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首页> 外文期刊>Surveys in Geophysics: An International Review Journal of Geophysics and Planetary Sciences >Estimation of elastic moduli in a compressible Gibson half-space by inverting Rayleigh-wave phase velocity
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Estimation of elastic moduli in a compressible Gibson half-space by inverting Rayleigh-wave phase velocity

机译：通过逆瑞利波相速度估计可压缩吉布森半空间中的弹性模量

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摘要

A Gibson half-space model (a non-layered Earth model) has the shear modulus varying linearly with depth in an inhomogeneous elastic half-space. In a half-space of sedimentary granular soil under a geostatic state of initial stress, the density and the Poisson's ratio do not vary considerably with depth. In such an Earth body, the dynamic shear modulus is the parameter that mainly affects the dispersion of propagating waves. We have estimated shear-wave velocities in the compressible Gibson half-space by inverting Rayleigh-wave phase velocities. An analytical dispersion law of Rayleigh-type waves in a compressible Gibson half-space is given in an algebraic form, which makes our inversion process extremely simple and fast. The convergence of the weighted damping solution is guaranteed through selection of the damping factor using the Levenberg-Marquardt method. Calculation efficiency is achieved by reconstructing a weighted damping solution using singular value decomposition techniques. The main advantage of this algorithm is that only three parameters define the compressible Gibson half-space model. Theoretically, to determine the model by the inversion, only three Rayleigh-wave phase velocities at different frequencies are required. This is useful in practice where Rayleigh-wave energy is only developed in a limited frequency range or at certain frequencies as data acquired at manmade structures such as dams and levees. Two real examples are presented and verified by borehole S-wave velocity measurements. The results of these real examples are also compared with the results of the layered-Earth model.
机译：吉布森半空间模型（非分层地球模型）的剪切模量在不均匀的弹性半空间中随深度线性变化。在初始应力为静力状态的沉积粒状土壤的半空间中，密度和泊松比不会随深度而显着变化。在这样的地球体中，动态剪切模量是主要影响传播波的色散的参数。我们通过反转瑞利波相速度来估计可压缩吉布森半空间中的剪切波速度。可压缩的吉布森半空间中瑞利型波的解析色散定律是以代数形式给出的，这使得我们的反演过程极其简单和快速。通过使用Levenberg-Marquardt方法选择阻尼系数，可以确保加权阻尼解决方案的收敛性。通过使用奇异值分解技术重建加权阻尼解，可以实现计算效率。该算法的主要优点是只有三个参数定义了可压缩的吉布森半空间模型。从理论上讲，要通过反演确定模型，仅需要三个不同频率的瑞利波相位速度。这在实际中很有用，因为瑞利波能量仅在有限的频率范围内或在某些频率下产生，如在大坝和堤坝等人造结构上获取的数据。给出了两个真实的例子，并通过钻孔S波速度测量进行了验证。这些实际示例的结果也与分层地球模型的结果进行了比较。

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