There is obviously a depth to this problem which I am missing - if the answer was easy Rick Hansen would not have had to prove anything.
However, as a starter, I recall too many decades ago to quote, a basic property of signal processing, that a time series sampled in amplitude at delta_t interval, is identical to a time series sampled in amplitude at 2*delta_t and sampled in derivative at the same 2*delta_t. It looks intuitively obvious in terms of the number of pieces of information. I suspect it is discussed in signal processing texts (all mine are now several decades old, and somewhat dusty). I would be delighted to hear a more erudite exposition; I would hesitate to set a MSc/PhD student onto the problem as a project, without first being sure that it is not covered as a principle or theorem of signal processing. Cheers, Michael Asten On Tue, 19 Feb 2019 at 19:45, Alan Reid via SEGMIN <[email protected]> wrote: > Dear GrvMag and SEGMin listers > > I’m addressing both lists because the matter concerns both… > > Years ago, the late great Richard Hansen told me he’d proved that, for a > conventional airborne magnetic total field survey, cross-line gradient > measurements gave you the equivalent of halving the line spacing. The proof > was for noise-free data, but hey, it's an indication of a usefulness that’s > widely recognised and exploited. > > I subsequently asked Richard for his proof and he’d lost it, but he > re-proved it another way. Regrettably, I’ve now also lost that proof. And > Richard is no longer available to ask…… Hence the enquiry and the > challenge. > > 1. Does anyone know of a published proof? If so, please may we have the > reference (and even maybe a link to a pdf? > > 2. If not, does anyone have a proof they’d be prepared to offer for > publication. I’d happily welcome it to “Geophysical Prospecting”, and I’m > sure “Geophysics” and some other journals would be equally welcoming. > > 3. If neither of the above, the challenge is to produce a proof. It’d make > a decent basis for an MSc, a pretty chapter in a PhD, and/or a worthwhile > paper. From a personal perspective, it’d also “complete” the survey design > criteria I published in 1980. > > Regards > > Alan B Reid PhD > Reid Geophysics Ltd > 7 Keymer House > Michel Grove > Eastbourne BN21 1JZ > UK > > Phone: +44 (0) 1323 735520 > Mobile: +44 (0) 781 692 4728 > Skype Name: alanbarryreid > mailto: [email protected] > web: http://www.reid-geophys.co.uk > > > ----------------------- > SEGMIN community mailing list service ([email protected]). > Change your personal options here: > https://lists.geosoft.com/mailman/options/segmin/michael.asten%40monash.edu > Colleagues can join here: > https://lists.geosoft.com/mailman/listinfo/segmin > Archives: https://lists.geosoft.com/mailman/private/segmin/ > NOTE that <Reply> will reply to all members of the list. >
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