Probing Depth-dependent Heterogeneities under Japan Using Transmitted Seismic Waves

目前，S的地球内部动力学主要是通过地震层析成像等确定性方法探测地球上的地震波速异常来推断的。异常是在地球内部按点绘制的，它可以被解释为对流地幔和地壳的快照。然而，这种确定性方法的空间分辨率受到地震仪稀疏地理分布的限制。考虑到当前地震台网的分布情况，全球层析成像解决的非均质性的长度尺度约为数百公里。另一方面，还有一些重要的地质过程，发生在地球上？S表面的长度尺度要小得多，从几十公里到几米不等。为了更好地了解地球动力学，失踪的？必须补充连续非均质谱高端(即那些小规模非均质)的信息。然而，地震层析成像还远远不能实现地壳以下结构的高分辨率确定性模型，必须设计一种新的方法。在本文提出的工作中，提出了一种新的随机反演理论，该理论基于波在随机介质中的传播，能够将小尺度非均质性作为一个集合来提供统计信息，如非均质性的尺寸分布、非均质性的波散射强度以及它们如何随深度分布。这一理论背后的物理原理是，在传输的地震体波中，小尺度的非均质性表现为地震阵列上的相位(或旅行时，或到达时间)和波幅的波动。这些观测到的波动然后被用来形成相干函数，该函数同时取决于两个地震台之间的距离和两个平面波之间的入射角。相干函数具有很高的深度分辨率，可以用来对随深度变化的非均质谱进行反演。这个新开发的数学框架将用于分析日本HiNet地震台网记录的数据。这个仪器密集的大口径网络有可能限制从地表到数百公里深度的异质光谱。拟议的工作可能涉及以下几个基本问题：(1)俯冲物质在地幔中的去向；(2)热手指、日本下方火山的源区和非火山区的地震波散射特性的表征；(3)对板幔相互作用和地幔楔体演化的地震约束；(4)对不同深度的地幔不均一性的多尺度分析可能提供一种手段，以隔离导致不同长度尺度的不同物理和化学机制。关于小尺度非均质性的统计信息在地球科学的其他学科中也是至关重要的，例如岩石学、地球化学、构造学和对流地球的流体动力学模拟。这里发展的数学方法可能会被用于其他与随机介质中的波传播相关的科学领域，如海洋声学、电磁波传播和通信、医学成像和日震学。

At present, the Earth?s interior dynamics are mainly inferred by detecting seismic wave velocity anomalies in the Earth using deterministic approaches such as seismic tomography. The anomaly is mapped point-wise within the Earth and it can be interpreted as a snapshot of the convective mantle and crust. However, the spatial resolution of such deterministic methods is limited by sparse geographic distribution of seismographs. Given the distribution of current seismograph networks, the length scale of the heterogeneity resolved by global tomography is on the order of several hundred kilometers. On the other hand, there are important geological processes, taking place on the Earth?s surface at much smaller length scales, from the order of tens of kilometers to meters. In order to gain a sound understanding of Earth dynamics, the ?missing? information at the high end (i.e., those small-scale heterogeneities) of the continuous heterogeneity spectrum must be supplemented. However, seismic tomography is far from achieving high-resolution deterministic models for structures below the crust, and a novel approach must be devised.In the work proposed here, a new stochastic inversion theory is formulated mathematically, which is based on wave propagation through random media, and it is able to yield statistical information on small-scale heterogeneities as an assemblage, such as the size distribution of heterogeneities, the wave scattering strength of the heterogeneity, and how they are distributed with depth. They physics behind the theory is that small-scale heterogeneities manifest themselves in transmitted seismic body waves as fluctuations of phase (or travel time, or arrival time) and wave amplitude across a seismic array. These observed fluctuations are then used to form coherence functions, which simultaneously depend on the distance between two seismic stations and the incident angles between two plane waves. The coherence function has sharp depth resolution and can be used to invert for the depth-dependent heterogeneity spectrum. This newly developed mathematical framework will be used to analyze data recorded by the HiNet seismic network in Japan. This densely instrumented large-aperture network has the potential to constrain heterogeneity spectra over depths from the surface to several hundred kilometers. The proposed work here may address several fundamental issues concerning: (1) the fate of subducted materials in the mantle (2) characterization of the seismic wave scattering properties for ?hot fingers?, source regions feeding the volcanoes under Japan, and non-volcanic regions; (3) seismic constraints on the slab-mantle interaction and evolution of the mantle wedge; (4) multi-scale analysis of mantle heterogeneities and at different depths may provide a means to isolate different physical and chemical mechanism that is responsible for each length scale. The statistical information on the small-scale heterogeneity is also critical in other disciplines of Earth sciences, for instance, petrology, geochemistry, tectonics and hydrodynamic modeling of the convective Earth. The mathematical methods developed here can potentially be used in other scientific areas related to wave propagation in random media, such as, ocean acoustics, electromagnetic wave propagation and communications, medical imaging, and helioseismology.