Inverse analysis of geomagnetic investigations for local anomaly detection using genetic algorithm

One of the most important goals in geomagnetic investigations is detecting local anomaly locations. Regional anomaly can be simulating as a trend surface, and local anomalies will be detected by comparison of measured data and simulated trend surface. The problem is trying to find best coefficients of trend surface model using inverse methods based on modern optimization techniques, which are faster and more accurate than common methods. The main idea of inverse method based on modern optimization approach is to search for a model, which gives its predicted values that are as close as possible to the observed ones. Extensive advances in computational techniques allowed researchers to develop new search strategies for use in optimization problems.
Genetic Algorithm is one of the evolutionary optimization algorithms, based on the population of chromosomes, which is widely used in engineering optimization problems. Evolutionary algorithms are developed based on swarm intelligence and social behavior of individuals in nature. Besides, the populations in evolutionary algorithms called agents affected by neighbor agents and the best agent. At the end, optimum solution will be specified with respect to optimize objective function.
In this paper, genetic algorithm is used for minimizing the differences between real and simulated data. In order to study geomagnetic anomaly, first, forward model should be developed and then, using inverse method based on GA, regional anomaly trend surface will be simulated. The objective function is define as  , where,  and  are positions of the field study locations that are measured by GPS and  is the magnetic value of the positions. Also, A, B, C, D, E and F are unknown coefficients that will be determined using inverse method. According to the objective function, a two-dimensional equation is proposed for simulating regional anomaly trend surface. Two-dimensional equations are better than one-dimensional and three-dimensional or higher dimensional equations. One-dimensional equations do not guarantee to cover all aspects of data.  Besides, three or higher dimensional equations are also not recommended for modeling data; because, over fitting to the data may be occurred. Therefore, the two-dimensional equation is the best model for simulating the regional anomaly trend surface. It is important to note that the optimization technique will usually perform well in nonlinear forward models. The unknown coefficients of trend surface on regional magnetic anomaly in Doroh area in southeast of Iran were optimized using inverse analysis, and finally the local anomalies were detected. In order to find locations of local geomagnetic anomalies, total anomaly trend  is subtracted from regional anomaly trend and then, the potential locations for drilling investigation are recognized.
Our experimental results demonstrate very promising results of the optimization technique for solving inverse problems using GA for detecting local geomagnetic anomaly trend surface, which is validating through drilling investigations. Besides, upward and reduce to pole filters and combination of them, which are common filters for detecting local geomagnetic anomaly locations, are used for conformation our results.