Mathematical Sciences: Transport Theory for Siesmic Wave Propagation. A Proposal for Collaborative Research Researchin Geosciences, Geography and Mathematical Sciences

9419073吴辐射输运理论是分析地壳中地震能量非相干输运的主要工具，地壳是一种非常复杂的、非均匀的弹性介质。但目前它的应用仅限于无限大的各向同性结构，没有考虑：(1)不同弹性波模式之间的能量传递，包括面波；(2)地壳中非均质性的各向异性；(3)平均传播速度的大尺度结构和不连续性(如莫霍面)；(4)能量传递过程中的相干效应。Papanicolaou和Wu建议合作，以系统和灵活的方式发展地震波传播中辐射传输理论的基础，以便尽可能减少或消除上述缺点。我们将使用我们对理论、计算和经验方法的广泛理解来分析随机介质中的波。

9419073 Wu Radiative transport theory is the principle tool for analyzing the incoherent transport of seismic energy in the earth's crust, which is a very complex, inhomogeneous elastic medium. But its use at present is limited to isotropic structures of infinite extend and does not account for: (i) energy transfer among different elastic wave modes, including surface waves, (ii) the anisotropic nature of the inhomogeneities in the earth's crust, (iii) the large scale structure and discontinuities in the mean propagation speeds (the Moho discontinuity, for example), (iv) coherent effects in the process of energy transfer. Papanicolaou and Wu propose to collaborate on developing the foundations of radiative transport theory in seismic wave propagation in a systematic and flexible way so that the above shortcomings can be minimized, or eliminated if possible. We will use our extensive understanding of theoretical, computational and empirical methods for the analysis of waves in random media.