Numerically-robust pseudoanalytical evaluation of Green´s functions in cylindrical-stratified media

A robust algorithm for computing the reponse of dipole-sources in cylindrical-stratified media is presented. A set of new bounded (range-conditioned) functions are introduced in order to handle the exponential behavior of the Bessel and Hankel functions for large arguments as well their behavior for very small arguments, from which the corresponding spectral Green´s function is determined. The new functions are defined in three nonoverlapping subdomains and used to stabilize the numerical computation under double-precision arithmetic. In addition, adaptively-chosen integration contours are employed in the complex plane to ensure fast convergence in all cases. The algorithm is in principle applicable to any range of frequencies of interest. We validated it at frequencies of interest to geophysical exploration, ranging from 10 MHz down to the low magnetotelluric frequency-range (around 0.01 Hz), and for layers with resistivities varying from 1000 Ω · m to 10^-8 Ω · m.