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《Chinese Journal of Geophysics》 2015-08
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Multi-Parameter full waveform inversion for acoustic VTI media using the truncated Newton method

WANG Yi;DONG Liang-Guo;State Key Laboratory of Marine Geology,Tongji University;  
It is important to reconstruct both seismic velocities and anisotropy parameters by anisotropic full waveform inversion(FWI).But the trade-off between different parameter classes increases its nonlinearity severely.The significant difference of magnitude orders between seismic velocities and anisotropy parameters makes the inversion problem poorly conditioned.Judiciously incorporating the inverse Hessian operator within the FWI scheme can help to alleviate the negative impacts of these two problems on FWI.The truncated Newton(TN)method can better estimate the inverse Hessian operator.Therefore,we use the TN method to tackle these two problems and simultaneously reconstruct both seismic velocities and anisotropy parameters for acoustic VTI media.The TN method has two advantages.On one hand,it does not need explicit Hessian matrix,which is prohibitive to build due to high computational cost and large memory requirements.To get the updated direction,the TN method solves Newton equation at each time of iteration with the conjugate gradient method(CG),which only uses Hessian-vector products.We compute these products by the finite difference method.On the other hand,the TN method can adjust flexibly the updated direction when the Hessian matrix is non-positive definite.The CG method at each step of the TN iteration is terminated as soon as a direction of negative curvature is generated.With this strategy the TN method may perform better than Limited-memory BroydenFletcher-Goldfarb-Shanno method(L-BFGS)for ill-conditioned problems.We test the inversion capability of the TN method with two numerical experiments.In each experiment,the NMO velocity and anisotropy parameter eta are inverted simultaneously.The LBFGS method is also tested for comparison.The first experiment is on a simple 2D VTI homogenous model with three different anomalies inside.The inversion is performed in the time domain with a full acquisition system.Inversion results show that the TN method can balance the updates of the two different parameters,and reconstruct more accurate models.In contrast,the L-BFGS method overestimates parameter eta but underestimates NMO velocity.The second experiment is on a more complex 2D model with a surface acquisition system.The two methods perform the same as they do in the first experiment.The reason for their different performances may be found from the Hessian analysis part that we have finished before the two experiments.We design a small size(51×51)inclusion model and compute explicitly the Hessian matrix of the background initial model.The analyses show that the Hessian matrix has several negative eigenvalues and a large condition number(illconditioned matrix),which may result in the failure of the L-BFGS method.The TN method better overcomes these difficulties.Hence,in the context of simultaneous inversion of two parameters for acoustic VTI media,the TN method can account for more accurate inverse Hessian operator than the L-BFGS method and get more accurate inversion results.It is a promising method for multi-parameter FWI.
【Fund】: 国家油气重大专项(2011ZX05005-005-007HZ)资助
【CateGory Index】: P631.4
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