基于显式垂直比例因子的显式分形插值地震数据重建

在前人工作的基础上对分形插值方法作了详细的探讨,给出了分形插值函数的显式表达方式.在量纲分析的基础上给出了垂直比例因子的局部显式表达式,旨在提高地震道插值重建的精度及突出局部信息,并从单道地震图的角度分析其在地震道插值重建中的应用效果.研究了垂直比例因子的变化对分形插值精度的影响.数值实验表明,随着垂直比例因子的增大,分形垂直的误差逐渐增大,二者之间呈显出指数增长的趋势.该法克服了随机分形插值方法必须进行多步迭代的弱点,提高了计算效率.通过对理论地震道插值重建的分析,说明了本文分形插值方法的高精度和高效率.本文提出的显式分形插值方法既能够突出地震道数据的局部信息,又较好地保持了地震道数据的总体变化趋势.

Seismic data reconstruction by explicit fractal interpolation based on explicit vertical scaling factors

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.