GPR full waveform sensitivity and resolution analysis using an FDTD adjoint method

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Abstract
GPR tomography is a useful tool for mapping the conductivity and permittivity distributions in the shallow subsurface. By exploiting the full GPR waveforms it is possible to image sub-wavelength features and improve resolution relative to what is possible using ray-based approaches. Usually, mere convergence in the data space is the only criterion used to appraise the goodness of the final result, therefore limiting the reliability of the inversion. A better indication of the correctness of an inverted model and its various parts could be obtained by means of a formal resolution and information content analysis. We present here a novel method for computing the sensitivity kernels (Jacobian matrix) based on an FDTD adjoint method. We show that the column sum of absolute values of the Jacobian, often used as a proxy for model resolution, is inadequate, such that a formal resolution analysis should be performed. The eigenvalue spectrum of the pseudo-Hessian matrix provides a measure of the information content of the experiment and shows the extent of the unresolved model space.

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