A scalar radiative transfer model including the coupling between surface and body waves
A scalar radiative transfer model including the coupling between surface and body waves
复制标题
标量辐射传输模型，包括表面波和体波之间的耦合
DOI：
10.1093/gji/ggz348
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发表时间：
2019
影响因子：
2.8
通讯作者：
M. Campillo
中科院分区：
文献类型：
--
作者：
L. Margerin;Andres Bajaras;M. Campillo
为了描述地震尾波中的能量输运，我们引入了一个标量近似的耦合表面波和体波的辐射传输方程组。我们的模型是基于Helmholtz方程在半空间几何混合边界条件。在这个模型中，绿色函数可以表示为体波和表面波的总和，这模拟了地球上的情况。第一步，我们研究了玻恩近似下点状物体的单次散射问题。使用的假设，体波的相位是随机的表面反射或与散射体的相互作用，我们表明，它成为可能的定义，以通常的方式，表面到身体和身体到表面的散射的横截面。采用独立散射近似，定义了考虑体波和表面波耦合的散射平均自由程。使用唯象的方法，然后，我们推导出一组耦合的输运方程满足的特定能量密度的表面波和体波在介质中包含一个均匀分布的点散射体。在我们的模型中，散射体波的平均自由程是深度相关的体-面耦合的结果。我们表明，在长时间的流逝，表面波和体波之间的均分，这是预测通常的模式计数参数的比例。我们从输运方程组导出扩散近似，并表明扩散率是各向异性和深度依赖的。这两个属性的物理起源进行了讨论。最后，我们提出的Monte Carlo解决方案的传输方程，这说明了收敛到均分在长时间的流逝，以及在产生尾波的表面波和体波之间的耦合的重要性。
To describe the energy transport in the seismic coda, we introduce a system of radiative transfer equations for coupled surface and body waves in a scalar approximation. Our model is based on the Helmholtz equation in a half-space geometry with mixed boundary conditions. In this model, Green’s function can be represented as a sum of body waves and surface waves, which mimics the situation on Earth. In a first step, we study the single-scattering problem for point-like objects in the Born approximation. Using the assumption that the phase of body waves is randomized by surface reflection or by interaction with the scatterers, we show that it becomes possible to define, in the usual manner, the cross-sections for surface-to-body and body-to-surface scattering. Adopting the independent scattering approximation, we then define the scattering mean free paths of body and surface waves including the coupling between the two types of waves. Using a phenomenological approach, we then derive a set of coupled transport equations satisfied by the specific energy density of surface and body waves in a medium containing a homogeneous distribution of point scatterers. In our model, the scattering mean free path of body waves is depth dependent as a consequence of the body-to-surface coupling. We demonstrate that an equipartition between surface and body waves is established at long lapse-time, with a ratio which is predicted by usual mode counting arguments. We derive a diffusion approximation from the set of transport equations and show that the diffusivity is both anisotropic and depth dependent. The physical origin of the two properties is discussed. Finally, we present Monte Carlo solutions of the transport equations which illustrate the convergence towards equipartition at long lapse-time as well as the importance of the coupling between surface and body waves in the generation of coda waves.