An alternative approach in establishing relation between vertical and horizontal gradients of 2D potential field |
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| Authors: | Indrajit G Roy |
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| Institution: | Spaceage Geoconsulting, Conder, ACT, Australia |
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| Abstract: | The relation in which the vertical and horizontal gradients of potential field data measured along a profile across a two‐dimensional source are a Hilbert transform pair is re‐established using complex domain mathematics. In addition, a relation between the measured field and its vertical gradient in terms of a closed‐form formula is also established. The formula is based on hypersingular or Hadamard's finite‐part integral. To estimate the vertical gradient directly from the field data, Linz's algorithm of computing Hadamard's finite‐part integral is implemented. Numerical experiments are conducted on synthetically generated total magnetic intensity data with a mild level of noise contamination. A model of a magnetically polarised vertical thin sheet buried at a finite depth within a non‐magnetic half‐space was considered in generating the synthetic response. The results from numerical experiments on the mildly noise‐contaminated synthetic response are compared with those from using classical Fourier and robust regularised Hilbert transform‐based techniques. |
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| Keywords: | Horizontal gradient Vertical gradient Hilbert transform Hypersingular integral Potential field |
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