8 0.48 2 2 $\infty $ 6.72 3.84 2
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表 3 Albarello和Lunedei（2011）使用的模型
Table 3. The model used in Albarello and Lunedei (2011)
层 层厚度$H/{\rm{m}}$ P波速度${V_{\rm{P}}}/\left({{\rm{m}} \cdot {{\rm{s}}^{ - 1}}} \right)$ S波速度${V_{\rm{S}}}/\left({{\rm{m}} \cdot {{\rm{s}}^{ - 1}}} \right)$ 密度$\rho /\left({{\rm{kg}} \cdot {{\rm{m}}^{{\rm{ - 3}}}}} \right)$ 品质因子${Q_{\rm{P}}}$ 品质因子${Q_{\rm{S}}}$ 泊松比$\nu $ 1 25 400 200 1900 50 25 0.3 2 5000 2000 1000 2500 100 50 0.3 3 $\infty $ 3500 2000 2500 100 50 0.257
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表 4 Albarello和Lunedei（2011）使用的地壳模型
Table 4. The crust model used in Albarello and Lunedei (2011)
层 $z/{\rm{km}}$ ${V_{\rm{P}}}/\left({{\rm{km}} \cdot {{\rm{s}}^{ - 1}}} \right)$ ${V_{\rm{S}}}/\left({{\rm{km}} \cdot {{\rm{s}}^{ - 1}}} \right)$ $\rho /\left({{\rm{g}} \cdot {\rm{c}}{{\rm{m}}^{{\rm{ - 3}}}}} \right)$ 1 35 5.9 3.41 2.67 2 $\infty $ 8.1 4.68 3.27
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表 5 不同地区的共振频率—沉积层厚度的经验关系（
$h = a{f^b}$ )Table 5. Empirical relationships between Resonance frequency and sediment thickness in different areas(
$h = a{f^b}$ )经验关系 研究区域 频率范围 备注 Ibs-von Seht and Wohlenberg, 1999 $h = 96{f^{ - 1.388}}$ 德国Lower Rhine Embayment西部地区，34个钻孔，102个台站 0.14～4.5 Hz 覆盖层厚度范围30～1 600 m，剪切波速大于800 m/s Delgado et al., 2000 $h = 55.64{f^{ - 1.268}}$ 西班牙Bajo Segura basin地区，使用23个台站的共振频率和土壤厚度对 1～10 Hz 沉积层厚度小于100 m，剪切波速度小于250 m/s Parolai et al., 2002 $h = 108{f^{ - 1.551}}$ 德国Cologne地区，使用32个钻孔 0.41～12.16 Hz 覆盖层厚度范围0.5～401 m，剪切波速大于800 m/s Hinzen et al., 2004 $h = 137{f^{ - 1.19}}$ 德国Lower Rhine Embayment地区 0.1～10 Hz 沉积层厚度小于500 m，剪切波速度小于400 m/s García-Jerez, 2006 $h = 194.6{f^{ - 1.14}}$ 西班牙南部Zafarraya盆地，17个台站 1～10 Hz 沉积层厚度小于200 m，剪切波速度范围120～1 100 m/s Motamed et al., 2007 $h = 135.19{f^{ - 1.9791}}$ 伊朗东南部Bam地区，49个地点 1～10 Hz 沉积层厚度小于100 m，剪切波速度小于750 m/s D'Amico et al., 2008 $h = 140{f^{ - 1.172}}$ 意大利Florence plain地区 1.03～7.47 Hz 9～115 m Tanircan et al., 2009 $h = 150.99{f^{ - 1.1531}}$ 土耳其İstanbul南部地区15个钻孔 0.3～6 Hz 沉积层厚度小于449 m Dinesh et al., 2010 $h = 58.3{f^{ - 0.95}}$ 