Inversion of ground-penetrating radar data for 2D electric parameters
用地质雷达数据资料反演二维地下介质的方法

This 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 up 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. These results are compared with the result obtained by using an 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.