An alternative approach in establishing relation between vertical and horizontal gradients of 2D potential field

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.