Modeling Transient Electromagnetic Logging Using Sine Transform and Levin-Sidi Extrapolation

Abstract: Transient electromagnetic logging (TEL) is of great significance for detecting deep formation structures outside the wellbore. Forward modeling using analytical solutions requires frequency-domain calculations followed by time-domain conversion. For electromagnetic field computations in horizontally stratified media, mature Hankel transform methods already enable precise solutions. However, for cylindrically stratified media, oscillatory integrals involving cosine functions must be evaluated. This study employs the sine transform to achieve frequency-to-time domain conversion for TEL, proposing a new set of 125-point sine transform filter coefficients with enhanced computational accuracy. For frequency-domain calculations in cylindrically stratified media, the Gauss-Legendre quadrature rule combined with Levin-Sidi extrapolation is adopted to accelerate the convergence of partial sum sequences toward the true integral value. The accuracy of the proposed computational method is verified through numerical experiments in both horizontally layered and cylindrically stratified media.