Accounting for Antenna in Half-Space Fresnel Coefficient Estimation

The problem of retrieving the Fresnel reflection coefficients of a half-space medium starting from measurements collected under a reflection mode multistatic configuration is dealt with. According to our previous results, reflection coefficient estimation is cast as the inversion of linear operator. However, here, we take a step ahead towards more realistic scenarios as the role of antennas (both transmitting and receiving) is embodied in the estimation procedure. Numerical results are presented to show the effectiveness of the method for different types of half-space media. 1. Introduction Subsurface imaging problem is relevant in several applicative contexts that range from geophysical to civil engineering applications [1]. In this framework, regardless of the imaging algorithm one may want to use, the knowledge of soil parameters is necessary in order to obtain properly focused images and free from artifacts proliferation [2]. By contrast, in realistic scenarios, such parameters are generally unknown or, at best, known with some degree of uncertainty. Therefore, a soil parameter estimation procedure must be run before imaging. Many procedures for estimating soil parameters are widespread in the literature. Reflectometry methods are very common [3]. There are methods which rely on fitting the moveout of hyperbolic diffraction pattern or measure travel time to a scatterer buried at known depth [4]. Other methods exploit different offset data and perform velocity or amplitude analysis to gather soil properties [5, 6]. Iterative imaging instead identifies soil parameters as those which return the more focalized reconstruction of a cooperative target [7]. Finally, further methods first retrieve reflection coefficient and then infer the soil properties by minimizing a nonlinear cost function by using optimization procedure [8]. Most of the methods quoted above require far zone approximation, so that asymptotic ray approximation works and generally assume soil as a homogeneous (at least transversally) half space. Moreover, time domain data, equivalently multifrequency data, are employed. In particular, this requires dealing with a non-linear inversions when the reflection coefficient is used to infer soil properties [8]. As well known, non-linear inversion are generally computationally demanding and can suffer from reliability problems due to the occurrence of false solutions. In these cases, one can take advantage from a priori information about the soil which allows to reduce the number searched for unknowns. However, this entails that soil dispersive law