Multi-parameter spectral inversion for GPR signals of subsurface layered media

Abstract

A frequency-domain spectral inversion algorithm is derived and verified in this paper, using which underground reflective surfaces' positions as well as each layer's thickness, dielectric permittivity and electric conductivity can be obtained simultaneously. Generalized reflection coefficients are first defined according to the transmission pattern of electromagnetic (EM) wave in subsurface layered media. With a three-layer model considered, the coefficients of each reflective surface are decomposed into even and odd component. Before inversion is carried out, a cost function is established to connect spectral of reflection coefficients and layer's parameters. Only with correct parameters, can the spectral be rightly synthesized and the cost function will be minimized. In order to solve this non-linear optimization problem, a modified Stochastic Hill-climbing Algorithm (SHA) is applied. Since more reliable initial parameter vector can greatly improve inversion efficiency and result accuracy, new strategies are adopted to decide the first vector. The first parameters are calculated step by step according to their different effects on coefficients spectral. Only part of the parameters is involved during each step, which makes the procedure very fast. The algorithm is applied on simulated data of a wedge model first, whose result suggests that accurate parameters can still be expected when thickness of the layer is less than tuning thickness and iteration times are also greatly reduced compared with that of inversion using initial vector with random parameters. At the end, a set of data coming from a highway GPR detection are used to test the algorithm and the result is also promising.