Classic L2-norm-based waveform tomography is often plagued by insurmountable cycle skipping problems;as a result,the iterative inversion falls into local minima,yielding erroneous images.According to the optimal trans...Classic L2-norm-based waveform tomography is often plagued by insurmountable cycle skipping problems;as a result,the iterative inversion falls into local minima,yielding erroneous images.According to the optimal transportation theory,we adopt a novel geometry-preserving misfit function based on the quadratic Wasserstein metric(W2-norm),which improves the stability and convexity of the inverse problem.Numerical experiments illustrate that W2-norm-based full-waveform tomography has a larger convergence radius and a faster convergence rate than the L2-norm and can effectively mitigate cycle skipping issues.We apply this method to the Longmen Shan area and obtain a reliable lithospheric velocity model.Our tomographic results indicate that the crystalline crust underlying the Sichuan Basin wedges into the crustal interior of the Tibetan Plateau,and the mid-lower crust of the eastern Tibetan Plateau is characterized by low shear-wave velocities,indicating that ductile crustal flow and strong interactions between terranes jointly dominate the uplift behavior of the Longmen Shan.Furthermore,we find that large earthquakes(e.g.,the Wenchuan and Lushan events)occur not only at the junction between high-and low-velocity regions but also in the transition zone from positive to negative radial anisotropy.These findings improve our understanding of the mechanism responsible for large earthquakes in this region.展开更多
We consider the relativistic Euler equations governing spherically symmetric,perfect fluid flows on the outer domain of communication of Schwarzschild spacetime,and we introduce a version of the finite volume method w...We consider the relativistic Euler equations governing spherically symmetric,perfect fluid flows on the outer domain of communication of Schwarzschild spacetime,and we introduce a version of the finite volume method which is formulated from the geometric formulation(and thus takes the geometry into account at the discretization level)and is well-balanced,in the sense that it preserves steady solutions to the Euler equations on the curved geometry under consideration.In order to formulate our method,we first derive a closed formula describing all steady and spherically symmetric solutions to the Euler equations posed on Schwarzschild spacetime.Second,we describe a geometry-preserving,finite volume method which is based from the family of steady solutions to the Euler system.Our scheme is second-order accurate and,as required,preserves the family of steady solutions at the discrete level.Numerical experiments are presented which demonstrate the efficiency and robustness of the proposed method even for solutions containing shock waves and nonlinear interacting wave patterns.As an application,we investigate the late-time asymptotics of perturbed steady solutions and demonstrate its convergence for late time toward another steady solution,taking the overall effect of the perturbation into account.展开更多
基金supported by the National Key R&D Program of China(Grant No.2017YFC1500301)the National Natural Science Foundation of China(Grant Nos.U1839206,42004077)。
文摘Classic L2-norm-based waveform tomography is often plagued by insurmountable cycle skipping problems;as a result,the iterative inversion falls into local minima,yielding erroneous images.According to the optimal transportation theory,we adopt a novel geometry-preserving misfit function based on the quadratic Wasserstein metric(W2-norm),which improves the stability and convexity of the inverse problem.Numerical experiments illustrate that W2-norm-based full-waveform tomography has a larger convergence radius and a faster convergence rate than the L2-norm and can effectively mitigate cycle skipping issues.We apply this method to the Longmen Shan area and obtain a reliable lithospheric velocity model.Our tomographic results indicate that the crystalline crust underlying the Sichuan Basin wedges into the crustal interior of the Tibetan Plateau,and the mid-lower crust of the eastern Tibetan Plateau is characterized by low shear-wave velocities,indicating that ductile crustal flow and strong interactions between terranes jointly dominate the uplift behavior of the Longmen Shan.Furthermore,we find that large earthquakes(e.g.,the Wenchuan and Lushan events)occur not only at the junction between high-and low-velocity regions but also in the transition zone from positive to negative radial anisotropy.These findings improve our understanding of the mechanism responsible for large earthquakes in this region.
基金supported by the Centre National de la Recherche ScientifiqueThe authors were supported by the Agence Nationale de la Recherche through the grants ANR 2006-2-134423 and ANR SIMI-1-003-01.
文摘We consider the relativistic Euler equations governing spherically symmetric,perfect fluid flows on the outer domain of communication of Schwarzschild spacetime,and we introduce a version of the finite volume method which is formulated from the geometric formulation(and thus takes the geometry into account at the discretization level)and is well-balanced,in the sense that it preserves steady solutions to the Euler equations on the curved geometry under consideration.In order to formulate our method,we first derive a closed formula describing all steady and spherically symmetric solutions to the Euler equations posed on Schwarzschild spacetime.Second,we describe a geometry-preserving,finite volume method which is based from the family of steady solutions to the Euler system.Our scheme is second-order accurate and,as required,preserves the family of steady solutions at the discrete level.Numerical experiments are presented which demonstrate the efficiency and robustness of the proposed method even for solutions containing shock waves and nonlinear interacting wave patterns.As an application,we investigate the late-time asymptotics of perturbed steady solutions and demonstrate its convergence for late time toward another steady solution,taking the overall effect of the perturbation into account.
