Seismic Data Reconstruction with Fractal Interpolation

Abstract

AbstractIn order to improve the accuracy of reconstructed seismic data, this paper makes a detailed investigation into the fractal interpolation method on the basis of the previous 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 is put forward. At the same time the interpolating accuracy is investigated from the point of accordingly seismic traces. The influence of the vertical scaling factors to the precision of the fractal interpolation is 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 and efficiency, the largest 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.