A Novel Propagator Coefficient Algorithm for Modeling Induction-Type Logging Responses in Cylindrically Layered Media

A novel amplitude propagator coefficient algorithm has been developed to simulate the responses of induction-type logging tool with coaxial antennas in cylindrical layered formations. First, this new algorithm incorporates boundary positions into the expressions of spectral electromagnetic (EM) fields, transforming the original layer coefficient solution into the amplitude computation at each boundary. These modified expressions not only prevent overflow issues but also enhance the physical clarity. The propagator coefficients and unknown amplitudes at the adjacent layers are connected, resulting in two linear equations. Each linear equation is further processed to reduce the number of successive unknowns from four to three. By combining all boundary conditions, the amplitudes can be recursively derived. A novel singularity subtraction scheme is also developed to increase the computational speed. By subtracting the slowly convergent part in the spectral domain, the convergence of residual spectral fields can be increased by three orders of magnitude. The algorithm is then utilized to investigate the influence of case pipe, mud filtrate invasion, as well as the drill collar on the responses of induction logging or logging-while-drilling (LWD) resistivity measurements.