YVESET and CHANNEL: A Subroutine Package for Stable Transformation of Sparse Frequency Domain Electromagnetic Data to the Time Domain

Abstract

It is often necessary to transform frequency domain (FD) response data for electromagnetic (EM) prospecting instruments near a system of conductors into the time domain (TD), in order to estimate the response of a TD EM system to the same system of conductors. Straightforward approaches utilizing interpolation and Fourier transform techniques are expensive and sensitive to data error. Lamontagne (1975) introduced a method in which the FD data is fitted by stabilized least squares techniques with a finite set of "basis functions" for which the Fourier transforms (FT's) are known. The TD response of the system can then be synthesized by performing a sum over the FT's of the basis functions using the same weights determined for the FD fit. Lamontagne's method has been implemented in a subroutine package including two alternative subroutines called YVESFT and CHANNEL which calculate the TD response of a system to a variety of primary field waveforms. CHANNEL calculates point-sampled impulse and step responses, and windowed UTEM, INPUT, PEM and SIROTEM responses in negligible computer time using analytical rules, and can also calculate the system's response to an arbitrary periodic waveform using a more time-consuming numerical approach. YVESFT is a smaller, somewhat simpler program which can calculate point-sampled impulse and step responses, and windowed step and UTEM responses using analytical formulas. Both packages are written in VAX-11 FORTRAN, and are fully documented both internally and externally. The routines have been extensively tested against numerical and analogue models and found to be fast, accurate and stable.