Second vertical derivative of potential fields using an adaptation of spline theory

Abstract

The second vertical derivative of magnetic fields is commonly used for resolution of anomalies in gravity and magnetic fields. It is also commonly used as an aid to geologic mapping i.e. for the delineation of geological discontinuities in the subsurface. Frequency domain methods for calculating second vertical derivatives often result in highly distorted outputs that cannot be reliably interpreted. In this paper we develop a space domain method for calculating the second vertical derivative of gravity and magnetic fields. This involves an adaptation of the theory of cubic splines. Commonly used in data interpolation. Results obtained from the application of the method to  observed gravity data from Kwello area, Kaduna State Nigeria shows that the study area is as presented, which shows that various lithologic boundaries are deduced from the zero contours of the second vertical derivative field

Keywords: Potential field, Second vertical derivative, Cubic spline, Kwello Gravity field.