One-Dimensional Modeling of Helicopter-Borne Electromagnetic Data Using Marquardt-Levenberg Including Backtracking-Armijo Line Search Strategy

Document Type: Research Paper

Authors

1 School of Mining, Petroleum and Geophysics Engineering, Shahrood University.

2 School of Mining, Petroleum and Geophysics Engineering, Shahrood University

3 Shahrood University

4 Institut für Geophysik und Geoinformatik TU Bergakademie Freiberg Gustav-Zeuner-Str. 12 09599 Freiberg, Germany

Abstract

In the last decades, helicopter-borne electromagnetic (HEM) method became a focus of interest in the fields of mineral exploration, geological mapping, groundwater resource investigation and environmental monitoring. As a standard approach, researchers use 1-D inversion of the acquired HEM data to recover the conductivity/resistivity-depth models.
Since the relation between HEM data and model parameters is strongly nonlinear, in the case of dealing with simple 1-D models which the number of model parameters is less than the number of measured data, i.e. overdetermined system, implementation of regularized nonlinear least square methods is a common approach to recover the model parameters. Among the least square methods, Marquardt-Levenberg acts as an integrated optimization algorithm which comprises both the gradient-descent and Gauss-Newton strategies. This algorithm resolves the deficiencies of the slow convergence of gradient-descent and the singularity of the sparse matrix in the Gauss-Newton. Furthermore, involving the line search strategy improves the objective function to ensure that the algorithm converges to the global optimum point. In this research work, we implemented the Marquardt-Levenberg including the backtracking-Armijo line search for HEM data inverse modeling. Moreover, we used a linear filter of the Fast Hankel Transform (FHT) to figure out the forward operator for data simulation.
Developing our algorithm via programming using MATLAB, we successfully obtained a resistivity model of layered earth. We employed the algorithm to recover a resistivity model from the HEM data acquired above the Alut region located at the northwest of Iran where is characterized by shear zone structure consisting of chlorite schist, Phyllite/Phyllonite, metamorphosed limestone and dolomite, mylonite and ultra-mylonite rock units. As a result, in accordance with the geological map the study area, we have successfully derived a resistivity-depth section of the subsurface along the HEM flight line and detected plausible shear zone and mylonitic granite as the favorite targets for the orogenic gold mineralization.

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