Browsing by Subject "Layered Green's Function"

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    Full waveform analysis of ground penetrating radar measurements.
    (2011-08) Cao, Yuejian
    The purpose of this study is to extend the use of ground penetrating radar methodology towards a more reliable and accurate interpretation of pavement conditions. First, a complete set of 3D layered electromagnetic Green's functions is derived by way of transverse electric and transverse magnetic scalar potentials, featuring a new "direct" formulation for the field forms of the spectral Green's functions. The improper integrals underpinning the computation of the corresponding point-load solutions in the spatial domain are evaluated via the method of asymptotic decomposition, wherein the singular behaviors are entirely extracted and integrated analytically -- so that the remaining residual components can be computed effectively and accurately via adaptive numerical quadrature. It is also found that, in the spectral domain, the decay of the (numerically-integrated) residual field forms is commensurate to that of their potential-form counterparts, which eliminates the perceived gap between the computation of the field forms and respective potential forms of the Green's functions in the spatial domain. The effectiveness and accuracy of the proposed methodology is evaluated via comparison with relevant examples in the literature. Second, utilizing the derived electromagnetic Green's function for a layered system due to a horizontal electric dipole, the GPR scan can be simulated over a wide range of pavement profiles. Examples are provided for GPR simulation on a three-layer pavement system. By virtue of this forward model, the best match of the GPR scan in terms of the full waveform can be recovered within thousands of simulations via a optimization routine, where the in-situ layer parameters associated with the measurement are found to be equal to the simulation inputs. The accuracy of the interpreted layer thickness from the proposed scheme is verified by ground truth, with average error around 2.3% compared to 7.5% average error for the traditional method. In addition, the proposed scheme allows an evaluation of the relevant pavement properties with no prior assumptions or subjective image adjustments, unlike the traditional method.