Dispersion constraints and the Hilbert transform for electromagnetic system response validation

Abstract

As a check on calibration and drift in each discrete sub-system of a commercial frequency-domain airborne electromagnetic system, we aim to use causality constraints alone to predict in-phase from wide-band quadrature data. There are several possible applications of the prediction of in-phase response from quadrature data including: (1) quality control on base level drift, calibration and phase checks; (2) prediction and validation of noise levels in in-phase from quadrature measurements and vice versa and in future; and (3) interpolation and extrapolation of sparsely sampled data enforcing causality and better frequency-domain – time-domain transformations. In practice, using tests on both synthetic and measured Resolve helicopter-borne electromagnetic frequency domain data, in-phase data points could be predicted using a scaled Hilbert transform with a standard deviation between 40 and 80 ppm. However, relative differences between base levels between flight could be resolved to better than 1 ppm, which allows an independent quality control check on the accuracy of drift corrections.