【摘要】 以分形理论为基础,借助于压缩映射原理和不动点理论及实变函数理论,给出了分形插值函数的显式表达形式,同时给出了垂直比例因子的局部显式表达式.利用该显式分形插值方法对稀疏采样的地震记录进行了插值加密处理,并对原始记录和分形插值重建记录进行了叠前逆时偏移处理.数值重建实验表明,显式分形插值重建的剖面与原始地震剖面非常类似,单道地震记录则表明显式分形插值重建的地震道是原始地震道的良好近似,缺失道的振幅和相位都得到了很好的估计.叠前偏移结果则表明,分形插值叠前偏移剖面是原始记录偏移剖面的良好近似,二者的分辨率几乎一样.更多还原

【Abstract】 Based on the fractal theories,contractive mapping principles as well as the fixed point theory,by means of affine transform,this paper develops a novel Explicit Fractal Interpolation Function(EFIF)and puts forward the locally explicit vertical scaling factor.Interpolation reconstruction has been made to the sparse sampling data by the explicit fractal interpolation method and the pre-stack reverse-time migration has been made using the original and reconstructed seismic data.The numerical experiments demonstrate that the seismic section and seismograms reconstructed by the explicit fractal interpolation method resemble the original ones very well.The waveform of the missing traces could be estimated very well and also the amplitudes of the interpolated traces are good approximations of the original ones.The imaging sections obtained by using the fractal interpolated data resemble the original ones very well.The numerical experiments demonstrate that even with the sparse sampling we can still obtain the high accurate images of the earth′s interior structure by means of the explicit fractal interpolation method.更多还原