Research On Multi-parameter Full Waveform Inversion With Gradient Preconditioning

Full-waveform inversion(FWI)is an important inversion method for the derivation of high resolution quantitative models of the subsurface media,which has the ability of recovering different physics parameters.However,because of the interparameter trade-off arising from inherent ambiguities between different physical parameters,each parameter gradient will be interfered with the cross-talk,which will eventually lead to the decline of the inversion accuracy.Since the off-diagonal elements of Hessian matrix-vector represent the coupling effect between different physics parameters,we calculate the inverse of Hessian matrix-vector implicitly by quasi-newton method to suppress the interparameter trade-off while not significantly increasing the computational cost.FWI is a strong nonlinear local optimization problem with low convergence efficiency and high dependence on initial models.However,the nonlinear degree of the multi-parameter full waveform inversion method is more intense due to the increase of the freedom degree of the model space.We used a frequency selection strategy based on Wiener filter to improve the stability of the multi-parameter full-waveform inversion method when the low-frequency information is missing or the seismic data's frequency is high.Because the inversion results of the deep structure is sensitive to the errors of overburden structure,we developed an inversion strategy to recover the model parameters from top to bottom based on a damping filter in time domain.In the gradient-based full waveform inversion method,the selection of step length directly affects the convergence speed.For the multi-parameter full-waveform inversion,besides the values of step-lengths,the energy balance between different parameters also needs to be considered.Due to the high sensitivity of density parameters in the inversion,the variation of density is usually underestimated and the variations of P-wave and S-wave velocities are overestimated correspondingly.Therefore,we calculate the weights of each parameter in the iteration and use them as the gradient preconditioning operators,which can improve the problem of unbalanced parameter update degree.For the multi-parameter elastic full-waveform inversion in time domain,the shallow structure inversion results are often better than deep ones due to the insufficient deep illumination.Based on approximate Hessian matrix-vector and the Green function,we derive the gradient preconditioners in detail.Numerical examples show that the gradient preconditioners we used are more efficient than the conventional ones which are based on the energy of background wave-fields.In this paper,we introduce the principle of the 2D time-domain multi-parameter isotropicelastic full waveform inversion and its optimization method,and the related formulas are derived in detail.The proposed methods are applied to the synthetic data to verify the efficiency and accuracy.Finally we make a discussion and draw some conclusions based on the research.