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首页> 外文期刊>Pure and Applied Geophysics >Doubly Stochastic Earthquake Source Model: 'Omega-Square'' Spectrum and Low High-Frequency Directivity Revealed by Numerical Experiments
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Doubly Stochastic Earthquake Source Model: 'Omega-Square'' Spectrum and Low High-Frequency Directivity Revealed by Numerical Experiments

机译：双重随机震源模型：通过数值实验揭示“欧米加-平方”频谱和低高频方向性

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摘要

Since its formulation in 1967-1970, the classical x~(-2) model of earthquake source spectrum awaits a consistent theoretical foundation. To obtain one, stochastic elements are incorporated both into the final structure of the fault and into the mode of rupture propagation. The main components of the proposed "doubly stochastic'' model are: (1) the Andrews's concept, that local stress drop over a fault is a random self-similar field; (2) the concept of rupture with running slip pulse, after Heaton; (3) the hypothesis that a rupture front is a tortuous, multiply connected ("lacy'') fractal polyline that occupies a strip of finite width close to the slip-pulse width; and (4) the assumption that the propagation distance of fault-guided, mostly Rayleigh waves from a failing spot on a fault is determined by the slip-pulse width. Waveforms produced by this model are determined based on the fault asperity failure model after Das and Kostrov. Properties of the model are studied by numerical experiments. At high frequency, simulated source spectra behave as x~(-2), and acceleration spectra are flat. Their level, at a given seismic moment and rms stress drop, is inversely related to the relative width of the slip pulse. When this width is relatively low, a well-defined second corner frequency (lower cutoff of acceleration spectrum) is seen. The model shows clear dependence of propagation-related directivity on frequency. Between the first and the second corner frequency, amplitude spectra are strongly enhanced for the forward direction; whereas, above the second corner frequency, directivity is significantly reduced. Still, it is not inhibited totally, suggesting incomplete incoherence of the simulated radiator at high frequencies.
机译：自1967-1970年提出以来，经典的震源谱x〜（-2）模型正在等待一致的理论基础。为了获得一个，随机元素被结合到断层的最终结构和破裂传播的模式中。提出的“双重随机”模型的主要组成部分是：（1）安德鲁斯的概念，即断层上的局部应力降是一个随机的自相似场;（2）在希顿之后，带有滑动脉冲的破裂的概念（3）断裂前沿是曲折的，多重连接的（“花边”）分形多义线的假说，它占据了一条接近滑脉冲宽度的有限宽度的条带; （4）假设故障引导的，主要是瑞利波从故障点上的传播点的传播距离取决于滑移脉冲宽度。该模型产生的波形是根据Das和Kostrov之后的故障粗糙故障模型确定的。通过数值实验研究了模型的性质。在高频下，模拟的源谱表现为x〜（-2），而加速度谱是平坦的。在给定的地震矩和均方根应力降下，它们的水平与滑移脉冲的相对宽度成反比。当该宽度相对较低时，可以看到明确定义的第二转折频率（加速度频谱的较低截止）。该模型显示出与传播有关的方向性对频率的明确依赖性。在第一个和第二个转折频率之间，正向的振幅谱将大大增强。而在第二转折频率以上，方向性明显降低。但是，它并没有被完全抑制，表明模拟辐射器在高频下不完全不相干。

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