印度Bangalore城市，34个钻孔 2～10 Hz 土壤厚度范围0～30 m，剪切波速范围150～300 m/s Gosar and Lenart, 2010 $h = 105.53{f^{ - 1.250}}$ 斯洛维尼亚Ljubljana Moor basin地区微动测量获得的53个共振频率和沉积物厚度对 0.8～9 Hz 沉积层厚度小于200 m Özalaybey et al., 2011 $h = 141{f^{ - 1.27}}$ 土耳其İzmit Bay，地区239个台站和405个重力测量 0～4 Hz 沉积层厚度小于1 400 m Sukumaran et al., 2011 $h = 102.1{f^{ - 1.47}}$ 印度Narmada河谷下游31个台站 0.2～10 Hz 第四纪沉积物厚度小于600 m Poggi et al., 2012 $h = 158.54{f^{ - 2.45}}$ 瑞士Lucerne城市 0～4 Hz 沉积层厚度范围120～150 m，剪切波速小于1 000 m/s Del Monaco et al., 2013 $h = 53.461{f^{ - 1.01}}$ 意大利中部拉奎拉市中心 0.1～20 Hz 沉积层厚度约300 m，剪切波速度小于1 000 m/s Paudyal et al., 2013 $h = 146.01{f^{ - 1.2079}}$ 尼泊尔Kathmandu Basin地区
172个台站0.488～8.9 Hz 沉积层厚度小于400 m Maresca and Berrino, 2016 $h = 129{f^{ - 1.38}}$ 意大利南部VolturaraIrpina盆地 0.06～10 Hz 沉积层厚度小于500 m Sant et al., 2017 $h = 110.18{f^{ - 1.97}}$ 印度Banni Plains地区31个台站 0.23～1.5931 Hz 土层分层面为分别为1 442～
1 965 m和44～160 mLiang et al., 2018 $h = 55{f^{ - 1.02}}$ 中国珠江三角洲地区52个钻孔 1～10 Hz 沉积层厚度7.9～39.6 m Joshi et al., 2018 $h = 56.8{f^{ - 1}}$ 印度Aravalli南部地区32个台站 0.221 9～27.111 9 Hz Mascandola et al., 2019 $h = 98{f^{ - 1.17}}$ 意大利Po Plain地区 0.2～1 Hz 沉积层厚度小于500 m Rupar, 2020 $h = 202.97{f^{ - 1.139}}$ 斯洛文尼亚中部Iška alluvial fan地区107次测量 1～20 Hz 陈棋福等，2008 $h = 96{f^{ - 1.388}}$ 中国北京城区（五环内） 使用Ibs-von Seht和Wohlenberg（1999）的结果，与峰值频率0.6 Hz，沉积层厚度195 m基本一致 王伟君，2011 $h = 96{f^{ - 1.388}}$ 中国河北保定 0.5～8 Hz 中国河北保定地区浅部速度结构，使用Ibs-von Seht和Wohlenberg（1999）的结果，覆盖层厚度小于500 m，剪切波速度范围300～500 m/s 曾立峰，2012 $h = 111.49{f^{ - 1.523}}$； $h = 151.48{f^{ - 1.566}}$ 中国兰州市麦积区和社棠镇38个台站和38个钻孔信息；西四十里铺、太京镇、西十里铺、秦城区和甘泉镇21个台站和21个钻孔信息 1～5 Hz 沉积层厚度范围10～100 m，剪切波速度范围187～351 m/s 刘宇实和师黎静，2018 $h = 82.19{f^{ - 0.766}}$ 中国哈尔滨20个钻孔与场地资料 1.23～4.89 Hz 覆盖层厚度范围41～84.5 m，剪切波速大于500 m/s 李文倩等，2019 $h = 43.53{f^{ - 0.638}}$ 筛选中国喀什乌恰地区9个强震动数字化观测台站 2～11 Hz 拟合结果标准差为0.061，覆盖层厚度范围8～27 m，剪切波速范围218～430 m/s 彭菲等，2020 $h = 103.2{f^{ - 1.251}}$ 中国三河—平谷地区3个转孔
和4个台阵0.2～10 Hz 第四纪层覆盖层厚度范围0～600 m，VS30普遍小于
180 m/s师黎静和陈盛扬，2020 $h = 91.93{f^{ - 1.066}}$ 中国新疆克拉玛依，42个钻孔，中国浙江沿海4个钻孔 0.58～12.5 Hz 中国新疆覆盖层5～96 m，VS>251 m/s；中国浙江沿海覆盖层100～180 m，VS<200 m/s
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