Inversion of Attributes and Full Waveforms of Ground Penetrating Radar Data Using PEST

Abstract:

We seek to establish a method, based on freely available software, for inverting GPR signals for the underlying physical properties (electrical permittivity, magnetic permeability, target geometries). Such a procedure should be useful for classroom instruction and for analyzing surface GPR surveys over simple targets.

We explore the applicability of the PEST parameter estimation software package for GPR inversion (www.pesthomepage.org). PEST is designed to invert data sets with large numbers of parameters, and offers a variety of inversion methods. Although primarily used in hydrogeology, the code has been applied to a wide variety of physical problems. The PEST code requires forward model input; the forward model of the GPR signal is done with the GPRMax package (www.gprmax.com).

The problem of extracting the physical characteristics of a subsurface anomaly from the GPR data is highly nonlinear. For synthetic models of simple targets in homogeneous backgrounds, we find PEST’s nonlinear Gauss-Marquardt-Levenberg algorithm is preferred. This method requires an initial model, for which the weighted differences between model-generated data and those of the “true” synthetic model (the objective function) are calculated. In order to do this, the Jacobian matrix and the derivatives of the observation data in respect to the model parameters are computed using a finite differences method. Next, the iterative process of building new models by updating the initial values starts in order to minimize the objective function. Another measure of the goodness of the final acceptable model is the correlation coefficient which is calculated based on the method of Cooley and Naff. An accepted final model satisfies both of these conditions.

Models to date show that physical properties of simple isolated targets against homogeneous backgrounds can be obtained from multiple traces from common-offset surface surveys. Ongoing work examines the inversion capabilities with more complex target geometries and heterogeneous soils.