Seismic data reconstruction with fractal interpolation
分形插值地震数据重建方法研究

In order to improve the accuracy of the reconstructed seismic data,this paper makes a detailed investigation into the fractal interpolation method on the basis of the former work,and analyzes theoretically a special kind of fractal interpolation function.The explicit presentation of the fractal interpolation function is applied and the locally explicit expression for the vertical scaling factors has been put forward.At the same time the interpolating accuracy has been investigated from the point of accordingly seismic traces.The influence of the vertical scaling factors to 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 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 and efficiency,the most node error is no more than 3% with respect to the numerical computation.The method not only makes the local information obvious but also preserves the overall characteristics well of the data investigated.