A space marching inversion algorithm for pulsed borehole radar in the time-domain

An iterative algorithm is developed to reconstruct the image of formation conductivity surrounding a borehole using time-domain data. The forward modeling employed in the algorithm is derived from the transmission line matrix (TLM) method, which is used to simulate electromagnetic waves propagating in formations with two-dimensional variations in cylindrical coordinates. A new structure of a transmission line node is used to simulate a coil-type transmitter antenna in a borehole. Since the inversion algorithm proceeds iteratively and the part of the formation involved in the inversion marches in space step by step, no optimization is necessary, and problems caused by optimization procedure such as inverting large-scale matrix and computation of Jacobian matrix numerically, are avoided. This method is especially useful in cases where the analytic gradient is not available. The inversion algorithm is tested in formations having both one- and two-dimensional conductivity variations with coil-type transmitters. Investigation depth and resolution for noise-free cases are also discussed in this paper.