Abstract
AbstractThis paper derives inversion formulas for reconstructing electric parameters of a medium from observed ground‐penetrating radar (GPR) data based on the two‐dimensional (2D) Maxwell's equations. By introducing an adjoint field calculated using the Maxwell's equations, the gradients of the objective function with respect to unknown parameters can be expressed explicitly. The procedure of inversion is, first of all, to build an initial model and to calculate guessed data. Secondly, to calculate adjoint fields by solving the adjoint wave equations, and thirdly to calculate the gradients and to modify the model. These steps are repeated until an acceptable result is obtained. In the modification of the model, the conjugate gradient method is used. Three reconstruction examples are illustrated. A permittivity profile is reconstructed from synthetic data received on a rough surface. A permittivity and a conductivity profile are reconstructed simultaneously from experimental data. Reconstruction results obtained by using the method of this paper are compared with a result obtained by using the inversion method based on the scalar wave equation where absorption is neglected, and with a migration profile obtained by using a wave equation migration method.
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