Inference in Curved-Ray Tomography: Solid Earth Structure

本文研究了弯曲射线层析成像在固体地球结构中的应用。目标是在基本层面上分析当前层析成像建模方法中涉及的“数据处理”的许多步骤；通过模拟或其他方式估计它们可能包含的偏差和错误；并通过使用现代估计技术来弥补误差。另一个目标是将现有严格的极值反演方法应用于层析重建。这些技术将被应用于开发数学和软件工具，以精确地确定在给定可用数据的数量和质量的情况下可能解决三维结构特征的程度，并使用新开发的在非线性泛函估计中限定不确定性的方法来考虑问题的非线性。

This research is concerned with inference in curved-ray tomography as applied to solid earth structure. An objective is to analyze at a fundamental level the many steps of "data processing" involved in the current approaches to tomographic modeling; to estimate by simulation and otherwise what biases and errors they may contain; and to remedy the error by using modern techniques of estimation. Another objective is to apply existing rigorous methods of extremal inversion to tomographic reconstruction. These techniques will be applied to develop mathematical and software tools to determine precisely the extent to which it is possible to resolve features of the 3- D structure given the quantity and quality of the data available, accounting for nonlinearity of the problem using newly-developed methods of bounding the uncertainty in estimation of nonlinear funtionals.