Collaborative Research: A Field Expansion Method for Acoustic Scattering from Topography: Extensions to Elasticity and the Inverse Problem

这项建议启动了一项新的合作，旨在通过将地形纳入地震波建模和减少这些方法对极低频数据的依赖来改进波形反演方法。 主要研究人员建议调整和改进用于模拟衍射光栅散射的方法。他们的方法扩展到线性弹性，并提供了一般的改进解决反问题。 需要显著的数学进步来开发用于该应用的稳健且有效的技术。边界摄动法将场扩展方法扩展到具有独立形貌的任意数量的层，并允许在二维中快速准确地模拟声波传播。 需要把弹性力学的一般方程推广到三维空间.此外，基于几何声学的与频率无关的离散化扩展到多层弹性模型是一个重要且必要的数学进步。 此外，在反问题的进展也是必要的，使该技术真正适用于地震成像问题。"全波形反演"的标准方法需要频率太低而无法实际记录的数据。 PI的方法将正问题转换为一系列地形相关算子的应用，其中界面形状相当明确。 提出了一些迭代方案的恢复这些形状，重新安排的组合物耦合到标准的正则化技术从理论不适定的问题。 地震波在沉积层中的传播特性在许多技术中是至关重要的，包括确定地球内部的性质和结构，地震检测和预测，以及碳氢化合物（石油和天然气）勘探。 鉴于其许多重要的应用，这并不奇怪，大量的数值和实验技术已被带到承担这个问题。 然而，在理解和能力方面仍然存在一些差距。PI通过复杂的数值模拟解决了其中的一些问题，这些模拟将通过实验室实验和青藏高原的实地测量进行验证。

This proposal initiates a new collaboration aimed at improving methods of waveform inversion by including topography in seismic wave modeling and reducing the reliance of these methods on data at extremely low-frequency. The Principal Investigators propose to adapt and improve methods developed for simulating scattering from a diffraction grating. Their approach has extensions to linear elasticity and provides general improvements for solving the inverse problem. Significant mathematical advances are required to develop robust and efficient techniques for this application. The Boundary Perturbation Method extends the Field Expansion approach to an arbitrary number of layers with independent topographies and allows for rapid and accurate simulation of acoustic wave propagation in two dimensions. Extensions to three dimensions and to the general equations of elasticity are required. Moreover, the extension of frequency-independent discretizations based on Geometric Acoustics to multilayered elastic models is a significant and necessary mathematical advance. Additionally, advances in the inverse problem are also necessary to make the technique truly applicable to the seismic imaging problem. The standard method of "full-waveform inversion" requires data at frequencies which are too low to record in practice. The PIs' approach casts the forward problem as the application of a sequence of topography-dependent operators where the interface shapes appear rather explicitly. A number of iteration schemes are proposed for the recovery of these shapes, using re-arrangements of the compositions coupled to standard regularizing techniques from the theory of ill-posed problems. The propagation properties of seismic waves in layers of sediment are crucial in many technologies including the determination of inner earth properties and structure, earthquake detection and prediction, and hydrocarbon (oil and gas) exploration. In light of its many important applications, it is not surprising that a vast array of numerical and experimental techniques have been brought to bear upon this problem. However, several gaps in understanding and capability still exist. The PIs' address some of these questions through sophisticated numerical simulations which will be validated against both laboratory experiments and field measurements from the Tibetan plateau.