3D inversion of gravity data of Safo mining site using linear programming and simplex algorithm

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Soltanabadi Rezvan; EBRAHIMZADEH ARDESTANI VAHID

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Journal: JOURNAL OF RESEARCH ON APPLIED GEOPHYSICS Year:2018 | Volume:4 | Issue:1 Page(s): 137-155

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Title

3D inversion of gravity data of Safo mining site using linear programming and simplex algorithm

Author(s)

Soltanabadi Rezvan | EBRAHIMZADEH ARDESTANI VAHID | Issue Writer Certificate

Keywords

Gravimetry

3D Inversion

Linear Programming

Euler Method

Constrained Optimization

Structural Inversion

Simplex Algorithm

Safo Mine

Abstract

Summary: The aim of this research is to develop methods to derive sharp images of subsurface, which show the geometry of the structures in the region of interest. Structural Inversion of gravity data-deriving robust images of the subsurface by delineating litho-type boundaries using density anomalies-is an important goal in a range of exploration settings (e. g., ore bodies, salt flanks). In this paper, an L1-norm based inversion approach is investigated. The density distribution of the subsurface is modeled on a uniform grid of cells. The model parameters are the density of each cell that is inverted by minimizing the L1-norm objective function using Linear Programming (LP) while satisfying a priori density constraints. LP method for Structural Inversion has two advantages: 1. It offers a natural way to incorporate a priori information regarding the model parameters. 2. It gives a subsurface image with sharp boundaries (structure). The inversion quality depends on a good priori estimation of the minimum depth of the anomalous body. Introduction LP is used as a method for performing Constrained Optimization. The constraints consist of linear inequalities in the variables, and the objective function is also a linear function of variables. LP can also be used to perform an implicit Structural Inversion. As we know, a set of inequalities has no solution, one solution or more than one solution. However, there are usually many combinations of the variables that satisfy all the constraints. The set of all these combination is called feasible set. A LP problem can be solved using simplex method. Methodology and Approaches To apply Linear Programming to exploration geophysics, an objective function should be defined, and some constraints should be set. In the case of gravity anomalies, the model vector m contains the density contrasts of the prisms with respect to some background values. First, subsurface should be parameterized with prisms for which density contrasts are sought. The unknowns are the density contrast of each homogenous prism relative to the background. Next, we use a L1-norm objective function to be minimized. The first constraint, which should be assumed, is an upper limit for density contrast as a priori. Then, we introduce some new variables and add additional constraints. The LP problem can be solved using simplex method. This method is based on that if an optimal solution exists, then an optimal extreme point also exists. Extreme points are then characterized in terms of basic feasible solutions. The LP method is first applied on free-noise synthetic gravity data, then, we test the method further by perturbing the synthetic data with low levels of noise and performing the inversion of all perturbed data sets. At the end, we perform the algorithm on real gravity data acquired from Safo Mine. All the results have been given and discussed in this paper. Results and Conclusions The inversion method, proposed in this paper, gives us a well shaped model even in the presence of substantial noise. This method can be used in exploration situation with sharp boundaries (density contrast) such as salt flank, ore bodies, dikes, etc. The need to know the top of the anomalous body, at first, appears to be a serious shortcoming of our approach, but here we use another method such as Euler Method to extract the minimum depth of the anomalous body. However, our focus is on delineating the structure laterally (sides of dikes, flanks… ). Information regarding the tops of such structures may often be available from other geophysical techniques or from geologic considerations.

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APA: Copy

Soltanabadi, Rezvan, & EBRAHIMZADEH ARDESTANI, VAHID. (2018). 3D inversion of gravity data of Safo mining site using linear programming and simplex algorithm. JOURNAL OF RESEARCH ON APPLIED GEOPHYSICS, 4(1 ), 137-155. SID. https://sid.ir/paper/268554/en

Vancouver: Copy

Soltanabadi Rezvan, EBRAHIMZADEH ARDESTANI VAHID. 3D inversion of gravity data of Safo mining site using linear programming and simplex algorithm. JOURNAL OF RESEARCH ON APPLIED GEOPHYSICS[Internet]. 2018;4(1 ):137-155. Available from: https://sid.ir/paper/268554/en

IEEE: Copy

Rezvan Soltanabadi, and VAHID EBRAHIMZADEH ARDESTANI, “3D inversion of gravity data of Safo mining site using linear programming and simplex algorithm,” JOURNAL OF RESEARCH ON APPLIED GEOPHYSICS, vol. 4, no. 1 , pp. 137–155, 2018, [Online]. Available: https://sid.ir/paper/268554/en

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