Two-Dimensional Linear Inversion of GPR Data with a Shifting Zoom along the Observation Line

Abstract

Abstract:Linear inverse scattering problems can be solved by regularized inversion of a matrix, whose calculation and inversion may require significant computing resources, in particular, a significant amount of RAM memory. This effort is dependent on the extent of the investigation domain, which drives a large amount of data to be gathered and a large number of unknowns to be looked for, when this domain becomes electrically large. This leads, in turn, to the problem of inversion of excessively large matrices. Here, we consider the problem of a ground-penetrating radar (GPR) survey in two-dimensional (2D) geometry, with antennas at an electrically short distance from the soil. In particular, we present a strategy to afford inversion of large investigation domains, based on a shifting zoom procedure. The proposed strategy was successfully validated using experimental radar data.

The ASI Integrated Sounder-SAR System Operating in the UHF-VHF Bands: First Results of the 2018 Helicopter-Borne Morocco Desert Campaign

“…It is worth stressing that, despite the adjoint inversion scheme defined by Equation 3is computationally efficient, the computational resources required are in any case high for the imaging problem at hand since large-scale (in terms of probing wavelength) data have to be processed. For this reason, we decided to adopt a shifting zoom approach [69], whose main steps are shown in Figure 5. More specifically, the measurement domain Γ and the survey area D are first partitioned into N partially overlapping subdomains, say Γ i and D i , i = 1, .…”

Theory for 1D GPR data inversion for a dissipative layered medium

“…Equations (4) and (5) form one set of equations that can be solved in the time domain for the up-and downgoing parts of the focusing wave field in the dissipative medium if the up-and downgoing components of the electric field at surface are known in the dissipative and in the effectual medium. Equations (6) and 7form a similar set that can be solved for the focusing wavefield in the effectual medium using the same data. Here, we present how to solve (4)- (5).…”

“…At present, most of the works on GPR inversion are based on model driven methods. There are some weaknesses of model driven inversion [5] [6] [7]. For instance, a good starting model is mandatory because the problem is ill-posed and suffers from non-uniqueness in the model solution.…”

GPR Investigation at the Archaeological Site of Le Cesine, Lecce, Italy

“…The fractioning of the investigation/observation domains, however, poses a relevant problem of reduced view angle [12] for all the targets close to any bound between two adjacent investigation domains. In [13], a method for mitigating such a problem has been introduced, called shifting zoom (or "shift and zoom"), and in [14] it has been applied to the creation of depth slices based on a linear inverse scattering algorithm. In this contribution, thanks to the shifting zoom, we will apply an inverse scattering algorithm to three electrically large sets of data and we will create depth slices based on this procedure.…”