Probabilistic Inversion: A New Approach to Inversion Problems in Pavement and Geomechanical Engineering

Abstract

A wide range of important problems in pavement and geomechnical engineering can be classified as inverse problems. In such problems, the observational data related to the performance of a system is known, and the characteristics of the system that generated the observed data are sought. There are two general approaches to the solution of inverse problems: deterministic and probabilistic. Traditionally, inverse problems in pavement and geomechanical engineering have been solved using a deterministic approach, where the objective is to find a model of the system for which its theoretical response best fits the observed data. In this approach, it is implicitly assumed that the uncertainties in the problem, such as data and modeling uncertainties, are negligible, and the “best fit” model is the solution of the problem. However, this assumption is not valid in some applications, and these uncertainties can have significant effects on the obtained results. In this chapter, a general probabilistic approach to the solution of the inverse problems is introduced. The approach offers the framework required to obtain uncertainty measures for the solution. To provide the necessary background of the approach, few essential concepts are introduced and then the probabilistic solution is formulated in general terms using these concepts. Monte Carlo Markov Chains (MCMC) and its integration with Neighborhood Algorithm (NA), a recently developed global optimization and approximation algorithm, are introduced as computational tools for evaluation of the probabilistic solution. Finally, the presented concepts and computational tools are used to solve inverse problems in Falling Weight Deflectometer (FWD) backcalculation and seismic waveform inversion for shallow subsurface characterization. For each application, the probabilistic formulation is presented, solutions defined, and advantages of the probabilistic approach illustrated and discussed.