Application of 2-D Hilbert transform in geophysical imaging with potential field data

Abstract

The relationship between two-dimensional (2-D) Hilbert transforms and three-dimensional (3-D) potential field data (gravity and magnetic) is reviewed and applied to quantitative interpretation of magnetic and gravity anomalies as well as their derivatives. The vertical and horizontal derivatives of potential field anomalies due to multiprism models were used to test the 2-D Hilbert transform algorithms and their application. The gravity and magnetic contour maps of the Sudbury area, Canada, were digitized and Hilbert-transformed to be correlated with satellite digital images and with the previously known geology. The results indicate that the 2-D Hilbert transform technique can, in a robust fashion, be utilized for the extrapolation of geological boundaries through overburdened areas and subsequently provide a mathematical tool for a step-by-step integration of potential field data and geological remote sensing.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>