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《Progress in Geophysics》 2007-02
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The significance of seismic wave field equations matrices and the energy positive definite quadratic form

NIU Bin-hua1,SUN Sheng1,SUN Chun-yan2,HUANG Xin-wu2,LI Jia1(1.School of Geophysics & Information Technology,China University of Geosciences,Beijing 100083,China2.School of Engineering & Technology,China University of Geosciences,Beijing 100083,China)  
"Field equations"-wave equations,velocity equations and energy equations-can represent the overall characteristic of the half space seismic wave field.This paper firstly pointed out that there is a field equation matrix for each of the equations.Secondly we analyzed and revealed that energy equations can be integrated into all field equation matrixes,and presented the generally adaptive expression of the energy equations based on the elastic matrix.At last the consistently symmetrical and positive definite properties between the energy matrices and the elastic matrices are clarified by using the theory of positive definite quadratic form of matrices.The physical meaning of the dynamical equilibrium relationships,velocity space-time distribution and energy propagation involved in the energy matrices can be described by the positive definite quadratic form of the energy matrices.The analytical methods and conclusions used and presented in this paper can be applied to such complex models as porous,viscoelastic and anisotropic medium.
【Fund】: 国家自然科学基金49974028项目;; 40474043项目;; 国家十五863计划海洋天然气水合物地震识别技术项目;; 国家十五863计划时间推移地震数学模型项目;; 国家十五863计划海洋天然气水合物地球化学勘查技术项目资助;; 中国地质大学(北京)“地下信息探测技术与仪器”和“岩石圈构造、深部过程及探测技术”教育部重点实验室联合资助
【CateGory Index】: P315
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