Analysis and interpretation of Ibuji spring magnetic anomaly using the Mellin transform

Abstract

The Mellin transform is a mathematical tool which has been applied in many areas of Mathematics, Physics and Engineering. Its application in Geophysics is in the computation of solution of potential problems for the determination of the mass as well as the depth to the basement of some solid mineral deposits. In this study, the Mellin transform is used to determine the depth to the top (h) and the depth to the bottom (H) of the basement of a profile of an anomalous magnetic body. Ibuji, the study area is located in Ifedore Local Government area of Ondo state, Nigeria, underlain by Precambrian complex rocks and bounded by geographical co-ordinate of Easting 5°00t’00″ to 5°4t’30″ and Northing 7°24t’00″ to 7°27t’36″. The magnetic anomaly profile due to a two- dimensional body(vertical thin sheet)over magnetic spring of the study area was digitised and the values of magnetic amplitude (nT) with respect to its horizontal distance (say interval of 5 m) obtained from the digitized profile was then used in the computation of Mellin transform using Matlab programs. In order to determine the depths H and h, the amplitudes were considered at three arbitrary point (s = ¼, ½ and ¾) such that, (0 < s < 1), where s is a complex variable of real positive integer. The value obtained for H was 47.95 m, which compared favourably with the result obtained using other methods. Meanwhile, the value obtained for h has a convergence restriction, whereby, at lower values of s, there is divergence, while at higher values of s, (about 0.9), the result converges and h was obtained to be 32.56 m. The Ibuji magnetic anomaly was therefore analysed to have a depth to the bottom (H) of 47.95 m and depth to the top of 32.56 m using this mathematical tool.