The determination of electromagnetic fields over layered earth structures involves evaluation of the Hankel transform integrals. The classical method of numerical integration is very tedious, as it involves evaluating infinite integrals containing product functions with Bessel functions that are oscillatory and thus time consuming even on high-speed digital computers. In contrast, the digital linear filter (convolution) method, which avoids Bessel function evaluations, is extremely rapid with regard to the ease with which it can be applied and to speed of calculations, and it provides accurate (five or more decimal accuracy) results. The speed of calculations can be further significantly increased while maintaining the same accuracy using a variable convolution approach. In some cases, the digital linear filter method has proved to be more rapid in calculations than the fast Fourier transform method.