| Geostatistics is an emerging branch of mathematics geological disciplines, it was developed in the sixties and seventies of the twentieth century. The object of geological is regionalized variables.Because of regional variables are widespread in nature, geostatistics has developed into an universal scientific method. Geostatistics kriging interpolation method, which is based on a statistical model, include such as autocorrelation relationship between the known data. kriging method not only need to consider the spatial relationships between the various known points, and also need to consider the relationship between the interpolation data and each of the known point, consider the structural and randomness of the variables. On the basic of two-dimensional kriging method, this thesis focused research on the expansion of kriging in three-dimensional, and discussed the impact of anisotropic,also discussed fast-search algorithm and fast-interpolation algorithm in three-dimensional.The realization of three-dimensional kriging consists of two main parts:the first part is use sample data to do a variation structure analysis, that is get the variogram. The first part contains the anisotropy analysis, variation scale analysis, calculate the experimental variogram, select the model of theoretical variogram and obtain the optimal solution of the model. The second part includes searching the three-dimensional neighborhood data, determine kriging equations, solving the kriging equations to obtain the weighting coefficient, and ultimately obtain the attribute values of the data to be interpolated. This thesis first introduces the existing interpolation method, and then recalled research status of kriging method, on the basis of the two-dimensional kriging method, we extended it to three-dimensional field. for the three-dimensional case kriging two major method made a thorough study, the specific work is as follows:(1) The method to do structural analysis of variance using known data is the least Squres. but in practice, if the selected the variation function model is not in the form of the polynomial, seeking the step of seeking optimal solution is more complicated; Moreover, the obtained optimal solution may not match the actual atrribute; Therefore, this thesis proposes the use of particle Swarm Optimization to obtain the optimal solution of the variogram model and make improvements on standard particle swarm algorithm for specific geological data characteristics.(2) In practical applications, there are a lot of known data and distribute irregular. for each of the interpolation data, only search the neighboring dozen to two dozen known point to its interpolation. Then, fast search for the neighboring points in three-dimensional space can be increased the speed of the whole interpolation algorithm. In addition, if spatial configurations of the neighboring data is different for each interpolation data, we needed several matrix assignment, inversion, multiplication, it can slower the speed of the interpolation algorithm. therefore, this thesis proposed fast interpolation algorithm based on the multigrid to reduce the times of matrix assignment, inverse, multiply, the algorithm can greatly reduce the time to realize the interpolation.(3) On the basis of theoretical studies, this thesis programming to realize kriging method in three-dimentional on the platform of VS2008and QT. This software include user interface, kriging interpolation algorithm, data display. The data used is the measured data obtained by drilling wells, including the location, depth, speed (attribute values). The simulation results show that:the improved PSO algorithm used in this thesis can obtain better variogram, thereby improving interpolation accuracy;The fast interpolation algorithm based on nested grid proposed in this thesis can effectively reduce the time of the entire interpolation. |
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