Generally speaking, the factors of both medium and tectonic that give rise to heterogeneity of the earth crust and mantle structures should be taken into account simultaneously in three dimensional seismic ray tracin...Generally speaking, the factors of both medium and tectonic that give rise to heterogeneity of the earth crust and mantle structures should be taken into account simultaneously in three dimensional seismic ray tracing. In this paper, the three dimensional structure models are constructed with the model similar to generation system in computer aid design and manufacturing (CAD/CAM). Based on the algorithm proposed by Cerveny et al . for complete seismic ray tracing in complex three dimensional structures, a new technique called the indirect approach method for two point seismic ray tracing in three dimensional laterally heterogeneous media has been put forward, and its numerical computing examples were given.展开更多
The variational data assimilation scheme (VAR) is applied to investigating the advective effect and the evolution of the control variables in time splitting semi-Lagrangian framework. Two variational algorithms are us...The variational data assimilation scheme (VAR) is applied to investigating the advective effect and the evolution of the control variables in time splitting semi-Lagrangian framework. Two variational algorithms are used. One is the conjugate code method-direct approach, and another is the numerical backward integration of analytical adjoint equation—indirect approach. Theoretical derivation and sensitivity tests are conducted in order to verify the consistency and inconsistency of the two algorithms under the semi-Lagrangian framework. On the other hand, the sensitivity of the perfect and imperfect initial condition is also tested in both direct and indirect approaches. Our research has shown that the two algorithms are not only identical in theory, but also identical in numerical calculation. Furthermore, the algorithms of the indirect approach are much more feasible and efficient than that of the direct one when both are employed in the semi-Lagrangian framework. Taking advantage of semi-Lagrangian framework, one purpose of this paper is to illustrate when the variational assimilation algorithm is concerned in the computational method of the backward integration, the algorithm is extremely facilitated. Such simplicity in indirect approach should be meaningful for the VAR design in passive model. Indeed, if one can successfully split the diabatic and adiabatic process, the algorithms represented in this paper might be easily used in a more general vision of atmospheric model.展开更多
波函数法(Wave Based Method,WBM)是近年来发展的基于间接Trefftz理论的结构—声辐射中频问题的一种重要方法。WBM函数收敛的充要条件是分析域为凸域。为提高使用WBM理论的应用范围和应用效率,根据多层次模型,提出了补域概念用于解决凹...波函数法(Wave Based Method,WBM)是近年来发展的基于间接Trefftz理论的结构—声辐射中频问题的一种重要方法。WBM函数收敛的充要条件是分析域为凸域。为提高使用WBM理论的应用范围和应用效率,根据多层次模型,提出了补域概念用于解决凹域问题。最后,以一个周边简支矩形薄板为例进行验证数值,计算结果表明了方法准确性和有效性。展开更多
文摘Generally speaking, the factors of both medium and tectonic that give rise to heterogeneity of the earth crust and mantle structures should be taken into account simultaneously in three dimensional seismic ray tracing. In this paper, the three dimensional structure models are constructed with the model similar to generation system in computer aid design and manufacturing (CAD/CAM). Based on the algorithm proposed by Cerveny et al . for complete seismic ray tracing in complex three dimensional structures, a new technique called the indirect approach method for two point seismic ray tracing in three dimensional laterally heterogeneous media has been put forward, and its numerical computing examples were given.
文摘The variational data assimilation scheme (VAR) is applied to investigating the advective effect and the evolution of the control variables in time splitting semi-Lagrangian framework. Two variational algorithms are used. One is the conjugate code method-direct approach, and another is the numerical backward integration of analytical adjoint equation—indirect approach. Theoretical derivation and sensitivity tests are conducted in order to verify the consistency and inconsistency of the two algorithms under the semi-Lagrangian framework. On the other hand, the sensitivity of the perfect and imperfect initial condition is also tested in both direct and indirect approaches. Our research has shown that the two algorithms are not only identical in theory, but also identical in numerical calculation. Furthermore, the algorithms of the indirect approach are much more feasible and efficient than that of the direct one when both are employed in the semi-Lagrangian framework. Taking advantage of semi-Lagrangian framework, one purpose of this paper is to illustrate when the variational assimilation algorithm is concerned in the computational method of the backward integration, the algorithm is extremely facilitated. Such simplicity in indirect approach should be meaningful for the VAR design in passive model. Indeed, if one can successfully split the diabatic and adiabatic process, the algorithms represented in this paper might be easily used in a more general vision of atmospheric model.
文摘波函数法(Wave Based Method,WBM)是近年来发展的基于间接Trefftz理论的结构—声辐射中频问题的一种重要方法。WBM函数收敛的充要条件是分析域为凸域。为提高使用WBM理论的应用范围和应用效率,根据多层次模型,提出了补域概念用于解决凹域问题。最后,以一个周边简支矩形薄板为例进行验证数值,计算结果表明了方法准确性和有效性。
