边界条件和偏移距的变化对分形插值精度的影响

地震数据空间道插值是地震资料预处理的重要内容之一。本文以分形理论为基础,借助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式及垂直比例因子的局部显式表达式。正演模拟中采用了吸收边界条件,边界条件的应用使得靠近边界的地震道分形插值重建的误差要高于远离边界的地震道,即随着检波器逐渐靠近边界,分形插值重建的误差逐渐增大。偏移距的变化也会对分形插值重建的精度产生影响,随着偏移距的增大,分形插值重建的误差有增大的趋势,但不明显。总体上来说,分形插值重建的地震道是原始地震道的良好近似,相位和振幅都得到了很好的恢复。

Influences of Boundary Condition and 0ffsets on the Precision of Fractal Interpolation

Spatial trace interpolation is one of the important issues in seismic data processing.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 and put forward the locally explicit vertical scaling factor.Absorbing boundary condition has been applied in forward modeling.The residuals of the reconstructed seismograms near the boundary are larger than that far away from the boundary.The changes of the offsets also affect the precision of the fractal interpolation,i.e.,with the increasing offsets the residuals are becoming larger and larger,but the trend is not obvious.All in all,the seismograms reconstructed by 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 a good approximation of the original ones.