Dispersion constraints and the Hilbert transform for electromagnetic system response validation
James Macnae 1 2 Ryan Springall 11 Applied Sciences, RMIT University, GPO Box 2476V, Melbourne, Vic. 3001, Australia.
2 Corresponding author. Email: james.macnae@rmit.edu.au
Exploration Geophysics 42(1) 1-6 https://doi.org/10.1071/EG10017
Submitted: 9 July 2010 Accepted: 19 December 2010 Published: 25 February 2011
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.
Key words: calibration, dispersion, drift, electromagnetic, HEM, Hilbert transform, Kramers–Kronig.
References
Boerner, D. E., and West, G. F., 1984, Efficient calculation of the electromagnetic fields of an extended source: Geophysics, 49, 2057–2060| Efficient calculation of the electromagnetic fields of an extended source:Crossref | GoogleScholarGoogle Scholar |
Brodie, R., and Sambridge, M., 2006, A holistic approach to inversion of frequency-domain airborne EM data: Geophysics, 71, G301–G312
| A holistic approach to inversion of frequency-domain airborne EM data:Crossref | GoogleScholarGoogle Scholar |
Davis, A., and Macnae, J., 2008, Measuring AEM waveforms with a ground loop: Geophysics, 73, F213–F222
| Measuring AEM waveforms with a ground loop:Crossref | GoogleScholarGoogle Scholar |
Deszcz-Pan, M., Fitterman, D. V., and Labson, V. F., 1998, Reduction of inversion errors in helicopter EM data using auxiliary information: Exploration Geophysics, 29, 142–146
| Reduction of inversion errors in helicopter EM data using auxiliary information:Crossref | GoogleScholarGoogle Scholar |
Fitterman, D. V., 1998, Sources of calibration errors in helicopter EM data: Exploration Geophysics, 29, 65–70
| Sources of calibration errors in helicopter EM data:Crossref | GoogleScholarGoogle Scholar |
Fitterman, D. V., and Yin, C., 2004, Effect of bird maneuver on frequency-domain helicopter EM response: Geophysics, 69, 1203–1215
| Effect of bird maneuver on frequency-domain helicopter EM response:Crossref | GoogleScholarGoogle Scholar |
King, F. W., 2009, Hilbert Transforms: Cambridge University Press.
Kramers, H. A., 1927, La diffusion de la lumiere par les atomes, Atti Cong. Intern. Fisica (Transactions of Volta Centenary Congress) Como, 2, 545–557.
Kronig, R. L., 1926, On the theory of the dispersion of X-rays: Journal of the Optical Society of America, 12, 547–557
| On the theory of the dispersion of X-rays:Crossref | GoogleScholarGoogle Scholar |
Ley-Cooper, Y., and Macnae, J., 2007, Amplitude and phase correction of helicopter EM data: Geophysics, 72, F119–F126
| Amplitude and phase correction of helicopter EM data:Crossref | GoogleScholarGoogle Scholar |
Macnae, J. C., 1984, Survey design for multicomponent electromagnetic systems: Geophysics, 49, 265–273
| Survey design for multicomponent electromagnetic systems:Crossref | GoogleScholarGoogle Scholar |
Valleau, N. C., 2000, HEM data processing: a practical overview: Exploration Geophysics, 31, 584–594
| HEM data processing: a practical overview:Crossref | GoogleScholarGoogle Scholar |
West, G. F., and Macnae, J. C., 1991, Physics of the electromagnetic induction exploration method, in M. N. Nabighian, ed., Electromagnetic methods in Applied Geophysics, Vol. 2 Part A: SEG.
Yin, C., and Hodges, G., 2009, Wire-loop surface conductor for airborne EM system testing: Geophysics, 74, F1–F8
| Wire-loop surface conductor for airborne EM system testing:Crossref | GoogleScholarGoogle Scholar |