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The interpretation of the generalised derivative operator
Author(s) -
Cooper G.R.J.
Publication year - 2018
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/1365-2478.12539
Subject(s) - derivative (finance) , operator (biology) , maxima and minima , second derivative , magnetization , gemology , potential field , geology , amplitude , fréchet derivative , directional derivative , interpretation (philosophy) , lie derivative , field (mathematics) , mathematical analysis , geometry , optics , mathematics , physics , geophysics , computer science , engineering geology , chemistry , magnetic field , seismology , quantum mechanics , pure mathematics , lie group , repressor , banach space , financial economics , tectonics , biochemistry , transcription factor , programming language , volcanism , economics , gene , adjoint representation of a lie algebra , lie conformal algebra
The Generalised Derivative Operator is an image‐processing tool for the enhancement of potential field data. It produces an amplitude‐balanced image of the derivative of a potential field in any direction in three‐dimensional space. This paper shows how, by using the correct inclination angle ϕ , the Generalised Derivative Operator can be used to produce images where its maxima/minima lie directly over dipping contacts and thin dykes with arbitrary magnetisation vectors. The dip of contacts and dykes can be found by varying ϕ until a symmetrical result is obtained (in the absence of unknown remanent magnetisation). Furthermore, the width of the peak of the Generalised Derivative Operator can then be used to determine the depth of the contact or dyke.