Generalized reliability measures of Kalman filtering for precise point positioning

To deal with the adverse influence of model failures on Kalman filtering （KF） estimation, it is necessary to investigate the generalized reliability theory, including the model failure detection and identification method as well as the separability and reliability theories. Although the generalized reliability theory for the least square has been discussed for many decades, the generalized reliability theory of KF is not widely discussed. Compared with the least square, KF includes not only the measurement model, but also the dynamic model. In KF, the predicted value of the state parameters from the dynamic model is considered as pseudomeasurements and combined with the observed measurements to compose the form of the least square. According to the reliability of the least square, the generalized reliability of KF is derived. Then, the dynamic model failure of precise point positioning is simulated to demonstrate the usage of the generalized reliability theory. The results show that the adverse influence of the dynamic model failure is more severe than that of the measurement model. Moreover, it is recommended that the model failure identification should always be used even if the overall model test passes. It is shown that the derived generalized reliability measures are suitable for the generalized KF estimation.

Boundary integral equations for dynamic rupture propagation on vertical complex fault system in half-space:Theory

The boundary integral equation method （BIEM） is now widely used in numerical studies on earthquake rupture dynamics, and is proved to be a powerful tool to deal with problems on complex fault system. However, since this method heavily lies on the specific forms of Green＇s function and only the Green＇s function in full-space has a closed analytic expression, it is usually limited to a full-space medium. In this study, as a first step to extend this method to an arbitrary complex fault system in half-space, the boundary integral equations （BIEs） for dynamic strike-slip on vertical complex fault system in half-space are derived based on exact Green＇s function for isotropic and homogeneous half-space. Effect of the geometry of the complex fault system are dealt with carefully. Final BIEs is composed of two parts： contribution from full-space, which has been thoroughly investigated by Aochi and his co-workers by using the Green＇s function for full-space, and that from free surface, which is studied in detail in this study.