Study On Method And Technology Of Full Waveform Inversion

Seismic wave full waveform inversion is a method based on the wave equation describing the propagation of seismic waves in a subsurface medium,and obtaining the relevant properties of the subsurface medium by means of the rich information contained in the seismic waveform.The core idea is to establish the model of the subsurface using the optimal matching of the observed data and simulated data.In fact,there are still many difficulties in the realization of full waveform inversion,such as the instability of the solution of the inversion problem,the strong nonlinearity of the inversion problem,the massiveness of the processed data,and the high complexity of time space,etc.Therefore,improving the efficiency and accuracy of seismic wave full waveform inversion is very theoretical and practical work.Forward numerical simulation is an important theoretical basis for full waveform inversion.The accuracy of the results affects the later work of seismic data processing.Due to the improvement of computer technology,wave equation forward modeling method develops rapidly.This method does not restrict the model structure,on the one hand it keeps the kinematic characteristics of seismic waves,and on the other hand it keeps the dynamic characteristics of seismic waves,so it is widely used in forward modeling.Forward modeling of wave equation can be carried out in time domain or in frequency domain.In the forward modeling of elastic wave in time domain,the first-order velocity-stress elastic wave equation in two-dimensional isotropic medium is used to derive the difference coefficients and corresponding difference accuracy of rational schemes under different difference schemes,and the stability conditions of higher-order staggered grids under different difference accuracy are analyzed.Wave field is numerically simulated using high-order staggered grid finite difference method under different difference accuracy.Numerical simulation results are analyzed and compared from wave field snapshots,synthetic seismograms and CPU time.It is pointed out that the difference schemes with time four and space twelve orders have higher calculation accuracy and efficiency.As the improvement,17-point difference scheme and 15-point difference scheme are proposed on the basis of 25-point difference scheme in frequency domain.The difference coefficients and dispersion conditions are recalculated,and the numerical solutions and impedance matrices obtained by the two schemes are compared.Finally,the experiment of complex model shows that the 15-point frequency-domain format with parallel strategy is more efficient than the traditional one with the same precision.In the inversion part,the acoustic equation is first regarded as the simplification of the elastic wave equation.The inversion algorithms and examples of acoustic wave equation in time domain and frequency domain are given.In the time domain full waveform inversion part,the multi-scale inversion method based on L-BFGS optimization algorithm is adopted.The core idea is to use the low-pass filter to decompose the observed data into different frequency bands and start from the low frequency band data.In the performance,the inversion result is used as the initial model of the high frequency band data,and then the details of the high frequency data inversion model construction are used to gradually improve the resolution of the imaging,thereby improving the inversion efficiency.The inversion experiment of the Marmousi model is carried out.The comparison between the inversion result and the single track velocity information proves that the inversion algorithm has higher inversion precision.In the full waveform inversion of the acoustic frequency,a multi-scale inversion algorithm in the frequency domain is given.The core idea is to invert all frequencies into several frequency bands.This method can complete the inversion process with fewer frequency points,and can achieve better results than using all frequency points for one inversion.The inversion experiments with simple models verify the effectiveness of the algorithm.The results of the Marmousi model inversion show that the algorithm can achieve better inversion results for complex models.In the full wave inversion of elastic wave,the multi-scale inversion algorithm of elastic wave time domain and frequency domain based on L-BFGS method is designed according to the idea of multi-scale inversion algorithm of acoustic wave.Then,using the simple model and the modified Marmousi2 model for inversion experiments,it is proved that both algorithms can achieve good inversion for both simple and complex models.At the end of the paper,the forward results and the initial inversion model,imaging accuracy and inversion efficiency of elastic wave in frequency domain and time domain are compared and analyzed.