Open AccessComplex conjugate for second-order derivative of 2D analytic signal of magnetic field anomaly
Author(s) -
Abdul Manan
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1341/8/082043
Subject(s) - conjugate , complex conjugate , polarity (international relations) , analytic signal , mathematics , taylor series , function (biology) , anomaly (physics) , field (mathematics) , signal (programming language) , order (exchange) , range (aeronautics) , analytic function , magnetic field , mathematical analysis , algorithm , signal processing , computer science , pure mathematics , physics , chemistry , materials science , condensed matter physics , quantum mechanics , cell , composite material , biology , telecommunications , biochemistry , evolutionary biology , programming language , radar , finance , economics
The complex conjugate approach for the second-order derivative of a function was obtained by truncating the Taylor series whose function has been expanded around x in the h-term in the complex conjugate argument. This approach was composed to resemble the Central-Difference form of the ordinary Finite-Difference Method. After being tested by comparing it with manual solution, this method was very accurate with relative errors obtained in the range of 0.088271927039904⩽RE⩽6.679993448987438x10 −07 . The combination of step h and interval δx in the formula of this approach that was appropriate for obtaining optimal computational results were h=1.0x10 −13 and δx = 1.0x10 −10 . Finding the appropriate combination of h and δx could be done easily and quickly, requiring no special treatment. The computational results of the derivatives were then used to compute second-order 2D Analytic Signals of magnetic field anomalies. Illustratively, Analytic Signal could transform bipolarity of magnetic data into positive polarity so that it would be very useful in processing and interpreting actual data.