Study On Two-parameter Inversion By Frequency Domain Full Waveform Inversion

Full waveform inversion(FWI)is an efficient method that can obtain the physical parameters,but commonly the inverted parameter is velocity.If some parameters can been inverted simultaneously,we can better understand the geological structure and the reservoir of oil and gas.But the difficulties in multi-parameter FWI are the variable influence of the different parameter classes on the phase and amplitude of the data and that the trade-off between different parameter classes can increase the nonlinearity of FWI severely.Considering the difficulties of multi-parameter inversion,the visco-acoustic wave equation is used to test the two-parameter inversion.This paper is mainly studied from the following points:(1)One of the advantages of wave equation in frequency domain is that the attenuation quality factor Q can be easily introduced.The visco-acoustic wave equation,which have taken the viscous property of medium into consideration when the wave propagation is modeled,is used to do the research on two-parameter inversion by frequency domain full waveform inversion.The parameters that been inverted are velocity and Q.(2)In the forward modeling,the visco-acoustic equation is discretized by the optimal 9-point difference scheme firstly.Then a large sparse matrix equations is constructed.In terms of absorbing boundary conditions,we chose the perfectly matched layer(PML)absorbing boundary conditions.Last we solve the forward modeling equation by the least squares QR(LSQR)method.(3)Based on the forward modeling,we use pre-gradient method to achieve the frequency-domain one-parameter and two-parameter waveform inversion.At the same time,the sensitivity analysis of the two-parameter is given.Last the trade-off between velocity and Q is weakened by the sequential inversion strategy.Last the experimental results show that simulate wave propagation process successfully and PML can absorb the artificial reflection effectively.And the inversion result of one parameter is good.The inversion result of velocity is good and the inversion result of Q remains to be improved,when the simultaneous inversion strategy is applied.The inversion result of velocity and Q can be improved when the sequential inversion strategy,but the parameter is inverted according to its sensitivity.