Study On The Solving Methods Of The Ill-posed Problems Of The Sbas Insar Deformation Model

Small baseline subset(SBAS)InSAR has been widely applied in monitoring slow surface deformation for a long time,such as urban land subsidence,mining subsidence,earthquakes,volcanoes,glaciers,frozen so1l and so on,which now has become one of the hottest issues about InSAR in the world.However,in practical applications,it was found that the ill-posed problems include the in-conditioned and the rank-deficient ones in solving the SBAS deformation model,which seriously affected the inversion accuracy and reliability of deformation information.Based on the basic theory of SBAS InSAR technology,a biased iterative estimation method based on Liu estimation and the Tikhonov regularization method are proposed and studied for the ill-posed problem of the SBAS deformation model.An improved Landweber iterative method was introduced to solve SBAS deformation model when its coefficient rank deficiency matrix.The main contents are as follows:(1)This paper systematically analyzed the principles and the practical data processing flow of traditional SBAS technology,and deeply studied about the selection of main image and interference pairs,the construction of coefficient matrix of SBAS deformation model and its solution.On this basis.taking as an example,SBAS technology was used to extract the time series of land subsidence and the annual average deformation rate of Beijing region from 2007 to 2010 with 29 scenes ENVISAT ASAR images.Thus we understand comprehensive of a practical data processing flow and key technology of the SBAS technology.(2)On the basis of Liu estimation,combined with the idea of-iteration a new biased iterative lethod was proposed for solving the problem of the SBAS deformation model with ill-conditioned coefficient matrix.It was proved theoretically that the iterative method converges under the condition of-1?d?1.The analytic expression of the iterative fortula was given using the spectral decomposition of the matrix.The properties of the estimation method were discussed.The paper selected 13 scenes KNVISAT ASAR images which covered Jining area to monitor the trend ot surface deformation using SBAS InSAR technique.Using the LS method.the Liu estimation method and the proposed iterative estimation method respectively to solve the SBAS deformation model,the results show that the proposed iterative estimation method is more accurate and stable than the LS method and the Liu estimation method.(3)An improved Tikhonov regularization method was proposed for solving ill-posed problels of the least square solution for the SBAS linear deformation model.In the method,firstly,the correlation between the small baseline interference pairs was used as weighted matrix to implement WLS estimation;secondly,the regularization parameter was determined using the L-curve criterion,and the regularization matrix was a diagonal matrix whose elements were the diagonal elements of the MSEM's inverse matrix.Then the stable solution of SBAS deformation model can be calculated by the Tikhonov regularization method.(4)To verify the stability of the improved Tikhonov regularization method for solving deformation model,the paper took 9 in 13 scenes ENVISAT ASAR images which covered Jining city and used the 9 scenes to make up 30 interference pairs.The LS method and improved Tikhonov regularization method were respectively used to solve SBAS deformation model.The comparison with leveling data showed that the improved Tikhonov regularization method has higher accuracies and reliabilities.In addition,this paper used 9 scenes to make up 18 interference pairs.The comparative results between 18 and 30 interference pairs showed that the improved Tikhonov regularization method was almost not affected by the degree of the ill-posed and more stable than the LS method.Another example was employed with 21 scenes ENVISAT ASAR images covered Beijing city,the LS method,the ridge estimation and the improved Tikhonov regularization method were used to solve SBAS deformation model.The results showed that the improved Tikhonov regularization method was more stable and more precise.(5)The Landweber iterative method was introduced to solve the SBAS linear deformation model in the case of coefficient matrix with rank-deficient.A method how to determine the numbc r of iterations was proposed.The results of numerical example showed that the proposed method has a more wide adaptability and more efficiency than the deviation principle.Taking 29 scenes ENVISAT ASAR images covered Beijing area to implement SBAS technology,the paper used SVD method and the improved Landweber iterative method to solve the rank deficiency SBAS deformation model.The comparative results showed that the proposed method was not only suitable for solving the rank deficiency SBAS deformation model,but also has a more accurate result than SVD method.