Based on strong and weak forms of elastic wave equations, a Chebyshev spectral element method （SEM） using the Galerkin variational principle is developed by discretizing the wave equation in the spatial and time dom...Based on strong and weak forms of elastic wave equations, a Chebyshev spectral element method （SEM） using the Galerkin variational principle is developed by discretizing the wave equation in the spatial and time domains and introducing the preconditioned conjugate gradient （PCG）-element by element （EBE） method in the spatial domain and the staggered predictor/corrector method in the time domain. The accuracy of our proposed method is verified by comparing it with a finite-difference method （FDM） for a homogeneous solid medium and a double layered solid medium with an inclined interface. The modeling results using the two methods are in good agreement with each other. Meanwhile, to show the algorithm capability, the suggested method is used to simulate the wave propagation in a layered medium with a topographic traction free surface. By introducing the EBE algorithm with an optimized tensor product technique, the proposed SEM is especially suitable for numerical simulation of wave propagations in complex models with irregularly free surfaces at a fast convergence rate, while keeping the advantage of the finite element method.展开更多
The subbottom profiling is an important means of marine engineering survey, hazardous geology study and continental shelf scientific research. The accuracy of subbottom profile data interpretation has a direct impact ...The subbottom profiling is an important means of marine engineering survey, hazardous geology study and continental shelf scientific research. The accuracy of subbottom profile data interpretation has a direct impact on the research and investigation results. Because some of profilers’ transducer and hydrophone are separately installed, when the survey area is very shallow, distortion of shallow layers will be caused if it is seen as a self-excited and self-collected single-channel seismic system. According to the principle of subbottom profiler, the distortion correction formula is deduced and analyzed, providing actual value to using C-View software to interpret such subbottom profile data more accurately. In addition, the seabed sediments sound velocity is one of the key parameters when acquiring and processing the subbottom profile data. On the basis of comparing some sound velocity forecasting empirical equations, the LU Bo’s equation was considered the most appropriate to predict the seabed sediments, sound velocity at near-shore of China. In a survey of an artificial island site, the LU Bo’s equation and the porosity data obtained from geological drilling were utilized to predict the sediments sound velocity, and the sound velocity structure profile was plotted, which was applied in processing the subbottom profile data of the artificial island investigation. The method of using porosity data to predict sediments sound velocity in processing subbottom profile data can improve the interpretation accuracy and it’s of practical significance.展开更多
Proximal point algorithms （PPA） are attractive methods for solving monotone variational inequalities （MVI）. Since solving the sub-problem exactly in each iteration is costly or sometimes impossible, various approx...Proximal point algorithms （PPA） are attractive methods for solving monotone variational inequalities （MVI）. Since solving the sub-problem exactly in each iteration is costly or sometimes impossible, various approximate versions ofPPA （APPA） are developed for practical applications. In this paper, we compare two APPA methods, both of which can be viewed as prediction-correction methods. The only difference is that they use different search directions in the correction-step. By extending the general forward-backward splitting methods, we obtain Algorithm Ⅰ; in the same way, Algorithm Ⅱ is proposed by spreading the general extra-gradient methods. Our analysis explains theoretically why Algorithm Ⅱ usually outperforms Algorithm Ⅰ. For computation practice, we consider a class of MVI with a special structure, and choose the extending Algorithm Ⅱ to implement, which is inspired by the idea of Gauss-Seidel iteration method making full use of information about the latest iteration. And in particular, self-adaptive techniques are adopted to adjust relevant parameters for faster convergence. Finally, some numerical experiments are reported on the separated MVI. Numerical results showed that the extending Algorithm II is feasible and easy to implement with relatively low computation load.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.40774099,10874202)the National High Technology Research and Development Program of China(Grant No.2008AA06Z205)
文摘Based on strong and weak forms of elastic wave equations, a Chebyshev spectral element method （SEM） using the Galerkin variational principle is developed by discretizing the wave equation in the spatial and time domains and introducing the preconditioned conjugate gradient （PCG）-element by element （EBE） method in the spatial domain and the staggered predictor/corrector method in the time domain. The accuracy of our proposed method is verified by comparing it with a finite-difference method （FDM） for a homogeneous solid medium and a double layered solid medium with an inclined interface. The modeling results using the two methods are in good agreement with each other. Meanwhile, to show the algorithm capability, the suggested method is used to simulate the wave propagation in a layered medium with a topographic traction free surface. By introducing the EBE algorithm with an optimized tensor product technique, the proposed SEM is especially suitable for numerical simulation of wave propagations in complex models with irregularly free surfaces at a fast convergence rate, while keeping the advantage of the finite element method.
文摘The subbottom profiling is an important means of marine engineering survey, hazardous geology study and continental shelf scientific research. The accuracy of subbottom profile data interpretation has a direct impact on the research and investigation results. Because some of profilers’ transducer and hydrophone are separately installed, when the survey area is very shallow, distortion of shallow layers will be caused if it is seen as a self-excited and self-collected single-channel seismic system. According to the principle of subbottom profiler, the distortion correction formula is deduced and analyzed, providing actual value to using C-View software to interpret such subbottom profile data more accurately. In addition, the seabed sediments sound velocity is one of the key parameters when acquiring and processing the subbottom profile data. On the basis of comparing some sound velocity forecasting empirical equations, the LU Bo’s equation was considered the most appropriate to predict the seabed sediments, sound velocity at near-shore of China. In a survey of an artificial island site, the LU Bo’s equation and the porosity data obtained from geological drilling were utilized to predict the sediments sound velocity, and the sound velocity structure profile was plotted, which was applied in processing the subbottom profile data of the artificial island investigation. The method of using porosity data to predict sediments sound velocity in processing subbottom profile data can improve the interpretation accuracy and it’s of practical significance.
基金Project (No. 1027054) supported by the National Natural Science Foundation of China
文摘Proximal point algorithms （PPA） are attractive methods for solving monotone variational inequalities （MVI）. Since solving the sub-problem exactly in each iteration is costly or sometimes impossible, various approximate versions ofPPA （APPA） are developed for practical applications. In this paper, we compare two APPA methods, both of which can be viewed as prediction-correction methods. The only difference is that they use different search directions in the correction-step. By extending the general forward-backward splitting methods, we obtain Algorithm Ⅰ; in the same way, Algorithm Ⅱ is proposed by spreading the general extra-gradient methods. Our analysis explains theoretically why Algorithm Ⅱ usually outperforms Algorithm Ⅰ. For computation practice, we consider a class of MVI with a special structure, and choose the extending Algorithm Ⅱ to implement, which is inspired by the idea of Gauss-Seidel iteration method making full use of information about the latest iteration. And in particular, self-adaptive techniques are adopted to adjust relevant parameters for faster convergence. Finally, some numerical experiments are reported on the separated MVI. Numerical results showed that the extending Algorithm II is feasible and easy to implement with relatively low computation load.
