A new method for computing electromagnetic induction sounding response curves

A mathematical method is proposed that allows to evaluate the integral expression for the vertical magnetic field (VMF) produced on the surface of a layered earth structure by an electromagnetic (EM) induction sounding current loop. The field integral is calculated analytically via the application of the residue theorem, once the fast-decaying exponential part of the integrand is approximated with a rational function. Differently from the commonly used merely numerical approaches like the digital filter technique, no sample-domain optimization process is required. The proposed method is used to compute the amplitude of the VMF over a two-layer earth model, and the obtained results agree well with those provided by digital filter algorithms.