The 2D Seismic Time-domain Multi-scale Full Waveform Inversion

At present more and more applications in complex structure area velocity modeling, but the speed of the traditional analysis method can not get the velocity model with high resolution, however, the seismic full waveform inversion uses pre-stack seismic wave field kinematics and dynamics information to construct the velocity model, and it can accurately describe the details of the model, which makes it become a hot research topic in recent years.This paper thoroughly studied two dimensional time domain full waveform inversion algorithm, and achieved a relatively complete two dimensional time domain multi-scale full waveform inversion system. While the inversion can not do without the forward work, so this paper firstly studies the high order finite difference method of the wave field simulation, and deduced the different order finite difference format, then gives the stability condition and the dispersion condition, and points out the key importance of the seismic wavelet in the actual application of full waveform inversion, and uses the two order Clayton-Enguist-majda as the absorbing boundary conditions. In the last part of the forward simulation, it makes tests on the theoretical model and verifies the effectiveness of the forward simulation method in the abnormal body model and the complex model, and the absorbing effect of the absorbing boundary conditions.As for the strong nonlinear problem of full waveform inversion, this paper first derives the classic seismic gradient method full waveform inversion. It uses the cross-correlation of the forward wave-field from the shot point and the reverse wave-field from the waveform residuals of the receiver point to construct the gradient direction. And this can avoid the calculation of the Jacobi matrix, so it can reduce the amount of calculation. On the basis of the gradient method full waveform inversion, this paper gives the algorithm flow of the conjugate gradient method. Taking into that the deep structure is difficult to inverse, it uses a gradient preconditioning method based on seismic wave energy to improve the inversion result of the deep structure, then deduces the iterative step linear search method. However, the use of fast convergent speed and local optimization method is inevitably affected by the local extremum. According to the characteristics of the full waveform inversion with multi-extremum, the multi-scale inversion strategy based on the Wiener lower pass filter is used. It uses the Wiener lower pass filter on the observed seismic data and seismic wavelet into different bands, the inversion is firstly begin in the low frequency band which is the large scale problem and the inversion objective function has few extremum points in this frequency band. The low frequency band inversion result can be as the initial velocity model of the high frequency band, and then inverse by the frequency band. The highest frequency band inversion result can be as the final result of the whole full waveform inversion. Finally, this paper bases on the C++language to implement the core code set algorithm, to verify the effectiveness of the algorithm, the anomalous body model and the complex Marmousi model is tested using this algorithm, the results show that the full waveform inversion method for abnormal body model and inversion of complex structure has good effect, this also confirmed the validity of the whole time domain this full waveform inversion method.