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Improving the accuracy and efficiency of the numerical simulation of ground penetrating radar (GPR) becomes a pressing need with the rapidly increased amount of inversion data and the growing demand for migration imaging quality. In this article, we present a numerical spectral element time-domain (SETD) simulation procedure for GPR forward modeling and further apply it to the reverse time migration (RTM) with complex geoelectric models. This approach takes into account the flexibility of the finite element methods and the high precision of the spectral methods. Meanwhile, in this procedure, the complex frequency shifted perfectly matched layer (CFS-PML) is loaded to effectively suppress the echo at the truncated boundary, and the per-element GPU parallel framework used can achieve up to 5.7788 times the efficiency compared with the CPU calculation. The experiments on SETD spatial convergence and CFS-PML optimal parameter selection showed that, under the same degree of freedom, the SETD offered substantially better accuracy compared with the traditional FETD. The experiments on RTM of different profiles with different orders of SETD via a complex geoelectric model verify the universality of the algorithm. The results indicate that the RTM imaging effect has been significantly improved with the increase of SETD order. It fully proves the great potential of efficient and high-precision SETD simulation algorithm in the RTM imaging direction and shows certain guiding significance for underground target structure exploration.

A High-Efficiency Spectral Element Method Based on CFS-PML for GPR Numerical Simulation and Reverse Time Migration