The GPR simulation of bi-phase random concrete medium using finite element of B-spline wavelet on the interval

Based on the separable wavelet theory, the scaling functions of one-dimensional B spline wavelet on the interval (BSWI) is employed to construct the two-dimensional B-spline wavelet bases on the interval. In order to solve the GPR wave equation, these constructed wavelet bases are used as the interpolation functions, and a transformation matrix is introduced to convert between the wavelet coefficient space and the physical space (radar electromagnetic field). In this study, the discrete format of GPR wave equation for two-dimensional interval B spline wavelet finite element is derived using Galerkin algorithm. And the integral values and the connection coefficients of the second order one-scale and second order two-scale BSWI functions are calculated. The detailed process of the algorithm is given. Then two typical examples are forward modeled using the BSWI method by Matlab program. The result shows that the BSWI with fewer units has the same precision as FEM. Increasing the scale of BSWI algorithm, the precision of the results is also improved, but it is time-consuming. Finally, the BSWI algorithm is applied to model bi-phase random concrete medium, and it proves that the random medium model theory can describe the practical distribution of concrete medium flexibly and effectively. Furthermore, this study found that the forward modeling profile is more accordant with practical profile, which demonstrates that medium model theory can simulate the transmission process of the radar wave more accurately. It also provides a theoretical basis for improving the detection results and interpretation accuracy of GPR.