GPR Tomography for mapping soil moisture and roots

For high resolution georadar tomography inverting of arrival times or amplitude data yields a distribution of electromagnetic velocity or an attenuation-related parameter that images anomalous subsurface features, e.g., voids, moisture content or clay heterogeneities. Tomographic reconstruction technique is widely used in geophysical and geological field investigations (Bregman, et al., 1989; Daily & Owen, 1991; Cai & McMechan, 1999). Solving the tomography problem depends mathematically on solving a system of linear equations iteratively (Peterson et al., 1985). The principle of the tomographic method shows a typical ray path from the transmitter (Tx) to a receiver (Rx) Ri (Fig. 1). Multiple Tx and Rx locations yield a number of such rays crossing the intervening material in different directions. The region between Tx and Rx lines are discretized into cells and the slowness sj of the cell j is assumed to be constant over the area covered by a single cell. The recorded travel time can be expressed as integral over the ray path Each of these integrals, in discrete form, becomes one equation in the linear tomographic system that is to be inverted for velocity and/or layer shape (from travel times) or for attenuation (from amplitudes). The linear system of equations has the form: t=As, where t is the GPR time vector, A is the distance matrix connecting Tx-Rx locations, and s is the GPR slowness vector. We used this principle to develop a new GPR tomography algorithm (SeismoRad computer program) for inverting surface and crosshole data (Hanafy, 2002).