The inverse problems of wave equation to recover unknown space-time dependent functions of wave speed and wave source are solved in this paper, without needing of initial conditions and no internal measurement of data...The inverse problems of wave equation to recover unknown space-time dependent functions of wave speed and wave source are solved in this paper, without needing of initial conditions and no internal measurement of data being required. After a homogenization technique, a sequence of spatial boundary functions at least the fourth-order polynomials are derived, which satisfy the homogeneous boundary conditions. The boundary functions and the zero element constitute a linear space, and then a new boundary functional is proved in the linear space, of which the energy is preserved for each dynamic energetic boundary function. The linear systems and iterative algorithms used to recover unknown wave speed and wave source functions with the dynamic energetic boundary functions as bases are developed, which converge fast at each time step. The input data are parsimonious, merely the measured boundary strains and the boundary values and slopes of unknown functions to be recovered. The accuracy and robustness of present methods are confirmed by comparing exact solutions with estimated results under large noises up to 20%.展开更多
Based on the rotation in the entire block and homogeneous strain model ( REHSM) ,we firstly analyze the motion and deformation features across the southern part of Tancheng- Lujiang fault zone from GPS velocity fields...Based on the rotation in the entire block and homogeneous strain model ( REHSM) ,we firstly analyze the motion and deformation features across the southern part of Tancheng- Lujiang fault zone from GPS velocity fields in period of 1999 ～ 2001,2001 ～ 2004,2004 ～ 2007 and 2007 ～ 2009. The results show a dextral strike-slip feature in the Weifang- Tancheng segment and sinistral strike-slip in the Tancheng-Lujiang segment. And the deformation perpendicular to the Tancheng-Lujiang fault zone alternates between tension and compression in different time-intervals. Then we resolve the relative rigid motion of blocks around Bohai Bay to the Circum-Bohai Sea area by deducting the entire rigid motion of the Circum-Bohai Sea area. We find that the Yanshan-Bohai seismic belt split this area into two parts,the northern part moving NW,and the other SE.展开更多
文摘The inverse problems of wave equation to recover unknown space-time dependent functions of wave speed and wave source are solved in this paper, without needing of initial conditions and no internal measurement of data being required. After a homogenization technique, a sequence of spatial boundary functions at least the fourth-order polynomials are derived, which satisfy the homogeneous boundary conditions. The boundary functions and the zero element constitute a linear space, and then a new boundary functional is proved in the linear space, of which the energy is preserved for each dynamic energetic boundary function. The linear systems and iterative algorithms used to recover unknown wave speed and wave source functions with the dynamic energetic boundary functions as bases are developed, which converge fast at each time step. The input data are parsimonious, merely the measured boundary strains and the boundary values and slopes of unknown functions to be recovered. The accuracy and robustness of present methods are confirmed by comparing exact solutions with estimated results under large noises up to 20%.
基金sponsored by the Basic Research Project of Institute of Earthquake Science,China Earthquake Administration ( 2011IES010102)
文摘Based on the rotation in the entire block and homogeneous strain model ( REHSM) ,we firstly analyze the motion and deformation features across the southern part of Tancheng- Lujiang fault zone from GPS velocity fields in period of 1999 ～ 2001,2001 ～ 2004,2004 ～ 2007 and 2007 ～ 2009. The results show a dextral strike-slip feature in the Weifang- Tancheng segment and sinistral strike-slip in the Tancheng-Lujiang segment. And the deformation perpendicular to the Tancheng-Lujiang fault zone alternates between tension and compression in different time-intervals. Then we resolve the relative rigid motion of blocks around Bohai Bay to the Circum-Bohai Sea area by deducting the entire rigid motion of the Circum-Bohai Sea area. We find that the Yanshan-Bohai seismic belt split this area into two parts,the northern part moving NW,and the other SE.
