Second-generation wavelet fi nite element based on the lifting scheme for GPR simulation*
Feng De-Shan 1,2, Zhang Hua 1,2, and Wang Xun 1,2
1. School of Geosciences and Info-Physics, Central South University, Changsha 410083, China.
2. Key Laboratory of Metallogenic Prediction of Nonferrous Metals, Ministry of Education, Changsha 410083, China.
Abstract Ground-penetrating radar (GPR) is a highly efficient, fast and non-destructive exploration method for shallow surfaces. High-precision numerical simulation method is employed to improve the interpretation precision of detection. Second-generation wavelet finite element is introduced into the forward modeling of the GPR. As the finite element basis function, the second-generation wavelet scaling function constructed by the scheme is characterized as having multiple scales and resolutions. The function can change the analytical scale arbitrarily according to actual needs. We can adopt a small analysis scale at a large gradient to improve the precision of analysis while adopting a large analytical scale at a small gradient to improve the efficiency of analysis. This approach is beneficial to capture the local mutation characteristics of the solution and improve the resolution without changing mesh subdivision to realize the efficient solution of the forward GPR problem. The algorithm is applied to the numerical simulation of line current radiation source and tunnel non-dense lining model with analytical solutions. Result show that the solution results of the secondgeneration wavelet finite element are in agreement with the analytical solutions and the conventional finite element solutions, thereby verifying the accuracy of the second-generation wavelet finite element algorithm. Furthermore, the second-generation wavelet finite element algorithm can change the analysis scale arbitrarily according to the actual problem without subdividing grids again. The adaptive algorithm is superior to traditional scheme in grid refi nement and basis function order increase, which makes this algorithm suitable for solving complex GPR forward-modeling problems with large gradient and singularity.
This work was supported by the National Natural Science Foundation of China (Nos. 41574116 and 41774132) and Hunan Provincial Innovation Foundation for Postgraduate (Grant Nos. CX2017B052) and the Fundamental Research Funds for the Central Universities of Central South University (Nos. 2018zzts693)
Corresponding Authors: Wang Xun (E-mail: wangxun0727@csu.edu.cn)
E-mail: wangxun0727@csu.edu.cn
About author: Feng De-shan, professor, doctoral supervisor. He received Ph.D. (2006) in Geophysical Prospecting and Information Technology from Central South University. Visiting scholar at Rice University, USA, 2013-2014. He is interested in the theory and application of GPR, forward modeling and inversion, and wavelet analysis. E-mail: fengdeshan@126.com
Wang Xun, Corresponding author, received his M.S. (2016) in Geological Engineering f r o m C e n t r a l S o u t h U n i v e r s i t y. He is presently a Ph.D. candidate in Geophysical Prospecting and Information Technology at Central South University. His main interests is numerical simulation of electromagnetic method. E-mail: wangxun0727@csu.edu.cn.
Cite this article:
. Second-generation wavelet fi nite element based on the lifting scheme for GPR simulation*[J]. APPLIED GEOPHYSICS, 2020, 17(1): 143-153.
2020, Vol. 17 
