UBC Theses and Dissertations
Cross-hole GPR imaging : traveltime and frequency-domain full-waveform inversion Van Vorst, Daryl
Ground-penetrating radar (GPR) has the potential for high-resolution imaging of near-surface material properties, including electrical conductivity and permittivity, which can be used for geological interpretation of the near subsurface. This thesis presents ray-based traveltime inversion and frequency-domain full-waveform inversion (FWI) techniques for application to borehole GPR surveys. Ray-based traveltime inversion is attractive for its speed, reliability, and ability to work in 3D, but the ray approximation involved limits recoverable detail to greater than one wavelength. The traveltime method presented here uses an efficient and easily programmed fast-sweeping eikonal solver to compute traveltimes. The inversion method also incorporates the unknown time offset between signal transmission and start of recording at the receiver as a model parameter that is recovered simultaneously with the material slowness. The resolution of FWI approaches the diffraction limit of one half wavelength, but at a substantial computational cost. The FWI inversion scheme presented here works in 2D and is unique in its simultaneous recovery of the source wavelet, conductivity, and permittivity. Its frequency-domain formulation allows for efficient factorization of the forward modeling operator and its subsequent application to multiple right-hand sides in order to quickly construct the forward model Jacobian. Efficient calculation of the Jacobian allows the use of the Gauss-Newton technique rather than the gradient descent method that is common for other GPR FWI inversions. Measured data must be converted from 3D to 2D before use with this 2D FWI technique. I present a graphical derivation of the perpendicular ray Jacobian, which is an essential part of 3D to 2D transformation. The graphical derivation provides the reader with an intuitive understanding of the Jacobian that is difficult to obtain from traditional mathematical treatments. I also illustrate that 3D to 2D transfer functions previously derived for the acoustic case are applicable to borehole GPR.
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