The theory of multifractal interpolation surface and its applications

The main feature of fractals is the self-similarity. The fractals in the nature have the characteristics of statistically self-similar or multifractal. This paper introduces the formulas of the self-affine fractal interpolation of surface, and gives the principles of the multifractal interpolation surface. The methods of dividing local interpolation neighborhood and determining multiple vertical compression ratios are described. Based on the measured fault surface data, the self-affine fractal surface and the multifractal surface are interpolated respectively. By comparison, multifractal interpolation surface is more consistent with the actual fault surface than the self-affine fractal surface.