A Versatile Nonlinear Inversion to Interpret Gravity Anomaly Caused by a Simple Geometrical Structure

Abstract

A geophysical interpretative method is proposed to depth, amplitude coefficient and geometrical shape factor determination of a buried structure from an observed gravity anomaly related to a cylinder or a sphere-like structure.The method is based on nonlinearly constrained mathematical modelling and also on stochastic optimization approaches. The proposed interpretative method first has been tested on theoretical synthetic models with different random errors at a certain depth, where a very close agreement has been observed between assumed and evaluated parameters. Subsequent field data have been considered for which the interpreted results by other methods are available for comparison. The agreement between the obtained results by the proposed technique and by other geophysical methods is good. A statistical analysis has been also carried out to demonstrate the accuracy and the precision of the suggested interpretative method.

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.…”

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

“…The mathematical model (3) is thereafter solved by using the adaptive simulated annealing random search algorithm (Appendix) and for more details about this algorithm; it can be referred to (INGBER, 1989;INGBER and ROSEN, 1992;INGBER, 1996;TLAS et al, 2005). The algorithm simultaneously allows the values of the three geophysical parameters (z, h, k) to be obtained.…”

“…These techniques include, for example, the Walsh transform (SHAW and AGARWAL, 1990), least-squares methods (ABDELRAHMAN and SHARAFELDIN, 1995b;ABDELRAH-MAN et al, 2001a, b), constrained and penalized non linear optimization technique (TLAS et al, 2005). Generally, the determination of the depth, shape factor, and amplitude coefficient of the buried structure is performed by these methods from the residual gravity anomaly, where the accuracy of the results obtained by them depends on the accuracy in which the residual anomaly can be separated and isolated from the observed gravity anomaly.…”

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.…”