The Research Of The Regularization Method For Coseismic Slip Distribution Inversion In Geodesy

Geodetic data are widely used in the field of seismic research co-seismic slip distribution inversion due to its wide coverage,simple observation conditions and high precision.The co-seismic slip distribution inversion is one of the ways to study and analyze the mechanism of earthquake.The Tikhonov regularization method is usually used to calculate the solution of co-seismic slip distribution.The precision of the solution is related to the choice of regularization parameters and regularization matrix.In addition,the determination of relative weight ratio of multi-source data joint inversion is also one of the main factors affecting the inversion accuracy of co-seismic sliding distribution.In addition,the determination of relative weight ratio of multi-source data joint inversion is also one of the main factors affecting the inversion accuracy of co-seismic sliding distribution.By improving the inversion precision of the coseismic slip distribution and obtaining more accurate source parameters,the rupture process of seismic source can be better understood.Higher parameter inversion accuracy has a great significance for scientific research and social work such as earthquake strain accumulation,post-earthquake slip mode understanding,earthquake disaster prediction and rescue.The determination of the regularization parameters and regularization matrix of the Tikhonov regularization for calculating the solution of co-seismic slip distribution inversion and the relative weight ratio of multi-source data joint inversion has researched in this paper.The main research contents and work of this paper are as follows:1.Researching the methods of determining the regularization parameters in the co-seismic slip distribution inversion.For the shortcomings of the common method —L curve method,the U curve method is introduced into the field of co-seismic slip distribution inversion.The inversion results of simulate experiments and actual earthquake case of Lushan in 2013 show that the inversion results with the regularization parameters by u-curve method is more accurate than L curve method,and doesn't need rely on the data fitting degree.In addition,we propose the Eclectic Intersection curve method(EI curve),which is based on the L curve method.the inversion results of simulate experiments and actual earthquake cases of L 'aquila earthquake in 2009 and Meinong,Taiwan earthquake in 2016 show that compared with the L curve method,the EI curve method has advantages of high computation efficiency,no need to depend on data fitting and so on.2.Researching the methods of determining the regularization matrix in the co-seismic slip distribution inversion.For the maximum slip is underestimated of the regularization matrix made by Laplacian second order smoothing matrix.We propose a new method of weighting to the Laplacian second-order smoothness matrices by the slip.The Laplacian smoothness constraint with unequal weights and the classic Laplacian constraint are used to carry out the simulation experiments.The simulation experiments show that the accuracy of the estimated maximum slip from our method is outperforming the classical Laplacian method by 12%-19%.Moreover,the estimations of the average slip and moment magnitude have been enhanced,which improved ranging from 4%-12.5 and 0.4%-9% over the inversion results of classic Laplacian smoothness constraint,respectively.The maximum slip inversion results of actual earthquake cases of L 'aquila earthquake in 2009 and Meinong,Taiwan earthquake in 2016 show that the inversion of Laplacian smoothness constraint with unequal weights are larger than that of the classic Laplacian smoothness constraint,which is consistent with the conclusion of simulation experiments.In short,the regularization matrix is made by the inequality Laplacian second order smoothing matrix can solve the problem that regularization matrix made by the tradition Laplacian second order smoothing matrix underestimates the maximum slip.3.Researching the relative weight ratio among the multi-source data for joint inversion of seismic slip distribution.The method uses the U-curve method to determine the optimal regularization parameter of the observed data in individual inversion,then uses the discriminant function minimization method to determine the relative weight ratio among the multi-source observed data.It can be seen from the root mean square error of the simulated experiment and the actual seismic experiments of L 'aquila earthquake in 2009 and Meinong,Taiwan earthquake in 2016,the RMS of our method is less than Variance component estimation method(VCE)and(U curve +VCE)methods to reduce the 33.3%-51.3%.Therefore,it shows that the relative weight determined by this method has certain advantages over the inversion result.