基于三次卷积插值的时间域多尺度全波形反演

Multiscale time domain full waveform inversion based on cubic convolution interpolation

时间域全波形反演采用全频带地震数据时容易陷入局部极值,通过滤波器对地震数据分频段开展时间域的多尺度反演研究。从一阶导数的高阶交错网格有限差分格式出发,给出了不同差分阶数下不同频段反演时可取的空间步长;采用巴特沃斯自相关滤波器将地震数据滤波成一系列不同频段的地震数据,从低频到高频依次反演,上一个低频段反演的结果作为下一个高频段反演的初始模型。考虑到不同频段反演时采用的空间步长不是简单的倍数关系,通过引入三次卷积插值技术来实现不同频段之间的插值。理论模型试算证明:在不同的反演频带下分别选择合适的空间步长,同时相应改变时间步长,能最大程度减少反演所需时间;三次卷积插值技术可实现粗网格大小与细网格大小为任意倍数的插值,基于三次卷积插值法反演可得到与常规统一网格步长反演法精度相当的结果。

The time domain full waveform inversion using the full band data is usually unsuccessful because the misfit error is easily trapped into local minima value.This problem can be solved with filter technique to realize the time domain multiscale inversion.Starting from the high-order staggered grid finite difference scheme,the space step corresponding to different frequency bands at different difference orders is given.The seismic data is filtered into different frequency-bands by the Butterworth autocorrelation filter to realize multiscale inversion.In the inversion,the low-frequency inversion result is used as the starting model in the high-frequency inversion.Considering that the spatial step of different frequency bands is not a simple multiple relation,the interpolation between different frequency-bands is realized by using the cubic convolution interpolation.The test of theoretical model proves that it can reduce the time required for the inversion,when the appropriate space step in different inversion bands is selected and the time step is changed correspondingly.The cubic convolution interpolation technique can realize the interpolation with discretionary ratio between coarse mesh and fine mesh.This method can not only realize the multi-scale inversion quickly,but also can get the same accuracy inversion result as the tra-ditional fixed-spatial-step method.