The Research On Frequency Domain Visco-Acoustic Full Waveform Inversion

With seismic exploration work deepening,oil development has gradually turned to lithology exploration on deep and complex media.The complexity of the media causes great difficulties for the acquisition,processing and interpretation of seismic data,especially the accurate acquisition of the physical parameters in complex media.In order to adapt to the increasingly complex oil and gas exploration targets,we select the viscoelastic medium equation,which is closer to the actual formation properties,to carry out full waveform inversion of formation velocity and quality factors(Q value).It has important theoretical meaning and application value on describing property of oil and gas reservoirs,implementing exploration targets and deepening geological cognition.Before introducing the theory of inversion,the paper first introduces the method of forward modeling on viscous medium in frequency domain,derives the wave equation in viscous medium,and compares the advantages and disadvantages of three different difference schemes in terms of angle dispersion.Finally,we choose optimized staggered difference scheme to discretize wave equation.Then,through test of corresponding model and the comparison with the wave field snapshot of pure sound,it shows the feature of absorption and attenuation in viscous medium.Then,we introduce the basic theory of FWI in frequency domain,including the convergence algorithm,model updating process,selection of step and frequency.Firstly,based on the inversion theory,we give the results of single parameter inversion,and the inversion result of both the velocity parameter and Q value are good enough.Before the two-parameter inversion,we analyze the sensitivity of velocity and Q value to objective function,and the results show that the sensitivity of velocity is much greater than that of Q value.Then,we carry out the test of two-parameter inversion,and velocity inversion results are ideal,though there are artifacts in Q inversion.In order to improve the results of simultaneous inversion of two parameters,we first optimize the convergence algorithm.The truncated Newton method is used to converge the objective function as this method can obtain more accurate Hessian operator than other convergence algorithms,and the exact Hessian matrix can reduce the coupling effect between the parameters.Then,we test the truncated Newton method on model,and it proves that it can focus parameters better in the case of insufficient illumination.And in two-parameter joint inversion,this method can reduce the coupling effect between the parameters and improve the artifact phenomenon to get better inversion results.In order to further improve the effect of joint inversion,we use two-step inversion strategy.That is to say,we only invert velocity firstly and then invert velocity and Q value at the same time.Results show that the two-step inversion strategy can obtain better Q results.Finally,in order to improve the efficiency of multi-source FWI in frequency domain,we use the sparse constraint in process of model updating,which can reduce the effect of crosstalk noise while improve the inversion efficiency.