Seismic data reconstruction by explicit fractal interpolation based on explicit vertical scaling factors
基于显式垂直比例因子的显式分形插值地震数据重建

In order to improve the accuracy of the reconstructed seismic data, this paper makes a detailed study into the fractal interpolation method on the basis of the former work. The explicit expression of the fractal interpolation function is applied and the locally explicit expression for the vertical scaling factors is put forward on the basis of dimension analysis. At the same time the interpolating accuracy is analyzed from the single trace seismographs. The influence of the vertical scaling factors on the precision of the fractal interpolation has been investigated. The numerical experiments demonstrate that the interpolating residual is in proportion to the exponent function with increasing vertical scaling factors. This explicit fractal interpolation method avoids the iteration that is inevitable in the traditional interpolation method, and then it improves the computational efficiency. By analyzing the theoretical seismograms and the reconstructed seismograms and the differences between them, the numerical results demonstrate that the fractal interpolation method put forward here has high accuracy. The method not only makes the local information obvious but also preserves the overall characteristics well of the seismic data.