New fast least-squares algorithm for estimating the best-fitting parameters due to simple geometric-structures from gravity anomalies

Abstract

A new fast least-squares method is developed to estimate the shape factor (q-parameter) of a buried structure using normalized residual anomalies obtained from gravity data. The problem of shape factor estimation is transformed into a problem of finding a solution of a non-linear equation of the form f(q) = 0 by defining the anomaly value at the origin and at different points on the profile (N-value). Procedures are also formulated to estimate the depth (z-parameter) and the amplitude coefficient (A-parameter) of the buried structure. The method is simple and rapid for estimating parameters that produced gravity anomalies. This technique is used for a class of geometrically simple anomalous bodies, including the semi-infinite vertical cylinder, the infinitely long horizontal cylinder, and the sphere. The technique is tested and verified on theoretical models with and without random errors. It is also successfully applied to real data sets from Senegal and India, and the inverted-parameters are in good agreement with the known actual values.

Inversion of residual gravity anomalies using tuned PSO

“…Tuned PSO in MATLAB has been applied to field residual gravity anomalies. The anomaly profile length of 268 m has been taken from the Mobrun sulfide body, Noranda, Canada (Nettleton, 1976;Essa, 2012). It is seen from Fig.…”

“…(Roy et al, 2000) method (Essa, 2012) The case study area Louga, on the west coast of Senegal, is used for another interpretation of gravity data using tuned PSO. The Senegal basin is part of the north-western African coastal basin -a typical passive margin basin opening west to the Atlantic.…”

“…In this paper, tuned PSO in MATLAB environment has also been applied to another field case study. The gravity anomaly of Louga area, west coast of Senegal, western Africa (Essa, 2014) has been chosen for tuned PSO analysis as shown in Fig. 6.…”

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.…”

“…The method uses all possible combinations of two characteristic points and their corresponding distances for automated determination of the best shape and depth parameters of the buried structure from gravity data. The advantage of the present technique over nonlinear least-squares methods and depth-shape curves methods (Abdelrahman et al, 2001b(Abdelrahman et al, & 2006Abdelrahman and El-Araby, 1996;Essa, 2007Essa, & 2014, is that it has the capability of minimizing the effect of random errors in the data points to enhance the interpretation results because the method uses all successful combinations of data points several times. When our statistical approach is used, the use of anomaly value at the origin plays a minor role in determining the model parameters.…”