Radiative transfer theory for the fractal structure and power-law decay characteristics of short-period seismogram
Radiative transfer theory for the fractal structure and power-law decay characteristics of short-period seismogram
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短周期地震记录分形结构及幂律衰减特性的辐射传输理论
DOI：
10.1093/gji/ggt338
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
H. and R. Fukushima,
中科院分区：
文献类型：
--
作者：
Sato;H. and R. Fukushima,
对于一次地震的短周期波地震记录，最大振幅随走时的幂而减小，尾波振幅也随从发震时刻开始测量的逝去时间的幂而减小。辐射传输理论常被用来合成由地球介质中的随机非均匀散射波组成的复杂地震记录的包络，然而，传统的假设散射体(非均质性)和本征吸收体均匀分布的理论预测，除了几何衰减外，弹道项振幅和尾波振幅都随着时间的增加而指数减小。为了解释它们的幂定律特性，本文提出了三维空间中各向同性散射体和本征吸收体分形随机均匀分布的辐射传递理论：半径成比例的≤−球体中散射体/吸收体的数密度，对于距离≫Rc为常数，但对于≪Rc为常数，其中引入角距以避免在较小的R处发散。D=3的情况对应于传统的均匀分布。对于d=2的情况，理论很好地预测了弹道波的均方幅度随走时的幂而减小，尾波的均方振幅随从起始时间测量的经过时间的幂而减小，其中每个幂都受散射系数、本征吸收系数和角距的控制。对于d=1的情况，弹道波的MS幅度衰减是时间的平方反比，尾波衰减要快得多。作为初步工作，我们以D=2为优先指标，分析了日本一次地方地震的地震记录包络。算例表明，分形散射介质的辐射传输理论对于研究地球介质中的小尺度非均匀分布是有用的。
For short periodS-wave seismograms of an earthquake, the maximum amplitude decreases according to a power of traveltime, and the coda amplitude also decreases according to a power of lapse time measured from the earthquake origin time. The radiative transfer theory has been often used for the envelope synthesis of complex seismograms composed of scattered waves due to random heterogeneities in the Earth medium; however, the conventional theory, which supposes uniform distributions of scatterers (heterogeneities) and intrinsic absorbers, predicts that both the ballistic term amplitude and the coda wave amplitude exponentially decrease with time increasing in addition to the geometrical decay. In order to explain their power-law characteristics, this paper proposes the radiative transfer theory for a fractally random and homogeneous distribution of isotropic scatterers and intrinsic absorbers with fractal dimensionD≤ 3 in the 3-D space: the number density of scatterers/absorbers in a sphere of radiusris proportional torD− 3for distancer≫rcbut constant forr≪rc, where the corner distancercis introduced to avoid divergence at a smallr. The case ofD= 3 corresponds to the conventional uniform distribution. For the case ofD= 2, the theory well predicts that the mean square (MS) amplitude of the ballistic-wave decreases according to a power of traveltime and the MS amplitude of coda waves decreases according to a power of lapse time measured from the origin time, where each power is controlled by the scattering coefficient, intrinsic absorption coefficient and corner distance. For the case ofD= 1, the ballistic-wave MS amplitude decay is the inverse square of time and the coda decay is much faster. As a preliminary work, fixingD= 2 asa priorichoice, we analyseS-seismogram envelopes of a local earthquake in Japan. The case study shows that the radiative transfer theory for a fractal scattering medium is useful for the study of the distribution of small-scale heterogeneities in the Earth medium.