Second-order solutions for random interfacial waves in N-layer density-stratified fluid with steady uniform currents

In the present paper, the random inter facial waves in N-layer density-stratified fluids moving at different steady uniform speeds are researched by using an expansion technique, and the second-order a symptotic solutions of the random displacements of the density interfaces and the associated velocity potentials in N-layer fluid are presented based on the small amplitude wave theory. The obtained results indicate that the wave-wave second-order nonlinear interactions of the wave components and the second-order nonlinear interactions between the waves and currents are described. As expected, the solutions include those derived by Chen (2006) as a special case where the steady uniform currents of the N-layer fluids are taken as zero, and the solutions also reduce to those obtained by Song (2005) for second-order solutions for random interfacial waves with steady uniform currents if N=2.

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.

基于量子蒙特卡罗的地震波反演方法

The primary approaches for people to understand the inner properties of the earth and the distribution of the mineral resources are mainly coming from surface geology survey and geophysical/geochemical data inversion and interpretation. The purpose of seismic inversion is to extract information of the subsurface stratum geometrical structures and the distribution of material properties from seismic wave which is used for resource prospecting, exploitation and the study for inner structure of the earth and its dynamic process. Although the study of seismic parameter inversion has achieved a lot since 1950s, some problems are still persisting when applying in real data due to their nonlinearity and ill-posedness. Most inversion methods we use to invert geophysical parameters are based on iterative inversion which depends largely on the initial model and constraint conditions. It would be difficult to obtain a believable result when taking into consideration different factors such as environmental and equipment noise that exist in seismic wave excitation, propagation and acquisition. The seismic inversion based on real data is a typical nonlinear problem, which means most of their objective functions are multi-minimum. It makes them formidable to be solved using commonly used methods such as general-linearization and quasi-linearization inversion because of local convergence. Global nonlinear search methods which do not rely heavily on the initial model seem more promising, but the amount of computation required for real data process is unacceptable. In order to solve those problems mentioned above, this paper addresses a kind of global nonlinear inversion method which brings Quantum Monte Carlo (QMC) method into geophysical inverse problems. QMC has been used as an effective numerical method to study quantum many-body system which is often governed by Schrödinger equation. This method can be categorized into zero temperature method and finite temperature method. This paper is subdivided into four parts. In the first one, we briefly review the theory of QMC method and find out the connections with geophysical nonlinear inversion, and then give the flow chart of the algorithm. In the second part, we apply four QMC inverse methods in 1D wave equation impedance inversion and generally compare their results with convergence rate and accuracy. The feasibility, stability, and anti-noise capacity of the algorithms are also discussed within this chapter. Numerical results demonstrate that it is possible to solve geophysical nonlinear inversion and other nonlinear optimization problems by means of QMC method. They are also showing that Green’s function Monte Carlo (GFMC) and diffusion Monte Carlo (DMC) are more applicable than Path Integral Monte Carlo (PIMC) and Variational Monte Carlo (VMC) in real data. The third part provides the parallel version of serial QMC algorithms which are applied in a 2D acoustic velocity inversion and real seismic data processing and further discusses these algorithms’ globality and anti-noise capacity. The inverted results show the robustness of these algorithms which make them feasible to be used in 2D inversion and real data processing. The parallel inversion algorithms in this chapter are also applicable in other optimization. Finally, some useful conclusions are obtained in the last section. The analysis and comparison of the results indicate that it is successful to bring QMC into geophysical inversion. QMC is a kind of nonlinear inversion method which guarantees stability, efficiency and anti-noise. The most appealing property is that it does not rely heavily on the initial model and can be suited to nonlinear and multi-minimum geophysical inverse problems. This method can also be used in other filed regarding nonlinear optimization.

岩石磨蚀性和TBM滚刀磨损机理研究

Using the popular CERCHAR testing to measure the abrasiveness of rock which is CERCHAR abrasiveness index(CAI). The digital imagine processing program IPP is used to quantify the rock texture such as the grain size, the shape of grain and the index of grain homogeneity. And the rock mechanical testing machine are used to measure the strength, hardness and elastic modulus. Basic on these three experiments, this paper finds the relationship between the CAI and physical and mechanical properties of rock. They are both the mesostructure and macroscopical properties of rock. According to the theory of tribology and wear, this paper finds the disc cutter wear mechanism during the machine and rock interaction process. The detail research results are as follows: (1) The size and form of the mineral grains constituting the rocks affect the abrasiveness of the rock. The rock abrasiveness CAI is a function of the product of the texture coefficient(TC) multiplying equivalent quarts content(Q%). (2) There is no obvious relationship between the rock abrasiveness CAI and the single macroscopical property of rock such as hardness, unconfined compressive strength, tensile strength and elastic modulus. But when taking the texture coefficient(TC) and the mineral composition in consideration, it shows that the rock abrasiveness CAI is relative to the combination of the rock mechanical property, the texture coefficient(TC) and the mineral composition. That is to say various factors which are from the mesostructure feature to the macroscopical property of rock control the rock abrasiveness. (3) The disc cutter penetrating into rock is a machine/rock interaction process. During this interaction, the wear of disc cutter is mainly coming from the abrasive of abrasiveness matters. First, the surface of the cutter ring is hunched, and then the material of the cutter ring is being wiped off during the iterative interaction. Second, the hard mineral in the rock and the muck will microcosmic cutting the surface material of cutter ring. (4) The disc cutters consumption is determined by the machine parameters and the geology condition. The machine parameters include the thrust and the revolution rate of the cutterhead. The geology condition include two aspects: the macroscopical properties which are the strength and/or hardness of rock, the presence of discontinuities in rock mass, the hardness, sharp, edge and size of the muck and so on. And the mesostructure features which are the hard mineral composition, the sharp and size of the grain of the rock.

