Tomographic imaging in civil engineering infrastructure

Abstract

This research was to assess the potential of tomographic imaging in a variety of geotechnical processes, with emphasis on matrix-based inversion algorithms. While most prior research in tomography has been based on simulated data, this research centers on case histories gathered under well-controlled, yet realistic field conditions. The goal is to invert a velocity images which reflects the state or evolution of a given soil parameter (e.g., stress, pore pressure, ion concentration) using a set of picked travel times.

Among inversion methods, matrix inversion methods are versatile and robust. However, efficient storage and computation are required. The sparsity of matrices involved in tomographic problems enable us to employ efficient storage and solvers.

In general, it is assumed that "picked travel times" correspond to paths of shortest travel path (Fermat's principle). If the velocity contrast in the medium is more than 15 to 20 percent, rays bend toward higher velocity regions. In this case, entries in the coefficient matrix depend on a prior estimate of the velocity field. Therefore, the relation between pixel velocities and travel times is non-linear in general. This non-linear inversion problem can be solved by employing iterative solutions with ray tracing.

Ray tracing methods can be categorized as: one-point methods, two-point methods, and whole-field methods. The computational time demand for ray tracing methods for each category is evaluated based on the number of segmental travel time calculations. The computational efficiency of the ray tracing methods is also compared for fundamental cases. Some evidence of the accuracy needed in ray tracing to solve the inversion problem, within the context of other errors in CE-tomography, are given.

Prior experience with simulated data has shown that the quality of inversion is unrealistically good when compared to inversions with real data. In part, this reflects the compatibility of forward simulation algorithms with hypotheses made in the inversion stage. A central goal of this thesis is to assess the potential of inversion with real data. A database of case histories has been compiled for this purpose. Part of this study is dedicated to the testing of pre-processing strategies in each case history. It is shown that data pre-processing can be employed to provide foresight about the medium, and help the selection of proper constraints. Distribution and amount of information, presence of accidental and systematic errors, degree of heterogeneity and anisotropy, and analysis of shadows are analyzed for all case histories.

A tomographic program based on sparse matrix algorithms was encoded as part of this study. The selected tomographic inversion methods are based on matrix analyses. Data structures are used to take advantage of the sparsity of the coefficient matrix and to avoid high memory and computational demand. Sine-arc ray tracing and straight rays are two possibilities. The program is in structured form to facilitate future additions and modifications.

Tomographic data are usually mixed-determined and ill-conditioned. Damped Least squares (DLSQ) and regularization add information in the form of constraints in order to decrease the ill-conditioning of the problem. The optimum dampening or regularization coefficient gives the best solution. Optimal damping or regularization coefficients should be determined in an inversion process. In this study, several guidelines are proposed to determine optimal damping or regularization coefficients.

Inverted images for all case histories in this study are given in Appendix F. The results indicate the ability of the method to invert large size, ill-conditioned, and noisy problems.