Three-dimensional gravity inversion using co-kriging stochastic algorithm; application of the method on the gravity data from Safoo mine site

Summary: In this paper, 3D inversion of gravity data for determination of subsurface density distribution is made using geostatistical co-kriging method. Co-kriging is a mathematical interpolation and extrapolation tool. It uses the spatial correlation between the secondary variables and a primary variable to improve the estimation of the primary variable at un-sampled locations. The Co-kriging method gives weights to the data so as to minimize the estimation variance (the co-kriging variance). In this paper, the primary variable is density, (estimated by ρ*) and the secondary variable is gravity g. For determination of kernel matrix, the subsurface area is divided into large number of rectangular blocks of known sizes and positions. The unknown density contrast of each prism is the parameter that should be estimated. In addition, the weighting matrix has also been used in order to improve the depth resolution. Preconditioned conjugate gradient method has been used for inversion. The computer program has been written in MATLAB and tested on synthetic gravity of a rectangular prism model. The results indicate that the geometry and density of the reconstructed model are close to those of the original model. The gravity data acquired in an area, which includes concealed manganese ore bodies (Safoo mine site), in northwest of Iran. The results show a density distribution in the subsurface from the depth of about 5 to 35-40 m. These results are in good agreement with the results of the borehole drilled in the site.
We may encounter two problems in gravity data inversion: non-uniqueness and non stability of solutions. The first one occurs for two reasons: The first reason is known as the theoretical ambiguity of the unknown nature of potential theory. The second reason is known as algebraic uncertainty, which is considered when the number of parameters is greater than the number of observations. The second problem may occur because of bad condition (ill-condition) of the kernel matrix and the presence of noise in the data. For finding a unique and stable solution, constraints should be considered in the objective function, and then, the new objective function, which is replaced the initial objective function, should be minimized.
Methodology and Approaches: For determination of kernel matrix, the subsurface of the survey area is divided into a large number of rectangular prisms of known sizes and positions. The unknown density contrast of each prism is the parameter to be estimated. This kind of parameterization is flexible for the reconstruction of the subsurface model, but generates more unknown model parameters than observations (here N Results and By applying co-kriging stochastic algorithm on synthetic data in states of without and with random noise, good results for the density and depth of the model have been achieved. By applying the method on actual data from Safoo manganese mine site, the results obtained for the depth and density of the subsurface ore body are in good agreement with the results of drilling implemented in the mine site. Furthermore, as a result of applying the method on the data, general shape of the subsurface ore body was well determined.