Radiative transfer of elastic waves in two-dimensional isotropic scattering media: Semi-analytical approach for isotropic source radiation
Radiative transfer of elastic waves in two-dimensional isotropic scattering media: Semi-analytical approach for isotropic source radiation
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DOI：
10.5047/eps.2011.03.006
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发表时间：
2011-09
期刊：
影响因子：
--
通讯作者：
H. Nakahara;K. Yoshimoto
中科院分区：
文献类型：
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作者：
H. Nakahara;K. Yoshimoto
我们制定的P-和S-波能量的辐射传输从一个各向同性辐射源在二维无限各向同性散射介质。为了稳定地数值计算地震图包络，我们采用了半解析方法：将P波和S波能量密度分为直达波项、单次散射项和多次散射项三部分，并分别对前两项和最后一项进行解析和数值计算。在单次散射项方面，用第一类完全椭圆积分解析地表示了P-to-S和S-to-P单次转换散射项。多重散射项由频率和波数的二重积分表示，并且可以通过离散波数求和和快速傅立叶变换进行数值计算。基于数值实现的结果证实了一个独立的数值计算，使用蒙特卡罗方法。我们的配方也适用于考虑P波和S波之间的平衡在较大的时间流逝。平衡的S-到-P的能量比再现和平衡时间是第一次推导出的二维情况下。我们的公式将为理解更复杂的情况提供参考。
We formulate the radiative transfer of P- and S-wave energy from an isotropically radiating source in a two-dimensional infinite isotropic scattering medium. For a stable numerical calculation of seismogram envelopes, we take a semi-analytical approach: Energy densities of P and S waves are divided into three parts of the direct-wave terms, the single-scattering terms, and the multiple-scattering terms, and the first two terms and the last term are evaluated analytically and numerically, respectively. Concerning the single-scattering terms, the P- to-S and S-to-P single conversion scattering terms are expressed analytically with a complete elliptic integral of the first kind. The multiple-scattering terms are represented by a double integral with respect to frequency and wavenumber, and can be numerically evaluated by a discrete wavenumber summation and a Fast Fourier Transform. The results based on the numerical implementation are confirmed with an independent numerical calculation using the Monte Carlo method. Our formulation is also applied to consider the equilibration between P and S waves at larger lapse times. The equilibrated S-to-P energy ratio is reproduced and the equilibration time is first derived for two-dimensional cases. Our formulation will be a reference for the understanding of more complex cases.