Discrete wavenumber solutions to numerical wave propagation in piecewise heterogeneous media - I. Theory of two-dimensional SH case
Discrete wavenumber solutions to numerical wave propagation in piecewise heterogeneous media - I. Theory of two-dimensional SH case
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DOI：
10.1111/j.1365-246x.2004.02135.x
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发表时间：
2004-05
影响因子：
2.8
通讯作者：
L. Fu;M. Bouchon
中科院分区：
文献类型：
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作者：
L. Fu;M. Bouchon
摘要针对任意震源产生的分段非均匀介质，提出了一种半解析、半数值合成地震记录的方法。该方法将离散波数格林函数表示与边界体积积分方程数值技术相结合。其表现仅限于二维反平面运动(SH波)。为了将介质的不同部分模拟到所需的精度，在离散波数域中分别表示入射波、边界散射波和体散射波，并使用近似方法在不同精度下灵活地处理它们。这些波通过广义Lippmann-Schwinger积分(GLSI)方程精确地叠加。对边界散射波采用全波形边界方法，精确模拟了强对比度边界的反射/透射率。对体非均质，本文提出了四种灵活的数值模拟方法，大大节省了计算时间和内存：(I)体散射波的隐式解，高精度地模拟体非均质的细微效应；(Ii)体散射波的半显式解，采用体积分的平均FresnelRadius近似，通过使系数矩阵变得稀疏来减少数值负担；(Iii)体散射波的显式解，使用光滑体非均质性的一阶Born近似；以及(Iv)用二阶/高阶Born近似显式求解实际体积非均匀的体积散射波。测试了这些解决方案对非均匀冲积山谷的无量纲频率响应，在那里，速度在大约5%-20%的范围内被随机扰动，这在大多数复杂的近地表地区并不罕见。数值实验表明，由于均匀山谷中引入的非均质性，可能会导致数倍的场地放大。试验还证实，体积散射波的一阶Born近似对于小于10%的速度扰动是严格有效的，对于一般应用，大约用于高达15%的速度扰动。体积散射波的二阶Born近似对于小于15%的速度扰动是严格有效的，而对于一般应用，大约用于20%的速度扰动。
SUMMARY A semi-analytical, semi-numerical method of seismogram synthesis is presented for piecewise heterogeneous media resulting from an arbitrary source. The method incorporates the discrete wavenumber Green’s function representation into the boundary‐volume integral equation numerical techniques. The presentation is restricted to 2-D antiplane motion (SH waves). To model different parts of the media to a necessary accuracy, the incident, boundary-scattering and volume-scattering waves are separately formulated in the discrete wavenumber domain and handled flexibly at various accuracies using approximation methods. These waves are accurately superposed through the generalized Lippmann‐Schwinger integral (GLSI) equation. The full-waveform boundary method is used for the boundary-scattering wave to accurately simulate the reflection/transmission across strong-contrast boundaries. Meanwhile for volume heterogeneities, the following four flexible approaches have been developed in the numerical modelling scheme present here, with a great saving of computing time and memory: (i) the solution implicitly for the volume-scattering wave with high accuracy to model subtle effects of volume heterogeneities; (ii) the solution semi-explicitly for the volume-scattering wave using the average Fresnelradius approximation to volume integrations to reduce numerical burden by making the coefficient matrix sparser; (iii)the solution explicitly for the volume-scattering wave using the first-order Born approximation for smooth volume heterogeneities; and (iv)the solution explicitly for the volume-scattering wave using the second-order/high-order Born approximation for practical volume heterogeneities. These solutions are tested for dimensionless frequency responses to a heterogeneous alluvial valley where the velocity is perturbed randomly in the range of ca 5‐20 per cent, which is not rare in most complex near-surface areas. Numerical experiments indicate that several times of site amplification can be expected as a result of heterogeneities introduced in a homogeneous valley. The test also confirms that the first-order Born approximation to the volume-scattering wave is strictly valid for velocity perturbation less than 10 per cent and approximately used for up to 15 per cent for general applications. The second-order Born approximation to the volume-scattering wave is strictly valid for velocity perturbation less than 15 per cent and approximately used for up to 20 per cent for general applications.