The Simplex Algorithm for Best-Estimate of Magnetic Parameters Related to Simple Geometric-Shaped Structures
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The Simplex Algorithm for Best-Estimate of Magnetic Parameters Related to Simple Geometric-Shaped Structures M. Tlas · J. Asfahani
Received: 3 December 2013 / Accepted: 18 June 2014 © International Association for Mathematical Geosciences 2014
Abstract This paper introduces a practical approach to interpret magnetic anomalies related to simple geometric-shaped models such as thin dike and horizontal cylinder. This approach is mainly based on both the deconvolution technique and on the simplex algorithm for linear programming to best-estimate the model parameters, for example the depth to the top or to the center of a buried structure, the effective magnetization angle and the amplitude coefficient from magnetic anomaly profile. This approach has been tested first on synthetic data sets corrupted by different white Gaussian random noise levels to demonstrate the capability and the reliability of the method. The results acquired show that the estimated parameter values derived by this approach are close to the assumed true values of parameters. The validity of this approach is also demonstrated using real field magnetic anomalies from the United States and Brazil. A comparable and acceptable agreement is shown between the results derived by this approach and those from the real field data information. Keywords Magnetic anomaly · Thin dike-like structure · Horizontal cylinder-like structure · Deconvolution technique · Simplex algorithm 1 Introduction Geological structures in mineral and petroleum exploration can be approximated by simple geological structures such as a fault, a sphere, a cylinder, or a dike. According to this approximation, many methods have been introduced for interpreting magnetic field anomalies due to simple geometric models in an attempt to best-estimate the magnetic parameters values, for example, the depth to the buried body, the ampli-
M. Tlas (B) · J. Asfahani Atomic Energy Commission, P. O. Box 6091, Damascus, Syria e-mail: [email protected]
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Math Geosci
tude coefficient, and the effective magnetization angle. The interpretation methods include matching standardized curves (Gay 1963, 1965; McGrath and Hood 1970), characteristic points and distance approaches (Grant and West 1965; Abdelrahman 1994), monograms (Prakasa Rao et al. 1986), Hilbert transforms (Mohan et al. 1982), Fourier transform techniques (Bhattacharyya 1965), correlation factors between successive least-squares residual anomalies (Abdelrahman and Sharafeldin 1996), leastsquares minimization methods (Silva 1989; McGrath and Hood 1973), linearized leastsquares method (Salem et al. 2004), normalized local wave number method (Salem and Smith 2005), analytic signal derivatives (Salem 2005), and Euler deconvolution method (Salem and Ravat 2003). Werner deconvolution method (1953) is designed to analyze magnetic fields of dipping magnetized dikes by separating the anomaly due to a particular dike from the interference of neighboring dikes. The application of the Werner deconvolution method has been thoroughly discussed
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