Multiscale time domain full waveform inversion based on cubic convolution interpolation

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 do- main multiscale inversion. Starting from the high-order staggered grid finite difference scheme,the space step corre- sponding 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-fre- quency 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 re- alized by using the cubic convolution interpolation. The test of theoretical model proves that it can reduce the time re- quired 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.