GNGTS 2013 - Atti del 32° Convegno Nazionale

4. The amplitudes of the reflected signals depend only on the partial reflections at each interface, having removed the effect of geometrical spreading and disregarding variations in antenna coupling and intrinsic and scattering attenuation effects. In such a system, at a given offset, the ray paths of the recorded signals are fixed by geometrical constraints, and are symmetrical with respect to the mid-axis. The method estimates the velocity distribution by reconstructing the travel paths through an iterative process, requiring as input the value of the offset ( x ), the velocity ( v 1 ) of the radar signal in the first layer, the peak amplitude ( Ai 1 ) of the wavelet incident on the first interface and the peak amplitudes ( As i ) and traveltimes (twt i ) of the reflected waves. By knowing the thicknesses of the first n -1 layers and the velocities of the radar signal in the first n layers, each cycle calculates the thickness of the n -th layers and the velocity of the radar wave in the ( n +1)-th layer, using the amplitude of the wavelet incident on the first interface and the amplitude and twt of the wave reflected by the n -th reflector. The thickness h n of the n -th layer is obtained by rearranging the reflection traveltime equation for the n -th interface: which reduces to the single reflection equation when n is equal to 1. In a 1-D system the travel paths are fixed at a given offset, and the incident angle for the k -th interface is equal to the transmission angle at the ( k -1)-th interface. Considering the propagation path of the wave reflected by the n -th interface and taking into account the small spread approximation (offset much smaller than depth), the angle of incidence k on the k -th interface can be approximated by: From such angles, the reflection and transmission coefficients of the first n-1 interfaces are obtained from the Fresnel equations of TE (or TM) antenna configuration, while the n -th reflection coefficient is obtained by reconstructing the incident and reflected amplitudes at the n -th interface: The EM velocity in the ( n +1)-th layer is given by the Snell equation: where n+1 is calculated in the TE antenna configuration. By iterating the procedure for all the reflected ray paths, it is possible to obtain thicknesses and velocities in all the imaged layers. Input parameters are a) velocity of the shallow layer; b) amplitude of the wave incident on the first interface; c) amplitude and twts of all the recorded reflections. Results and discussion. We first tested the new methodology on 1-D velocity models, from which synthetic GPR traces were calculated by using a known wavelet, taking into account only the partial reflection and transmission from each interface, both downward and upward, while disregarding dissipations and geometrical spreading as requested by the inversion algorithm. The shape of the wavelet used in the forward modeling is not important, since the only trace data requested by the inversion process are just the peak reflected amplitudes and the traveltimes associated with such reflections. The new procedure was then applied to the simulated traces to reconstruct the models’ velocity distributions. 114 GNGTS 2013 S essione 3.2