The Using of a Quadratic Method in the 2-D Inverse Modeling of Gravity Data to Achieve an Improved Model

Summary
The inversion of gravity data is one of the most important steps in the interpretation of these data. The purpose of this work is to estimate the distribution of the unknown subsurface model by the measured data on the ground. The main problem in the inversion of the data obtained from the operation of the gravity survey is the non-uniqueness response due to the inversion of geophysical data. Linear inversion of gravity data is an underdetermined and bad-condition. It is important to determine the optimal regularization parameter for the inversion of gravity data. One of these methods is the Generalized Cross-Validation (GCV). In this research, the quadratic method has been used as an optimization method.
 
Introduction
Inversion of gravity data is one of the most important steps in the interpretation of practical gravity data. The goal of inversion is to estimate the density distribution of an unknown subsurface model from a set of known gravity observations measured on the surface. Inversion of gravity data is an underdetermined and ill-posed problem. In addition, the non-uniqueness of the solution is the main issue of the inversion. One way to achieve a suitable model result in the inversion is to carry out the inversion with smoothness and smallness constraints. The solution can then be obtained by minimization of an objective function that consists of a misfit function and one of Tikhonov regularization functions. The regularization parameter makes a trade-off between misfit and regularization function. The determination of an optimal regularization parameter is highly important in gravity data inversion. There are different methods for automatic estimation of the regularization parameter in inversion. The GCV method is one of the most popular methods for choosing optimal regularization parameters in the inversion of gravity data.
 
Methodology and Approaches
In this paper, we use the quadratic method to minimize the Tikhonov objective function. Also, in order to obtain the regularization parameter of the generalized cross-validation (GCV) method. The GCV method has been adapted for the solution of inverse problems. The basic idea for GCV is that a good solution to the inverse problem is one that is not unduly sensitive to any particular datum. In this method, the optimal regularization parameter minimizes the GCV function. We have developed an algorithm for 2-D inversion of gravity data that uses the GCV method for choosing optimal regularization parameter, and then, the inverse problem is solved by the quadratic algorithm. To evaluate the reliability of the introduced method, the gravity data of a synthetic model contaminated by 5 percent random noise have been inverted using the developed method. Finally, The introduced algorithm has been used for 2-D inversion of gravity data from San Nicolas massive sulfide deposit. The results are consistent with geological information.
 
Results and Conclusions
In this paper, the GCV method has been developed for choosing the optimal regularization parameter in 2-D constrained inversion of gravity data using the quadratic algorithm. Data from the synthetic model have been inverted using the introduced algorithm and acceptable results have been obtained. The geometrical parameters of the synthetic model have been obtained from the inversion process with acceptable accuracy. After validation of the algorithm performance on the synthetic model, it has been applied for 2-D inversion of gravity data from San Nicolas massive sulfide deposit. The results of geological information in the area confirm the results of the 2-D inversion.