Fair Function Minimization for Direct Interpretation of Residual Gravity Anomaly Profiles Due to Spheres and Cylinders

Abstract

A new interpretative approach is proposed to interpret residual gravity anomaly profiles in order to determine the depth, the amplitude coefficient and the geometric shape factor of simple spherical and cylindrical buried structures. This new approach is based on both Fair function minimization and on stochastic optimization modeling. The validity of this interpretative approach is demonstrated through studying and analyzing two synthetic gravity anomalies, using simulated data generated from a known model with different random noises components and a known statistical distribution. Being theoretically proven, this new approach has been applied on three real field gravity anomalies from Sweden, Senegal and the United States. The agreement between the results obtained by the proposed method and those obtained by other interpretation methods is good and comparable.

Interpretation of residual gravity anomaly caused by simple shaped bodies using very fast simulated annealing global optimization

“…Salem and Ravat (2003) presented a new automatic method for the interpretation of magnetic data, called AN-EUL which is a combination of the analytic signal and the Euler deconvolution method. Asfahani and Tlas (2012) developed the fair function minimization procedure. Fedi (2007) proposed a method called depth from extreme points (DEXP) to interpret any potential field.…”

Global nonlinear optimization for the interpretation of source parameters from total gradient of gravity and magnetic anomalies caused by thin dyke

“…This anomaly was interpreted by several authors as spherical structure [Tlas et al 2005, Asfahani and Tlas 2012, Mehanee 2014.…”

“…The depth obtained by Tlas et al 2005 (z = 9.17 km), Asfahani and Tlas, 2012 (z = 9.13 km), Mehanee, 2014 (z = 12.2 km) are presented as interpreted as sphere. Moreover, Mehanee, 2014 andBiswas, 2015 also interpreted the same anomaly as vertical cylinder as well where the depth is estimated at 4.59 and 4.6 km respectively.…”

“…2001], Fourier transform [Odegard and Berg 1965, Bhattacharyya 1965, Sharma and Geldart 1968, Euler deconvolution [Thompson 1982], Mellin transform [Mohan et al 1986], Hilbert transforms [Mohan et al 1982], least squares minimization approaches [Gupta 1983, Silva 1989, McGrath and Hood 1973, Lines and Treitel 1984, Abdelrahman 1990, Abdelrahman et al 1991, Abdelrahman and El-Araby 1993, Abdelrahman and Sharafeldin 1995a, Werner deconvolution [Hartmann et al 1971, Jain 1976, Kilty 1983; Walsh Transformation [Shaw and Agarwal 1990], Continual least-squares methods [Abdelrahman and Sharafeldin 1995b, Abdelrahman et al 2001a, b, Essa 2012, Euler deconvolution method [Salem and Ravat 2003], Fair function minimization procedure andAsfahani 2011a, Asfahani andTlas 2012], DEXP method [Fedi 2007], deconvolution technique [Tlas and Asfahani 2011b]; Regularised inversion [Mehanee 2014, Mehanee andEssa 2015]; Simplex algorithm [Tlas and Asfahani 2015], simulated annealing methods [Gokturkler and Balkaya 2012], Very fast simulated annealing Acharya 2016, Biswas andSharma 2016a, b;Biswas 2015, b, Sharma and Biswas 2013a, particle swarm optimization [Singh and Biswas 2016] and Differential Evolution ] have been used to solve similar kind of no...…”

Depth and shape solutions from residual gravity anomalies due to simple geometric structures using a statistical approach

“…The methods include, for example, the Walsh transform technique (Shaw and Agarwal, 1990), use of quadratic equations (Nandi et al, 1997), least-squares minimization approaches (Abdelrahman and Sharafeldin, 1995;Abdelrahman et al, 2001b;Essa, 2014), iterative methods (Abdelrahman and El-Araby, 1996), constrained and penalized nonlinear optimization techniques (Tlas et al, 2005), use of a common intersection point of depth curves (Essa, 2007), non-convex and nonlinear Fair function minimization, adaptive simulated annealing, and stochastic optimization algorithm (Asfahani and Tlas, 2012), deconvolution technique and use of simplex algorithm for linear optimization (Asfahani and Tlas, 2015). However, most of these methods, particularly those given by Abdelrahman and Sharafeldin (1995), Abdelrahman et al (2001b), Abdelrahman and El-Araby (1996) and Essa (2007Essa ( & 2014 are based on defining the anomaly value at the origin [g(max)] and it remains as a fixed parameter in the process, and hence they are highly subjective in determining the shape and depth of the buried structure from the residual gravity anomaly profile.…”