Numerical modelling of ground‐penetrating radar using Chebyshev expansion and Lie product formula

In this paper, we have presented two highly accurate numerical schemes for modelling of ground‐penetrating radar (GPR) in two dimensions. These schemes have been derived from the analytical solution of Maxwell's equations. The first scheme uses Lie product formula and Taylor expansion, and the second scheme uses Chebyshev expansion. The accuracy of the proposed schemes has been evaluated by comparison with the analytical solution for a homogeneous medium. We have also shown simulations of some geoelectric models with different structural complexities, and the results confirm the accuracy of the proposed schemes. Moreover, we have presented a wavefield separation method based on Poynting vector information, which is capable of separating the wavefield in any direction. The proposed numerical schemes have been applied to reverse time migration using the Poynting vector. A comparison with conventional reverse time migration results shows that the migration noise is well suppressed using the wavefield separation based on the Poynting vector and cross‐correlation imaging condition, resulting in higher precision imaging results.