Second-order Stokes wave solutions for intefacial waves in three-layer stratified fluid with background current

In this paper, interfacial waves in three-layer stratified fluid with background current are investigated using a perturbation method, and the second-order asymptotic solutions of the velocity potentials and the second-order Stokes wave solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory, and the Kelvin-Helmholtz instability of interfacial waves is studied. As expected, for three-layer stratified fluid with background current, the first-order asymptotic solutions (linear wave solutions), dispersion relation and the second-order asymptotic solutions derived depend on not only the depths and densities of the three-layer fluid but also the background current of the fluids, and the second-order Stokes wave solutions of the associated elevations of the interfacial waves describe not only the second-order nonlinear wave-wave interactions between the interfacial waves but also the second-order nonlinear interactions between the interfacial waves and currents. It is also noted that the solutions obtained from the present work include the theoretical results derived by Chen et al (2005) as a special case. It also shows that with the given wave number k (real number) the interfacial waves may show Kelvin-Helmholtz instability.

A kind of extended Korteweg-de Vries equation and solitary wave solutions for interfacial waves in a two-fluid system

This paper considers interfacial waves propagating along the interface between a two-dimensional two-fluid with a flat bottom and a rigid upper boundary. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. It just focuses on the weakly non-linear small amplitude waves by introducing two small independent parameters: the nonlinearity ratio epsilon, represented by the ratio of amplitude to depth, and the dispersion ratio mu, represented by the square of the ratio of depth to wave length, which quantify the relative importance of nonlinearity and dispersion. It derives an extended KdV equation of the interfacial waves using the method adopted by Dullin et al in the study of the surface waves when considering the order up to O(mu(2)). As expected, the equation derived from the present work includes, as special cases, those obtained by Dullin et al for surface waves when the surface tension is neglected. The equation derived using an alternative method here is the same as the equation presented by Choi and Camassa. Also it solves the equation by borrowing the method presented by Marchant used for surface waves, and obtains its asymptotic solitary wave solutions when the weakly nonlinear and weakly dispersive terms are balanced in the extended KdV equation.

青藏高原横波速度与各向异性结构及其壳幔形变印迹

As the most spectacular and youngest case of continental collision on the Earth, to investigate the crust and mantle of Tibetan plateau, and then to reveal its characters of structure and deformation, are most important to understand its deformation mechanism and deep process. A great number of surface wave data were initially collected from events occurred between 1980 and 2002, which were recorded by 13 broadband digital stations in Eurasia and India. Up to 1,525 source-station Rayleigh waveforms and 1,464 Love wave trains were analysed to obtain group velocity dispersions, accompanying with the detail and quantitative assessment of the fitness of the classic Ray Theory, errors from focal and measurements. Assuming the model region covered by a mesh of 2ox2o-sized grid-cells, we have used the damped least-squares approach and the SVD to carry out tomographic inversion, SV- and SH-wave velocity images of the crust and upper mantle beneath the Tibetan Plateau and surroundings are obtained, and then the radial anisotropy is computed from the Love-Rayleigh discrepancy. The main results demonstrate that follows, a) The Moho beneath the Tibetan Plateau presents an undulating shape that lies between 65 and 74 km, and a clear correlation between the elevations of the plateau and the Moho topography suggests that at least a great part of the highly raised plateau is isostatically compensated. b) The lithospheric root presents a depth that can be substantiated at ~140 km (Qiangtang Block) and exceptionally at ~180 km (Lhasa Block), and exhibits laterally varying fast velocity between 4.6 and 4.7 km/s, even ~4.8 km/s under northern Lhasa Block and Qiangtang Block, which may be correlated with the presence of a shield-like upper mantle beneath the Tibetan Plateau and therefore looked as one of the geophysical tests confirming the underthrusting of India, whose leading edge might have exceeded the Bangong-Nujiang Suture, even the Jinsha Suture. c) The asthenosphere is depicted by a low velocity channel at depths between 140 and 220 km with negative velocity gradient and velocities as low as 4.2 km/s; d) Areas in which transverse radial anisotropy is in excess of ~4% and 6% on the average anisotropy are found in the crust and upper mantle underlying most of the Plateau, and up to 8% in some places. The strength, spatial configuration and sign of radial anisotropy seem to indicate the existence of a regime of horizontal compressive forces in the frame of the convergent orogen at the same time that laterally varying lithospheric rheology and a differential movement as regards the compressive driving forces. e) Slow-velocity anomalies of 12% or more in southern Tibet and the eastern edge of the Plateau support the idea of a mechanically weak middle-to-lower crust and the existence of crustal flow in Tibet.

利用台阵面波资料研究华北克拉通北缘燕山褶皱带及其邻区的地壳与上地幔结构

The continent of eastern China, especially the North China Craton (NCC), has endured intensive tectonic renovation during Mesozoic and Cenozoic, with the presence of widespread magmatism, high heat flow and development of large sedimentary basins and mountain ranges. The cratonic lithosphere of the region has been destroyed remarkably, which is characterized by not only a significant reduction in thickness but also complex modifications in physical and chemical properties of the lithosphere. As for the tectonic regime controlling the evolution of the NCC, various models have been put forward, including the impingement of mantle plumes (“mushroom cloud” model), the collision of south China block and north China block, the subduction of the Pacific plate, etc. Lithosphere delamination and thermal erosion were proposed as the two end-member mechanisms of the lithospheric thinning. However, given the paucity of the data, deep structural evidence is currently still scarce for distinguishing and testifying these models. To better understand the deep structure of the NCC, from 2000 to the present, temporary seismic array observations have been conducted in the NCC by the Seismological Laboratory of the Institute of the Geology and Geophysics, Chinese Academy of Sciences under the North China Interior Structure Project (NCISP). Many arrays extend from the North China Craton and the off-craton regions, and traverse a lot of main tectonic boundaries. A total of more than 300 broadband seismic stations have been deployed along several profiles that traversed the major tectonic units within the craton’s interior, at the boundary areas and in the neighboring off-craton regions. These stations recorded abundant high-quality data, which provides an unprecedented opportunity for us to unravel the deep structural features of the NCC using seismological methods. Among all the seismological methods, the surface wave method appears to be an efficient and widely adopted technique in studying the crustal and upper mantle structures. In particular, it can provide the absolute values of S-wave velocity that are difficult to obtain with other methods. Benefiting from the deployment of dense seismic arrays, progresses have been made in improving the spatial resolution of surface wave imaging, which makes it possible to resolve the fine-scale velocity structures of the crust and upper mantle based on surface wave analysis. Meanwhile, the differences in the S-wave velocities derived from Rayleigh and Love wave data can provide information on the radial anisotropy beneath the seismic arrays. In this thesis, using the NCISP-III broadband data and based on phase velocity dispersion analysis and inversion of fundamental mode Rayleigh and Love waves, I investigated the lateral variations in the S-wave velocity structure of the crust and uppermost mantle beneath the Yanshan Belt and adjacent regions at the northeastern boundary of the NCC. Based on the constructed structural images, I discussed possible deep processes of the craton destruction in the study region.

The experimental studies on electrical conductivities and P-wave velocities of anorthosite at high pressure and high temperature

National Science Foundation of China (No. 10032040 and No. 49874013) and Joint Earthquake Science Foundation of China (No. 101119).