MATLAB-based algorithm to estimate depths of isolated thin dike-like sources using higher-order horizontal derivatives of magnetic anomalies

This paper presents an easy-to-use open source computer algorithm (code) for estimating the depths of isolated single thin dike-like source bodies by using numerical second-, third-, and fourth-order horizontal derivatives computed from observed magnetic anomalies. The approach does not require a priori information and uses some filters of successive graticule spacings. The computed higher-order horizontal derivative datasets are used to solve nonlinear equations for depth determination. The solutions are independent from the magnetization and ambient field directions. The practical usability of the developed code, designed in MATLAB R2012b (MathWorks Inc.), was successfully examined using some synthetic simulations with and without noise. The algorithm was then used to estimate the depths of some ore bodies buried in different regions (USA, Sweden, and Canada). Real data tests clearly indicated that the obtained depths are in good agreement with those of previous studies and drilling information. Additionally, a state-of-the-art inversion scheme based on particle swarm optimization produced comparable results to those of the higher-order horizontal derivative analyses in both synthetic and real anomaly cases. Accordingly, the proposed code is verified to be useful in interpreting isolated single thin dike-like magnetized bodies and may be an alternative processing technique. The open source code can be easily modified and adapted to suit the benefits of other researchers.