The intersection method is one of the basic approaches for locating earthquakes and is not only robust but also efficient. However, its location accuracy is not high, especially for focal depth because the velocity mo...The intersection method is one of the basic approaches for locating earthquakes and is not only robust but also efficient. However, its location accuracy is not high, especially for focal depth because the velocity model used for the conventional intersection method is based on homogeneous or laterally homogeneous media, which is too simple. In order to improve the accuracy, we have modified the existing intersection method. In the modified approach, the earthquake loci are not assumed to be circular or hyperbolic and calculation accuracy is improved using a minimum traveltime tree algorithm for tracing rays. The numerical model shows that the modified method can locate earthquakes in complex velocity models.展开更多
In this paper, we present a novel geometric method for efficiently and robustly computing intersections between a ray and a triangular Bezier patch defined over a triangular domain, called the hybrid clipping （HC） a...In this paper, we present a novel geometric method for efficiently and robustly computing intersections between a ray and a triangular Bezier patch defined over a triangular domain, called the hybrid clipping （HC） algorithm. If the ray pierces the patch only once, we locate the parametric value of the intersection to a smaller triangular domain, which is determined by pairs of lines and quadratic curves, by using a multi-degree reduction method. The triangular domain is iteratively clipped into a smaller one by combining a subdivision method, until the domain size reaches a prespecified threshold. When the ray intersects the patch more than once, Descartes＇ rule of signs and a split step are required to isolate the intersection points. The algorithm can be proven to clip the triangular domain with a cubic convergence rate after an appropriate preprocessing procedure. The proposed algorithm has many attractive properties, such as the absence of an initial guess and insensitivity to small changes in coefficients of the original problem. Experiments have been conducted to illustrate the efficacy of our method in solving ray-triangular Bezier patch intersection problems.展开更多
For the underwater long baseline(LBL)positioning systems,the traditional distance intersection algorithm simplifies the sound speed to a constant,and calculates the underwa-ter target position parameters with a nonlin...For the underwater long baseline(LBL)positioning systems,the traditional distance intersection algorithm simplifies the sound speed to a constant,and calculates the underwa-ter target position parameters with a nonlinear iteration.However,due to the complex underwater environment,the sound speed changes with time and space,and then the acoustic propagation path is actually a curve,which inevitably causes some errors to the traditional distance intersection positioning algorithm.To reduce the position error caused by the uncertain underwater sound speed,a new time of arrival(TOA)intersection underwater positioning algorithm of LBL system is proposed.Firstly,combined with the vertical layered model of the underwater sound speed,an implicit positioning model of TOA intersection is constructed through the constant gradient acoustic ray tracing.And then an optimization function based on the overall TOA residual square sum is advanced to solve the position parameters for the underwater target.Moreover,the particle swarm optimization(PSO)algorithm is replaced with the tra-ditional nonlinear least square method to optimize the implicit positioning model of TOA intersection.Compared with the traditional distance intersection positioning model,the TOA intersec-tion positioning model is more suitable for the engineering practice and the optimization algorithm is more effective.Simulation results show that the proposed methods in this paper can effectively improve the positioning accuracy for the underwater target.展开更多
基金This work is supported by the National Natural Science Foundation of China(40674044)the Special Foundation for Basic Professional Scientific Research (DQJB06A02)
文摘The intersection method is one of the basic approaches for locating earthquakes and is not only robust but also efficient. However, its location accuracy is not high, especially for focal depth because the velocity model used for the conventional intersection method is based on homogeneous or laterally homogeneous media, which is too simple. In order to improve the accuracy, we have modified the existing intersection method. In the modified approach, the earthquake loci are not assumed to be circular or hyperbolic and calculation accuracy is improved using a minimum traveltime tree algorithm for tracing rays. The numerical model shows that the modified method can locate earthquakes in complex velocity models.
基金Project supported by the National Natural Science Foundation of China （Nos. 61100105, 61572020, and 61472332）, the Natural Science Foundation of Fujian Province of China （No. 2015J01273）, and the Fundamental Research Funds for the Central Universities, China （Nos. 20720150002 and 20720140520）
文摘In this paper, we present a novel geometric method for efficiently and robustly computing intersections between a ray and a triangular Bezier patch defined over a triangular domain, called the hybrid clipping （HC） algorithm. If the ray pierces the patch only once, we locate the parametric value of the intersection to a smaller triangular domain, which is determined by pairs of lines and quadratic curves, by using a multi-degree reduction method. The triangular domain is iteratively clipped into a smaller one by combining a subdivision method, until the domain size reaches a prespecified threshold. When the ray intersects the patch more than once, Descartes＇ rule of signs and a split step are required to isolate the intersection points. The algorithm can be proven to clip the triangular domain with a cubic convergence rate after an appropriate preprocessing procedure. The proposed algorithm has many attractive properties, such as the absence of an initial guess and insensitivity to small changes in coefficients of the original problem. Experiments have been conducted to illustrate the efficacy of our method in solving ray-triangular Bezier patch intersection problems.
基金supported by the National Natural Science Foundation of China(61903086,61903366,62001115)the Natural Science Foundation of Hunan Province(2019JJ50745,2020JJ4280,2021JJ40133)the Fundamentals and Basic of Applications Research Foundation of Guangdong Province(2019A1515110136).
文摘For the underwater long baseline(LBL)positioning systems,the traditional distance intersection algorithm simplifies the sound speed to a constant,and calculates the underwa-ter target position parameters with a nonlinear iteration.However,due to the complex underwater environment,the sound speed changes with time and space,and then the acoustic propagation path is actually a curve,which inevitably causes some errors to the traditional distance intersection positioning algorithm.To reduce the position error caused by the uncertain underwater sound speed,a new time of arrival(TOA)intersection underwater positioning algorithm of LBL system is proposed.Firstly,combined with the vertical layered model of the underwater sound speed,an implicit positioning model of TOA intersection is constructed through the constant gradient acoustic ray tracing.And then an optimization function based on the overall TOA residual square sum is advanced to solve the position parameters for the underwater target.Moreover,the particle swarm optimization(PSO)algorithm is replaced with the tra-ditional nonlinear least square method to optimize the implicit positioning model of TOA intersection.Compared with the traditional distance intersection positioning model,the TOA intersec-tion positioning model is more suitable for the engineering practice and the optimization algorithm is more effective.Simulation results show that the proposed methods in this paper can effectively improve the positioning accuracy for the underwater target.
