Ray tracing methods for inverse problems

Abstract

We discuss the origin, use and implementation of ray tracing methods for nonlinear inverse modelling problems associated with wave propagation phenomena. These methods have a long tradition in acoustic and elastodynamic wave propagation problems for various important applications, and they can surely be helpful in other realms, including electromagnetic wave propagation and diffusion dominated phenomena. The subjacent models used for forward simulation have increased in complexity and dimension as computer power has enabled us to solve such problems in an acceptable amount of time. Thus, we will devote part of this paper to discuss modelling issues and the parallel implementation of algorithms for applications in earth sciences.

Refraction corrected transmission ultrasound computed tomography for application in breast imaging

“…͑3͒ into a more implementation-accessible form 30 ͑here, to be most general, we formulate the expression in 3D͒,…”

Aircraft design optimization

“…Multi-modal, ill-conditioned problems require global optimization techniques and regularization [13,15] and present some of the most challenging problems for robust initialization and ulterior accurate solution. In high-dimensional spaces the available techniques are problematic at their best and one often must resort to surrogate models, divide and conquer techniques and parallel computing, in order to even have a chance to solve the problem in a reasonable time [2,7,14,15].…”

“…In high-dimensional spaces the available techniques are problematic at their best and one often must resort to surrogate models, divide and conquer techniques and parallel computing, in order to even have a chance to solve the problem in a reasonable time [2,7,14,15].…”

A comparison of methods for the analysis of compressional, shear, and surface wave seismic data, and determination of the shear modulus

“…This data set was recorded with a sample interval of 0.1 ms in a time-window of 410 ms. The first method used for data processing was the delay-time method (Pakiser and Black, 1957;Palmer, 1986) followed by ray-tracing (Yacoub et al, 1970;Pereyra, 2000). The former is used to obtain a first-approximation depth-model, while the latter adjusts the result by iterations to minimize the discrepancies between measured arrival times and the corresponding times traced through the depth model.…”