2-DIMENSIONAL FORWARD ALGORITHM FOR TIME SPECTRAL RESISTIVITY

The 2 dimensional forward calculation for time spectral resistivity (TSR) is to compute the electric field transient response caused by a 3-D electric current dipole on the 2-D polarizable earth surface. As part of the so called 2.5-D numerical simulation for time domain electromagnetic field, this 2 dimensional forward calculation is still a difficult problem in geophysics. In this paper, a new algorithm is established for this problem with the following four features: (1) A 2-D finite element method is adopted to subdivide a triangular lattice by adding two diagonal lines in the rectangular lattice, and at the same time to eliminate unknown variables to be calculated at the central node of the rectangular lattice by using the Gauss elimination. Therefore, this method can be used not only to simulate accurately any complex 2-D geoelectric section, but also to save the calculation load. (2) A new algorithm for the computation of the secondary field is directly employed to compute only a primary field of the two components of electric and magnetic fields along the geoelectric structure. Such a method is advantageous not only in the relatively high computation precision, but also in the absence of much increase in calculation load. (3) The new G-S transformation method is used to make the inverse Laplace transformation, and, at the same time, the delay theorem of the Laplace transformation is used to calculate the interpolation at the intervals of the multiplication time, resulting in the rapid calculation of the transient electromagnetic responses to the dense samples. (4) This algorithm can be used to compute the transient electromagnetic response to the polarizable and conductive earth (including the IP and EM effects).