This work presents an efficient method that allows to accurately calculate the time-harmonic vertical magnetic field generated at the center of a large current-carrying coil of wire positioned above a layered ground. The method consists of evaluating the integral representation for the vertical magnetic field by using a hybrid procedure. At first, the direct and ideal reflected fields are extracted from the total magnetic field and expressed in explicit form. Then, the non-analytic part of the integrand of the remaining contribution is replaced with a sum of partial fractions, obtained by using a rational function fitting algorithm. Finally, the resulting sum of integrals is analytically evaluated and turned into a sum of modified Bessel functions of the second kind. The obtained expression for the magnetic field is then used to evaluate the voltage induced in a small receiving loop co-axial with the transmitting loop.