Data-driven inversion of GPR surface reflection data for lossless layered media

Abstract

Abstract-Two wavefields can be retrieved from the measured reflection response at the surface. One is the Green's function at a chosen virtual receiver depth level in a layered model generated by a source at the surface. The other wavefield consists of the upgoing and downgoing parts of a wavefield that focuses at the virtual receiver depth level. From the upgoing part of the focusing wavefield an image can be computed at one-way vertical travel time and with correct amplitudes of the local reflection coefficients as a function of incidence angle. These reflection coefficient values can be used to invert for electric permittivity and magnetic permeability. From these values and the known image times the layer thickness values can be obtained for each layer. This method renders the full waveform inversion problem for horizontally layered media a linear problem.

Marchenko Inversion of GPR Data for a 1d Dissipative Medium

“…It is a full waveform inversion method if the electric and magnetic parameters are obtained as a function of the subsurface position. Recently, some datadriven methods based on the Marchenko scheme have been proposed [11,15,17]. It was shown that the wave fields and focusing wave fields inside an unknown medium can be retrieved by solving a set of Marchenko-type equations [11,19].…”

“…Recently, some datadriven methods based on the Marchenko scheme have been proposed [11,15,17]. It was shown that the wave fields and focusing wave fields inside an unknown medium can be retrieved by solving a set of Marchenko-type equations [11,19]. The Marchenko inversion scheme can be implemented as long as the Green's function or/and the focusing function are obtained because the local reflectivity or impedance can be obtained as a starting point for further inversion [11,17].…”

“…It was shown that the wave fields and focusing wave fields inside an unknown medium can be retrieved by solving a set of Marchenko-type equations [11,19]. The Marchenko inversion scheme can be implemented as long as the Green's function or/and the focusing function are obtained because the local reflectivity or impedance can be obtained as a starting point for further inversion [11,17]. The theory for 1D GPR inversion based on Marchenko redatuming has been derived for a lossless medium [11].…”

“…The Marchenko inversion scheme can be implemented as long as the Green's function or/and the focusing function are obtained because the local reflectivity or impedance can be obtained as a starting point for further inversion [11,17]. The theory for 1D GPR inversion based on Marchenko redatuming has been derived for a lossless medium [11]. A 3D Marchenko redatuming method for dissipative acoustic media has been developed [13].…”

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

“…It can be used to eliminate the effect of internal multiples in a seismic or GPR image [9][10] [11]. A GPR inversion method for lossless medium based on Marchenko method has been developed [12]. This is a data-driven method, but it can deal only with lossless media and still needs to know the source signature.…”