特大地震激发地球自由振荡的数值模拟研究

Large earthquakes, such as the Chile earthquake in 1960 and the Sumatra-Andaman earthquake on Dec 26, 2004 in Indonesia, have generated the Earth’s free oscillations. The eigenfrequencies of the Earth’s free oscillations are closely related to the Earth’s internal structures. The conventional methods, which mainly focus on calculating the eigenfrequecies by analytical ways, and the analysis on observations can not easily study the whole processes from earthquake occurrence to the Earth’s free oscillation inspired. Therefore, we try to use numerical method incorporated with large-scale parallel computing to study on the Earth’s free oscillations excited by giant earthquakes. We first give a review of researches and developments of the Earth’s free oscillation, and basical theories under spherical coordinate system. We then give a review of the numerical simulation of seismic wave propagation and basical theories of spectral element method to simulate global seismic wave propagation. As a first step to study the Earth’s free oscillations, we use a finite element method to simulate the propagation of elastic waves and the generation of oscillations of the chime bell of Marquis Yi of Zeng, by striking different parts of the bell, which possesses the oval crosssection. The bronze chime bells of Marquis Yi of Zeng are precious cultural relics of China. The bells have a two-tone acoustic characteristic, i.e., striking different parts of the bell generates different tones. By analysis of the vibration in the bell and the spectrum analysis, we further help the understanding of the mechanism of two-tone acoustic characteristics of the chime bell of Marquis Yi of Zeng. The preliminary calculations have clearly shown that two different modes of oscillation can be generated by striking different parts of the bell, and indicate that finite element numerical simulation of the processes of wave propagation and two-tone generation of the chime bell of Marquis Yi of Zeng is feasible. These analyses provide a new quantitative and visual way to explain the mystery of the two-tone acoustic characteristics. The method suggested by this study can be applied to simulate free oscillations excited by great earthquakes with complex Earth structure. Taking into account of such large-scale structure of the Earth, small-scale low-precision numerical simulation can not simply meet the requirement. The increasing capacity in high-performance parallel computing and progress on fully numerical solutions for seismic wave fields in realistic three-dimensional spherical models, Spectral element method and high-performance parallel computing were incorporated to simulate the seismic wave propagation processes in the Earth’s interior, without the effects of the Earth’s gravitational potential. The numerical simulation shows that, the results of the toroidal modes of our calculation agree well with the theoretical values, although the accuracy of our results is much limited, the calculated peaks are little distorted due to three-dimensional effects. There exist much great differences between our calculated values of spheroidal modes and theoretical values, because we don’t consider the effect the Earth’ gravitation in numerical model, which leads our values are smaller than the theoretical values. When , is much smaller, the effect of the Earth’s gravitation make the periods of spheroidal modes become shorter. However, we now can not consider effects of the Earth’s gravitational potential into the numerical model to simulate the spheroidal oscillations, but those results still demonstrate that, the numerical simulation of the Earth’s free oscillation is very feasible. We make the numerical simulation on processes of the Earth’s free oscillations under spherically symmetric Earth model using different special source mechanisms. The results quantitatively show that Earth’s free oscillations excited by different earthquakes are different, and oscillations at different locations are different for free oscillation excited by the same earthquake. We also explore how the Earth’s medium attenuation will take effects on the Earth’s free oscillations, and take comparisons with the observations. The medium attenuation can make influences on the Earth’s free oscillations, though the effects on lower-frequency fundamental oscillations are weak. At last, taking 2008 Wenchuan earthquake for example, we employ spectral element method incorporated with large-scale parallel computing technology to investigate the characteristics of seismic wave propagation excited by Wenchuan earthquake. We calculate synthetic seismograms with one-point source model and three-point source model respectively. Full 3-D visualization of the numerical results displays the profile of the seismic wave propagation with respect to time. The three-point source, which was proposed by the latest investigations through field observation and reverse estimation, can better demonstrate the spatial and temporal characteristics of the source rupture processes than one-point source. Primary results show that those synthetic signals calculated from three-point source agree well with the observations. This can further reveal that the source rupturing process of Wenchuan earthquake is a multi-rupture process, which is composed by at least three or more stages of rupture processes. In conclusion, the numerical simulation can not only solve some problems concluding the Earth’s ellipticity and anisotropy, which can be easily solved by conventional methods, but also finally solve the problems concluding topography model and lateral heterogeneity. We will try to find a way to fully implement self-gravitation in spectral element method in future, and do our best to continue researching the Earth’s free oscillations using the numerical simulations to see how the Earth’ lateral heterogeneous will affect the Earth’s free oscillations. These will make it possible to bring modal spectral data increasingly to bear on furthering our understanding of the Earth’s three-dimensional structure.

