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

Abstract

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.Electronic supplementary materialThe online version of this article (doi:10.1186/s40064-016-3030-7) contains supplementary material, which is available to authorized users.

Inversion of Source Parameters from Magnetic Anomalies for Mineral/Ore Deposits Exploration Using Global Optimization Technique and Analysis of Uncertainty

“…The main objective of geophysical inversion is to apply the same BoltzmannÕs law and to minimize an objective function or the error function in geophysical data modeling. Various optimization methods such as simulated annealing (SA), genetic algorithms (GA), artificial neural networks (ANN), particle swarm optimization (PSO) and differential evolution (DE) (El-Kaliouby and AlGarni 2009;Monteiro Santos 2010;Sharma and Biswas 2011;Sen and Stoffa 2013;Sharma and Biswas 2013;Biswas 2015;Ekinci 2016;Ekinci et al 2016;Balkaya et al 2017) were regularly used to optimize geophysical data and have been applied to derive diverse geophysical information (Rothman 1985(Rothman , 1986Dosso and Oldenburg 1991;Zhao et al 1996;Martínez et al 2010;Li et al 2011;Sharma 2012;Sen and Stoffa 2013). Sen and Stoffa (2013) discussed in detail the SA.…”

“…Many linear and linearized inversions such as least squares, linearized least squares, normalized local wave number method, analytic signal derivatives, second-horizontal derivatives, Euler deconvolution method, simplex algorithm, fair function minimization have also been developed (McGrath and Hood 1973;Silva 1989;Salem and Ravat 2003;Salem et al 2004;Salem 2005;Salem and Smith 2005;Tlas and Asfahani 2011a, b;Abdelrahman and Essa 2015;Tlas and Asfahani 2015). Global optimization methods such as simulated annealing, very fast simulated annealing, regularized inversion, particle swarm optimization and higher-order horizontal derivative methods (Gokturkler and Balkaya 2012;Sharma and Biswas 2013;Biswas and Sharma 2014a, b;Mehanee 2014a, b;Biswas 2015;Singh and Biswas 2015;Biswas 2016;Biswas and Acharya 2016;Ekinci 2016) have been effectively applied to solve nonlinear parametric inversion problems. A combined work of various other modeling methods can be found in Abo-Ezz and Essa (2016), Abdelrahman and Essa (2005) and Abdelrahman et al (2003Abdelrahman et al ( , 2009Abdelrahman et al ( , 2012.…”

High-Precision Inversion of Buried Depth Inurban Underground Iron Pipelines Based on Am-Pso Algorithmfor Magnetic Anomaly

“…Merchaoui et al [23] introduced the particle adaptive mutation mechanism to effectively avoid the premature convergence problem of particle swarm optimization algorithm and improved the accuracy of algorithm search. The basic particle swarm particle position calculation formula and velocity update formula are as shown in Equations (10) and (11) [21]:…”

“…The optimization results showed that the method could uniquely determine all model parameters in the case of determined magnetic anomalies, and the calculation time of the whole process is very short. Ekinci [10] used the numerical second-order, third-order and fourth-order horizontal derivatives calculated from the observed magnetic anomalies to estimate the depth of an isolated dike-like magnet source body. This method does not require prior information and is in line with the real results.…”

Parameter Estimations from Gravity and Magnetic Anomalies Due to Deep-Seated Faults: Differential Evolution versus Particle Swarm Optimization

“…Briefly, the algorithm is inspired by the behaviors of bird flocks and fish schools (Pallero et al, 2015). In this naturally inspired derivative-free metaheuristic technique, the best solution involving the model parameters is sought in the model space using a particle population having random positions and velocities (Srivastava and Agarwal, 2010;Göktürkler and Balkaya, 2012;Ekinci, 2016;Singh and Biswas, 2016;Essa and Munschy, 2019). In the algorithm, the position vector of a particle describes a pilot solution (Das et al, 2008).…”