Multi-objective optimization model, interpolation method and surface reconstruction method for surface reconstruction

Abstract

The invention provides a multi-objective optimization model for curved surface reconstruction, an interpolation method based on the multi-objective optimization model for curved surface reconstructionand a geological curved surface reconstruction method. The multi-objective optimization model is defined in the description. The interpolation method comprises the steps of building a multi-objectiveoptimization model for curved surface reconstruction; transforming an expression of the multi-objective optimization model into a first expression; solving the expression of z'i to obtain a second expression containing an unknown number zi; substituting the second expression into the first expression to obtain a third expression; and calculating the partial derivative of all zi in the third expression, and enabling the partial derivative to be 0 so as to obtain values of interpolation results z1, z2,... zn, zn+1. The curved surface reconstruction method comprises the step of performing interpolation on grid points by adopting the interpolation method based on the multi-objective optimization model for curved surface reconstruction. The method provided by the invention is slightly affectedby isolated points, high in control for the trend of the curved surface in supplementary interpolation and more capable of enhancing the smoothness of the interpolation results while ensuring the accuracy of interpolation as far as possible.

Description

technical field [0001] The invention relates to the technical field of geophysical exploration, more specifically, to a surface reconstruction multi-objective optimization model, an interpolation method based on the surface reconstruction multi-objective optimization model and a geological surface reconstruction method. Background technique [0002] With the continuous development of economy and society, the application of surface reconstruction in oil and gas reservoir exploration, medical research, computer graphics and other scientific fields has attracted more and more attention. People have a growing demand for the performance and efficiency of complex surface reconstruction. Complex geological surfaces are a focus of space surface reconstruction research. The irregularity and data point sparsity of geological surfaces are not available in general surface reconstruction. It is difficult to find the corresponding surface mathematical expressions like general surface recon...

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Problems solved by technology

Nearest neighbor method, distance inverse weighting method and Kriging interpolation method are three commonly used interpolation methods in geological surface reconstruction. Although these methods are widely used by geologists, there are inevitably some defects. These defects can be summarized as the following three points: (1) The distribution of data points around the point to be interpolated is uneven. The method cannot guarantee the correct trend of the surface at the position of the point to be interpolated

(2) The traditional interpolation method is difficult to correctly deal with the situation of incongruous isolated points around the points to be interpolated, which is often affected, making the interpolation results rough and poor in smoothness

(3) Due to the sparsity of geological surface data, it is not easy to obtain smoother interpolation results by conventional interpolation methods

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