b'A Sliding Doors momentFeatureGunns 1976 paper is widely acknowledged as a breakthrough in exploration geophysics (personal communication Alan Reid), as Peter sorted out the notation and the application of the convolution theorem to all potential \x1deld signals. This importantly included the vertical derivative.When Peter Gunn joined AGSO (now Geoscience Australia) around 1993, he immediately set about the process of creating a practice manual for airborne magnetic and radiometric surveying. This e\x1eort resulted in publication of the now famous AGSO Journal of Australian Geology & Geophysics, 11 (2). This journal has been a best seller for many years. The purpose of the publication was to present the methodologies and ideas of various specialists who were active in the disciplines that contributed to the acquisition, processing, presentation, and evaluation of airborne magnetic and radiometric data.The joint paper Enhancement and Presentation of Airborne geophysical data, written by Peter Milligan and Peter Gunn in this volume, is a good summary of this pivotal moment. It lays out the derivative methods that became dominant. Figure 1.Explanatory \x1dgure from the MAGMAGE project where the complex At this same time, Peter Gunn approached me to championtrace analysis methods from seismic were looked at for magnetics.the MAGMAGE project. He was concerned that innovative thinking would stagnate once the \x1cat earth version of practiceInstead of using the more proper Fast Fourier Transform, for was sorted. This is the classic trap of engineering science. Themany years a Hartley Transform was used in many codes to save \x1drst approximation that seems to keep folks happy is what ismemory. With the bene\x1dt of what we now know, this was also settled upon, and an entrenched set of followers develops. Theless stable than the FFT methods.15 MAGMAGE projects mentioned in the proposal led to many innovations, but not all were \x1dnished or followed up in time. Di\x1eerentiation by integrationNow we jump to 2021 and a phone call from Richard Smith, Geophysics Professor at Laurentian University, Sudbury. He started by saying he could not \x1dnd any interested commercial partners in Canada, and would I have a look at the whole subject of di\x1eerentiation? Je\x1e Thurston, who had worked with Richard in the Fugro R&D team in Ottawa during late 1990s, had returned to looking at the fundamentals. The practical technique comes from a 1981 paper authored by Bengt Fornberg titled Numerical Di\x1eerentiation of Analytic Functions and is based on Cauchys Integral Formula.While more involved than Hammings FIR methods, this approach, using complex numbers, is inherently more stable and avoids the horrible band-pass side-e\x1eects of FIR \x1dlters. Turns out Hamming himself had recognised this problem in his textbook but did not take it further or suggest any alternatives.Now for the tie back to the complex trace analysis, where the TMI and its Hilbert transform is used to calculate well-conditioned, high-order derivatives of gravity and magnetic data. Je\x1e left Fugro in late 2000 and subsequently became part The front cover of the AGSO Journal of Australian Geology & Geophysics, 11 (2). of the R&D team at Intrepid, which started an investigation and Looking again, from the perspective of 2023, at least one or twoseries of experiments and case studies.projects did not go anywhere, but still deserve a run. Project 1, Instantaneous plot of anomaly maxima and minima developedThe importance of di\x1eerentiationinto a project where the complex trace analysis methods fromWhy is di\x1eerentiation so important in exploration geophysics?seismic were looked at for magnetics (Figure 1).The magnetic trace from airborne magnetic surveys was treatedBasically, all interpretation methods for edge detection, depth as the real part of a complex magnetic trace and the imaginarydetermination, inversion and source body property estimation part is minus the Hilbert transform (quadrature) of the real part.depend upon the quality of the estimated gradients. It would It is this project that \x1coundered without the help of Cauchy. Ifseem even magnetic compensation algorithms look to be caught only that sliding door had opened in 1995. up in all this required revision. The limitations of existing popular tools that use FIR methods has led to a recognition that only Even into the 1990s, practical applications of digital \x1dlters werelimited gradient products can be produced. It has also forced more hampered by lack of CPU power, restricted CORE memories, disce\x1eorts in our industry to measure gradients during acquisition to space (a 5-megabyte disc was considered the ultimate), etc. avoid using poor estimates from digital di\x1eerentiation.JUNE 2023 PREVIEW 34'