各向同性与各向异性介质中地震波旅行时正演模拟与反演成像

By seismic tomography, interesting results have been achieved not only in the research of the geosphere with a large scale but also in the exploration of resources and projects with a small scale since 80'. Compared with traditional inversion methods, seismic tomography can offer more and detailed information about subsurface and has been being paid attention by more and more geophysicists. Since inversion based on forward modeling, we have studied and improved the methods to calculate seismic traveltimes and raypaths in isotropic and anisotropic media, and applied the improved forward methods to traveltime tomography. There are three main kinds of methods to calculate seismic traveltime field and its ray path distribution, which are ray-tracing theory, eikonal equation by the finite-difference and minimum traveltime tree algorithm. In ray tracing, five methods are introduced in the paper, including analytic ray tracing, ray shooting, ray bending, grid ray tracing and rectangle grid ray perturbation with three points. Finite-difference solution of eikonal equation is very efficient in calculation of seismic first-break, but is awkward in calculation of reflection traveltimes. We have put forward a idea to calculate traveltimes of reflected waves using a combining way of eikonal equation method and other one in order to improve its capability of dealing with reflection waves. The minimum traveltime tree algorithm has been studied with emphases. Three improved algorithms are put forward on the basis of basic algorithm of the minimum traveltime tree. The first improved algorithm is called raypath tracing backward minimum traveltime algorithm, in which not only wavelets from the current source but also wavelets from upper source points are all calculated. The algorithm can obviously improve the speed of calculating traveltimes and raypaths in layered or blocked homogeneous media and keep good accuracy. The second improved algorithm is raypath key point minimum traveltime algorithm in which traveltimes and raypaths are calculated with a view of key points of raypaths (key points of raypths mean the pivotal points which determine raypaths). The raypath key point method is developed on the basis of the first improved algorithm, and has better applicability. For example, it is very efficient even for inhomogeneous media. Another improved algorithm, double grid minimum traveltime tree algorithm, bases upon raypath key point scheme, in which a model is divided with two kinds of grids so that the unnecessary calculation can be left out. Violent undulation of curved interface often results in the phenomenon that there are no reflection points on some parts of interfaces where there should be. One efficacious scheme that curved interfaces are divided into segments, and these segments are treated respectively is presented to solve the problem. In addition, the approximation to interfaces with discrete grids leads to large errors in calculation of traveltimes and raypaths. Noting the point, we have thought a new method to remove the negative effect of mesh and to improve calculation accuracy by correcting the traveltimes with a little of additional calculation, and obtained better results.

三种权重赋值方法下项目的权重决策

It is a weighting process to justify the importance of different items. This paper is about how the estimator distributes profiling the weights to different items. This paper is about using design of psychological experiment to figure out the profiles of the weights of different ranked items in three weighting methods, and in the experiment we use five topics as experimental materials. At the same time, we controlled the factors such as the familiarity about the topic and the number of items. Then we use the curve estimation to figure out the exact profiles and use ANOVA to test the topic effects. Curve estimation result shows that there is difference between the profiles of the weights of different ranking items in three weighting methods. To PA, the weighting profile is logarithmic curving style, and to DR, the weighting profile is linear style. ANOVA result shows that there are topic effects to different weighting profiles. But to go ahead, when we use point allocation (PA) to the more important items, the topics seems to have little effects. The methods have relatively more effect than the topics. The result also indicates that to PA methods, there is no significant difference the weight profiles between the fix-sum and the open-sum. This result has a contribution to the basic research to the management science and social science.