Stochastic generalized porous media equation with jump is considered. The aim is to show the moment exponential stability and the almost certain exponential stability of the stochastic equation.
An efficient approximate scheme is presented for wave-propagation simulation in piecewise heterogeneous media by applying the Born-series approximation to volume-scattering waves. The numerical scheme is tested for di...An efficient approximate scheme is presented for wave-propagation simulation in piecewise heterogeneous media by applying the Born-series approximation to volume-scattering waves. The numerical scheme is tested for dimensionless frequency responses to a heterogeneous alluvial valley where the velocity is perturbed randomly in the range of 5 %–25 %,compared with the full-waveform numerical solution. Then,the scheme is extended to a heterogeneous multilayered model by calculating synthetic seismograms to evaluate approximation accuracies Numerical experiments indicate that the convergence rate of this method decreases gradually with increasing velocity perturbations. The method has a fast convergence for velocity perturbations less than 15 %. However,the convergence becomes slow drastically when the velocity perturbation increases to 20 %. The method can hardly converge for the velocity perturbation up to 25 %.展开更多
基金Project supported by the Tianyuan Foundation of National Natural Science of China(No.11126079)the China Postdoctoral Science Foundation(No.2013M530559)the Fundamental Research Funds for the Central Universities(No.CDJRC10100011)
文摘Stochastic generalized porous media equation with jump is considered. The aim is to show the moment exponential stability and the almost certain exponential stability of the stochastic equation.
基金supported by the National Natural Science Foundation of China (Grant Nos. 41204097 and 41130418)the China National Major Science and Technology Project (2011ZX05023-005-004)
文摘An efficient approximate scheme is presented for wave-propagation simulation in piecewise heterogeneous media by applying the Born-series approximation to volume-scattering waves. The numerical scheme is tested for dimensionless frequency responses to a heterogeneous alluvial valley where the velocity is perturbed randomly in the range of 5 %–25 %,compared with the full-waveform numerical solution. Then,the scheme is extended to a heterogeneous multilayered model by calculating synthetic seismograms to evaluate approximation accuracies Numerical experiments indicate that the convergence rate of this method decreases gradually with increasing velocity perturbations. The method has a fast convergence for velocity perturbations less than 15 %. However,the convergence becomes slow drastically when the velocity perturbation increases to 20 %. The method can hardly converge for the velocity perturbation up to 25 %.
