Time-domain staggered-grid finite-difference simulation of GPR data

Simulation of digital ground penetrating radar (GPR) wave propagation in two-dimensional media is developed, tested, and implemented using finite-difference (FD) time-domain numerical method. The first-order effect of TE mode is considered due to operating frequency of current GPR instruments. Frequency-dependent attenuation is incorporated to account for significant change in the recorded response. The Staggered grid technique is used to sample the fields and approximate the spatial derivatives with fourth-order FDs. The temporal derivatives are approximated by explicit second-order difference time-marching scheme. By combining paraxial approximation of one-way wave equation (A2) and damping mechanism (Sponge filter), we obtain composite absorbing boundary methds that effectively absorb both incoming and outgoing waves. Each method has two types of mechanisms. A fixed and a floating A2 absorbing boundary conditions that operate at one grid point are proposed. Also, the superimposed artificial damping and alternated physical attenuation properties of the media within the absorbing region are employed to keep waves impinging on the boundary from reflecting back into grid. By applying any combination of absorbing mechanism, one can effectively minimize unphysical reflections from the computation domain boundary. The method enables us to use very thin absorbing boundaries. The model can be parameterized through velocity, relative electrical permittivity, electrical conductivity, magnetic permeability, loss tangent, Q value, and attenuation coefficient. According to this scheme one can model widely varying electrical properties of near-surface earth materials. The capability of simulating common-source, constant-offset and zero-offset gathers is demonstrated through various synthetic examples.