  We present an efficient and robust semi-analytical formulation to compute the
electric potential due to arbitrary-located point electrodes in
three-dimensional cylindrically stratified media, where the radial thickness
and the medium resistivity of each cylindrical layer can vary by many orders of
magnitude. A basic roadblock for robust potential computations in such
scenarios is the poor scaling of modified-Bessel functions used for computation
of the semi-analytical solution, for extreme arguments and/or orders. To
accommodate this, we construct a set of rescaled versions of modified-Bessel
functions, which avoids underflows and overflows in finite precision
arithmetic, and minimizes round-off errors. In addition, several extrapolation
methods are applied and compared to expedite the numerical evaluation of the
(otherwise slowly convergent) associated Sommerfeld-type integrals. The
proposed algorithm is verified in a number of scenarios relevant to geophysical
exploration, but the general formulation presented is also applicable to other
problems governed by Poisson equation such as Newtonian gravity, heat flow, and
potential flow in fluid mechanics, involving cylindrically stratified
environments.
