Multitaper spectral method to estimate the elastic thickness of South China: Implications for intracontinental deformation

The effective elastic thickness （Te） represents the thickness of the elastic layer or the flexural rigidity of the lithosphere, the equivalent of which can be calculated from the spectral analysis of gravity and topographic data. Studies of Te have profound influence on intracontinental deformation, and coupling of the tectonic blocks. In this paper, we use the multitaper spectral estimation method to calculate the coherence between Bouguer gravity and topography data, and to obtain the Te map of South China. Through the process of correction, we discuss the relationships of Te versus heat flow, and Te versus seismicity. The results show that Te distribution of South China is affected by three factors：the original age, which controls the basic feature;the Mesozoic evolution, which affects the Te distribution;and the neotectonic movement, which shaped the final distribution. The crust age has a positive correlation with the first-order Te distribution;thus the Yangtze Craton has a relatively higher Te （about 50 km） whereas the Te in Cathaysia block is only 10e20 km. By analysis and comparison among the tectonic models of South China, the Te distribution can be well explained using the flat-subduction model. As is typical with neotectonics, the region with a higher heat flow is related with a lower Te. The seismicity does not have a clear relationship with Te, but the strong seismicity could cause a low Te. Seismogenic layer （Ts） has a similar trend as Te in the craton, whereas in other areas the relationship is complex.

Gradient estimates for parabolic systems from composite material

In this paper, we derive W^(1,∞) and piecewise C^(1,α) estimates for solutions, and their t-derivatives, of divergence form parabolic systems with coefficients piecewise H¨older continuous in space variables x and smooth in t. This is an extension to parabolic systems of results of Li and Nirenberg [Comm Pure Appl Math, 2003, 56:892–925] on elliptic systems. These estimates depend on the shape and the size of the surfaces of discontinuity of the coefficients, but are independent of the distance between these surfaces.

Waveguide invariant estimation in elastic Pekeris waveguide

Focus on sound intensity, particle velocity, complex sound intensity and waveguide impedance, the formation mechanism of interference structures in range-frequency domain for the above four kinds of physical quantities in Pekeris waveguides is analyzed based on Nor- mal Mode Theory. Also, a sea-trial with broadband radiated source is conducted to verify the analysis results. Both the simulation results and the analysis of sea-trial data indicate that, in range-frequency domain, the four kinds of physical quantities will exhibit a stable interfer- ence structure which can be expressed with waveguide invariant /3. Among these quantities, the coherent components of complex sound intensity can better reflect the interference char- acteristics of the waveguide. Finally, a multi-scale linear filter is introduced to deal with the sea-trial LOFAR （Low Frequency Analysis Recording） spectrum, the processing results show that the proposed filter can effectively enhance the interference characteristics in images, and conductively detect and extract striations＇ information from interference structures in LOFAR spectrum.

Superconvergence and recovery type a posteriori error estimation for hybrid stress finite element method

Superconvergence and recovery type a posteriori error estimators are analyzed for Pian and Sumihara's 4-node hybrid stress quadrilateral finite element method for linear elasticity problems. Superconvergence of order O(h^(1+min){α,1}) is established for both the displacement approximation in H^1-norm and the stress approximation in L^2-norm under a mesh assumption, where α > 0 is a parameter characterizing the distortion of meshes from parallelograms to quadrilaterals. Recovery type approximations for the displacement gradients and the stress tensor are constructed, and a posteriori error estimators based on the recovered quantities are shown to be asymptotically exact. Numerical experiments confirm the theoretical results.