Ray tracing is a basic aspect in tomography. To solve the caustic problem in inhomogeneous media using Maslov asymptotic theory, we need to calculate the position and slowness vector at every point. Therefore, ray tra...
详细信息
Ray tracing is a basic aspect in tomography. To solve the caustic problem in inhomogeneous media using Maslov asymptotic theory, we need to calculate the position and slowness vector at every point. Therefore, ray tracing must rely on the ray equations in Hamiltonian form. In this paper, fourth order symplectic scheme and nonsymplectic Runge-Kutta scheme are compared in ray tracing for sinusoidal velocity model. The result indicates that ray paths obtained by two schemes are almost the same. But on keeping Hamilton quantities, the symplectic scheme is far better than the Runge-Kutta scheme. On computing travel time for Htamiltonian system with T parameter, we use trapezoid formula for numerical integration. The result coincides with that obtained using Hamiltonian system with t parameter.
In this paper, we discuss the convergence properties of the memoryless quasi-Newton method proposed by Shanno (1978). In the two-dimensional quadratic case, we prove the global convergence of the method without any li...
详细信息
In this paper, we discuss the convergence properties of the memoryless quasi-Newton method proposed by Shanno (1978). In the two-dimensional quadratic case, we prove the global convergence of the method without any line search; if an exact line search is made at the first iteration, then the method gives the exact solution at most at the forth iteration. Numerical experiments further demonstrate these properties of the memoryless quasi-Newton method.
暂无评论