Optimization and Inversion of GPR Model for Estimating Properties of Layered Media

Abstract

GPR is an electromagnetic technique that is used for examining shallow subsurface of the ground media. GPR has wide range of applications. One such application is road thickness evaluation and its quality measurement. Estimation of ground parameters requires accurate modelling of the layered medium. Two widely used modelling techniques are analytical modelling techniques and numerical modelling techniques. Numerical modelling involves solving Maxwells equations which is very complex and consumes lot of time. However as this technique needs fewer assumptions, the modelling is very accurate. FDTD, FEM and MOM are the few examples of numerical modelling. On the other hand analytical modelling techniques are approximated models hence are application specific. Valid assumptions on the medium result in simplified problem and make the modelling easy and precise. Few of the models that use analytical method of modelling are full wave model, surface reflection coefficient method, common midpoint method etc. As a part of research work, a 2-layered ground media is modelled using modified FWM which is a simplified model derived from FWM. An objective function is defined in least square sense to invert this model. The objective function is also called cost function or error function. This error function has to be minimized using an optimization technique. Parameters of the medium for which the objective function is minimum are the estimated parameters of the medium. Accuracy of the inversion depends on two major factors 1) accurate forward modelling of the medium 2) efficient optimization technique. As the objective function has multiple minima, it is not possible to optimize it using local optimization techniques. Hence it requires a global optimization technique. Here direct search method along with gradient technique is proposed for minimizing the error function.