末次盛冰期以来中国陆地生态系统碳储量变化研究

Carbon is an essential element for life, food and energy. It is also a key element in the greenhouse gases and therefore plays a vital role in climatic changes. The rapid increase in atmospheric concentration of CO_2 over the past 150 years, reaching current concentrations of about 370 ppmv, corresponds with combustion of fossii fuels since the beginning of the industrial age. Conversion of forested land to agricultural use has also redistributed carbon from plants and soils to the atmosphere. These human activities have significantly altered the global carbon cycle. Understanding the consequences of these activities in the coming decades is critical for formulating economic, energy, technology, trade, and security policies that will affect civilization for generations. Under the auspices of the International Geosphere-Biosphere Programme (IGBP), several large international scientific efforts are focused on elucidating the various aspects of the global carbon cycle of the past decade. It is only possible to balance the global carbon cycle for the 1990s if there is net carbon uptake by terrestrial ecosystems of around 2 Pg C/a. There are now some independent, direct evidences for the existence of such a sink. Policymarkers involved in the UN Framework Convention on Climate Change (UN-FCCC) are striving to reach consensuses on a 'safe path' for future emissions, the credible predictions on where and how long the terrestrial sink will either persist at its current level, or grow/decline in the future, are important to advice the policy process. The changes of terrestrial carbon storage depend not only on human activities, but also on biogeochemical and climatological processes and their interaction with the carbon cycles. In this thesis, the climate-induced changes and human-induced changes of carbon storage in China since the past 20,000 years are examined. Based on the data of the soil profiles investigated during China's Second National Soil Survey (1979-1989), the forest biomass measured during China's Fourth National Forest Resource Inventory (1989-1993), the grass biomass investigated during the First National Grassland Resource Survey (1980-1991), and the data collected from a collection of published literatures, the current terrestrial carbon storage in China is estimated to -144.1 Pg C, including -136.8 Pg C in soil and -7.3 Pg C in vegetation. The soil organic (SOC) and inorganic carbon (SIC) storage are -78.2 Pg C and -58.6 Pg C, respectively. In the vegetation reservoir, the forest carbon storage is -5.3 Pg C, and the other of-1.4 Pg C is in the grassland. Under the natural conditions, the SOC, SIC, forest and grassland carbon storage are -85.3 Pg C, -62.6 Pg C, -24.5 Pg C and -5.3 Pg C, respectively. Thus, -29.6 Pg C organic carbon has been lost due to land use with a decrease of -20.6%. At the same time, the SIC storage also has been decreased by -4.0 Pg C (-6.4%). These suggest that human activity has caused significant carbon loss in terrestrial carbon storage of China, especially in the forest ecosystem (-76% loss). Using the Paleocarbon Model (PCM) developed by Wu et al. in this paper, total terrestrial organic carbon storage in China in the Last Glacial Maximum (LGM) was -114.8 Pg C, including -23.1 Pg C in vegetation and -86.7 Pg C in soil. At the Middle Holocene (MH), the vegetation, soil and total carbon were -37.3 Pg C, -93.9 Pg C and -136.0 Pg C, respectively. This implies a gain of-21.2 Pg C in the terrestrial carbon storage from LGM to HM mainly due to the temperature increase. However, a loss of-14.4 Pg C of terrestrial organic carbon occurred in China under the current condition (before 1850) compared with the MH time, mainly due to the precipitation decrease associated with the weakening of the Asian summer monsoon. These results also suggest that the terrestrial ecosystem in China has a substantial potential in the restoration of carbon storage. This might be expected to provide an efficient way to mitigate the greenhouse warming through land management practices. Assuming that half of the carbon loss in the degraded terrestrial ecosystem in current forest and grass areas are restored during the next 50 years or so, the terrestrial ecosystem in China may sequestrate -12.0 Pg of organic carbon from the atmosphere, which represents a considerable offset to the industry's CO2 emission. If the ' Anthropocene' Era will be another climate optimum like MH due to the greenhouse effect, the sequestration would be increased again by -4.3 - 9.0 Pg C in China.