2D reconstruction of gravity anomalies using the level set method

Document Type : Research Article

Authors

1 M.Sc. Graduated, Department of Earth Physics, Institute of Geophysics, University of Tehran, Tehran, Iran

2 Assistant Professor, Department of Earth Physics, Institute of Geophysics, University of Tehran, Tehran, Iran

Abstract

In order to properly understand the subsurface structures, the issue of inversion of geophysical data has received much attention from researchers. Since accurate reconstruction of the shape and boundaries of the mass using gravimetric data is very important in some issues, it is important to use an effective and efficient method that has a high ability to draw and reconstruct the boundaries of a mass. In recent years, the level set method introduced by Asher and Stein has been widely used to solve this problem. From the expansion of the level set function in some bases of the problem, the effective number of parameters is greatly reduced and an optimization problem is created which its behavior is better than the least squares problem. As a result, the level set parameterization method will be presented for the reconstruction of inversion models. A common advantage of the parametric level set method is the careful examination of the boundary for optimum sensitivities, which significantly reduces the dimensional problem, and many of the difficulties of traditional level set methods, such as regularization, reconstruction, and basis function. Level set parameterization is performed by radial basis functions (RBF); which causes an optimal problem with an average number of parameters and high flexibility; and the computational and optimization process for Newton's method is more accurate and smooth. The model is described by the zero contour of a level-set function, which in turn is represented by a relatively small number of radial basis functions. This formulation includes some additional parameters such as the width of the radial basis functions and the smoothness of the Heaviside function. The latter is of particular importance as it controls the sensitivity to changes in the model. In this algorithm adaptively chooses the required smoothness parameter and tests the method on a suite of idealized Earth models.
 In this evolutionary approach, the reduction gradient method usually requires many iterations for convergence, and the functions are weakened for low-sensitivity problems. Although the use of Quasi- Newton methods to improve the level set function increases the degree of convergence, they are computationally challenging, and for large problems and relatively finer grids, a system of equations must be solved in each iteration. Moreover, based on the fact that the number of underlying parameters in a parametric approach is usually much less than the number of pixels resulting from the discretization of the level set function, we make a use of a Newton-type method to solve the underlying optimization problem.
In this research, the algorithm is used to investigate its strengths and weaknesses for applying geophysical gravity data, coding and programming, and it is tested using several two-dimensional synthetic models. Finally, the method is tested on gravity data from the Mobrun ore body, north east of Noranda, Quebec, Canada.
The results of this study show that the application of the optimization algorithm of the level set function will lead to a relatively more accurate and realistic detection of mass boundaries. It shows that the tested mass has spread from a depth of 10 meters to a depth of 160 meters.

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References

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Journal of the Earth and Space Physics
Volume 48, Issue 1
online publication date: 9 May 2022
May 2022
Pages 49-62

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