GPR Full Waveform Frequency-Space Domain Modeling by the Full Spectral Methods

Summary Accurate differentiation matrices operators by the full spectral method have been applied to the temporal and spatial domains of the transverse electric (TE) and transverse magnetic (TM) modes of the GPR full waveform. By Fourier transform, these operators are simply complex frequency and wavenumber which must be sampled appropriately to produce accurate results. This full spectral method contrasts with the pseudo-spectral method that transforms only a component (either the time or space) to the Fourier domain and leaves the second component in its regular domain. The finite difference approach supplies its approximate differentiation matrices operator in time and space domains thus leading to inherent truncation error. Convolution of the differentiation matrices operator with the medium parameter is performed; and the inversion of the system of linear equations produce the accurate GPR full waveform modeling results for different permittivity models.