局域Bjerhammar问题解算理论和断层位错引起的单层密度变化
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摘要
为了利用大地测量数据解算地壳内部密度时变 ,并为研究地震孕育过程和地震前兆中物质密度时变信息提供理论依据 ,研究了局域 Bjerhammar球面单层密度时变问题的平面解算理论 ;给出了不同投影下 Bjerhammar球面单层密度时变及相关重力位场的严格解式 ;导出了局域 Bjerhammar问题解算理论的使用条件 ,即满足一定精度要求的门限 R和ψ0 的严格解析关系式 ;给出了不同 Bjerhammar平面上的 q*t 之间的关系式 ,并根据一般迭代解算 q*t 的收敛特性 ,提出了空间域的分步迭代算法和空间域、波数域 (二步 )混合算法 ,从理论上解决了解算局域单层密度时变的稳定问题 (当 R较小或 H较大时 )。然后以此为基础 ,研究了位错引起的单层密度变化 ,并给出了不同点位错、断层位错类型引起的单层密度变化的解析表达式和断层位错在不同深度或不同 Bjerhammar球上引起的单层密度变化图像。
In order to solve the time change of crustal density from the geodetic data, and provide theorical bases for studying the earthquake precursor and the earthquake preparation process, first, the plane solving theory of the time change problem on Bjerhammar sphere are systematically and deeply studied and results are as follows: ①The strict formulas of the time change of the single layer density on the Bjerhammar sphere and its gravity potential or field among different projections are given; ②The application condition of the proximative plane solving theory on local Bjerhammar's problem are derived, it is the analytic formula strictly satisfying the threshold of R and q* t which adopted in accordance with certain precision requirement; ③The relation formula among the q* t on different Bjerhammar planes is given, and according to the convergence character of the general iteration for solving q* t, the algorithm of steping iteration in space field and the mixed algoritum in both the space and wave number field are presented, which theoretically resolves the stable problem of the time change of the local single layer density when R is smaller or H is larger. Based on the above, the single layer density caused by dislocation is studied and the following results are obtained: (1)The analytic formulas of the single layer density caused by point dislocation and fault dislocation; (2)The picture of the single layer density caused by fault dislocation.
In order to solve the time change of crustal density from the geodetic data, and provide theorical bases for studying the earthquake precursor and the earthquake preparation process, first, the plane solving theory of the time change problem on Bjerhammar sphere are systematically and deeply studied and results are as follows: ①The strict formulas of the time change of the single layer density on the Bjerhammar sphere and its gravity potential or field among different projections are given; ②The application condition of the proximative plane solving theory on local Bjerhammar's problem are derived, it is the analytic formula strictly satisfying the threshold of R and q* t which adopted in accordance with certain precision requirement; ③The relation formula among the q* t on different Bjerhammar planes is given, and according to the convergence character of the general iteration for solving q* t, the algorithm of steping iteration in space field and the mixed algoritum in both the space and wave number field are presented, which theoretically resolves the stable problem of the time change of the local single layer density when R is smaller or H is larger. Based on the above, the single layer density caused by dislocation is studied and the following results are obtained: (1)The analytic formulas of the single layer density caused by point dislocation and fault dislocation; (2)The picture of the single layer density caused by fault dislocation.
引文
1 许厚泽 ,朱灼文 .地球外部重力场的虚拟单层密度表示 .中国科学 (B辑 ) ,1 984,(6) :575～ 580 .
2 夏哲仁 ,蒋福珍 .外部重力场及地球内部密度时间变化的联合确定 .测绘学报 ,1 990 ,1 9(3) :2 0 0～ 2 0 7.
3 操华胜 ,朱灼文 ,王晓岚 .地球重力场的虚拟单层密度表示理论的数字实现 ,测绘学报 ,1 985,1 4 (4) :2 62～2 73.
4 申重阳 ,甘家思 ,朱思林 ,等 .点位错引起的单层密度变化 .地壳形变与地震 ,1 997,1 7(1 ) :1～ 9.
5 申重阳 ,朱思林 ,蒋福珍 ,等 .重力和形变资料联合反演地壳密度时变的一种方法 .地壳形变与地震 ,1 996,1 6(3) :1 4～ 2 1 .
6 申重阳 ,甘家思 ,朱思林 ,等 .Bjerhammar球面单层密度的平面近似算法 .地震研究文集 (3) .北京 :地震出版社 ,1 996,36～ 41 .
7 申重阳 .Bjerhammar球面单层密度时间变化的实用解算理论 .地壳形变与地震 ,1 999,1 9(2 ) :9～ 1 6.
8 力武常次 ,佐藤良辅 ,荻原幸男编著 .地球科学中的数学物理方法 (下册 ) .北京 :地震出版社 ,1 988,1 34～1 37.
9 Okubo S. Gravity and potential changesdueto shearand tensilefaultsin a half- space.JGR,1 992 ,97(B5) :71 34～ 71 4 4 .
1 0 Okada Y. Surface deformation due to shear and tensile faults in half- pace.Bll.Seism.Soc.Am,1 985,75:1 1 35～ 1 1 54.
1 1 Bjerhammar A. A new theory of gravimetric geodesy.Royal Institute of Technology,Division ofGeodesy,Stockholm,1 963.
1 2 Okubo S.Potential and gravity changes raised by point dislocation.Geophys.J.Int.,1 991 ,1 0 5:573～586
2 夏哲仁 ,蒋福珍 .外部重力场及地球内部密度时间变化的联合确定 .测绘学报 ,1 990 ,1 9(3) :2 0 0～ 2 0 7.
3 操华胜 ,朱灼文 ,王晓岚 .地球重力场的虚拟单层密度表示理论的数字实现 ,测绘学报 ,1 985,1 4 (4) :2 62～2 73.
4 申重阳 ,甘家思 ,朱思林 ,等 .点位错引起的单层密度变化 .地壳形变与地震 ,1 997,1 7(1 ) :1～ 9.
5 申重阳 ,朱思林 ,蒋福珍 ,等 .重力和形变资料联合反演地壳密度时变的一种方法 .地壳形变与地震 ,1 996,1 6(3) :1 4～ 2 1 .
6 申重阳 ,甘家思 ,朱思林 ,等 .Bjerhammar球面单层密度的平面近似算法 .地震研究文集 (3) .北京 :地震出版社 ,1 996,36～ 41 .
7 申重阳 .Bjerhammar球面单层密度时间变化的实用解算理论 .地壳形变与地震 ,1 999,1 9(2 ) :9～ 1 6.
8 力武常次 ,佐藤良辅 ,荻原幸男编著 .地球科学中的数学物理方法 (下册 ) .北京 :地震出版社 ,1 988,1 34～1 37.
9 Okubo S. Gravity and potential changesdueto shearand tensilefaultsin a half- space.JGR,1 992 ,97(B5) :71 34～ 71 4 4 .
1 0 Okada Y. Surface deformation due to shear and tensile faults in half- pace.Bll.Seism.Soc.Am,1 985,75:1 1 35～ 1 1 54.
1 1 Bjerhammar A. A new theory of gravimetric geodesy.Royal Institute of Technology,Division ofGeodesy,Stockholm,1 963.
1 2 Okubo S.Potential and gravity changes raised by point dislocation.Geophys.J.Int.,1 991 ,1 0 5:573～586
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