This paper discusses the stability of solutions to a class of Cauchy problems for Laplace equations under two kinds of nonclassical circumstances. By means of conformal mapping and Tikhonov, Luan Wengui and Yamamoto&#...This paper discusses the stability of solutions to a class of Cauchy problems for Laplace equations under two kinds of nonclassical circumstances. By means of conformal mapping and Tikhonov, Luan Wengui and Yamamoto's methods for solving ill-posed problems respectively, the stability estimations of weighted Holder type and logarithmic type, have been obtained accordingly.展开更多
The existing methods of downward continuation of potential field cannot be used to continue the aeromagnetic data to the marine surface because of the limited continuation distance. An iteration method for the downwar...The existing methods of downward continuation of potential field cannot be used to continue the aeromagnetic data to the marine surface because of the limited continuation distance. An iteration method for the downward continuation of potential field with a much larger continuation distance has been developed, which can continue the aeromagnetic data to the marine surface and get the marine - magnetic chart with the same scale as the aeromagnetic data. This downward continuation method will greatly raise the ef- ficiency of marine - magnetic investigation. The principle of the iteration method is presented. The method is demonstrated on synthetic models and real aeromagnetic data. Also, the error brought by continuation is discussed. The efficiency of the iteration method for the downward continuation of potential field is compared with the fast fourier transform （FFT） method, the former is much better than the latter.展开更多
文摘This paper discusses the stability of solutions to a class of Cauchy problems for Laplace equations under two kinds of nonclassical circumstances. By means of conformal mapping and Tikhonov, Luan Wengui and Yamamoto's methods for solving ill-posed problems respectively, the stability estimations of weighted Holder type and logarithmic type, have been obtained accordingly.
基金The National Natural Science Foundation of China under contract No.40644022the China Post-doctor Science Foundation under contract No.20050335090.
文摘The existing methods of downward continuation of potential field cannot be used to continue the aeromagnetic data to the marine surface because of the limited continuation distance. An iteration method for the downward continuation of potential field with a much larger continuation distance has been developed, which can continue the aeromagnetic data to the marine surface and get the marine - magnetic chart with the same scale as the aeromagnetic data. This downward continuation method will greatly raise the ef- ficiency of marine - magnetic investigation. The principle of the iteration method is presented. The method is demonstrated on synthetic models and real aeromagnetic data. Also, the error brought by continuation is discussed. The efficiency of the iteration method for the downward continuation of potential field is compared with the fast fourier transform （FFT） method, the former is much better than the latter.
