基于广义正交多项式迭积微分算子的地震波场数值模拟研究

Seismic Numerical Modeling is one of bases of the Exploratory Seismology and Academic Seismology, also is a research field in great demand. Essence of seismic numerical modeling is to assume that structure and parameters of the underground media model are known, simulate the wave-field and calculate the numerical seismic record that should be observed. Seismic numerical modeling is not only a means to know the seismic wave-field in complex inhomogeneous media, but also a test to the application effect by all kinds of methods. There are many seismic numerical modeling methods, each method has its own merits and drawbacks. During the forward modeling, the computation precision and the efficiency are two pivotal questions to evaluate the validity and superiority of the method. The target of my dissertation is to find a new method to possibly improve the computation precision and efficiency, and apply the new forward method to modeling the wave-field in the complex inhomogeneous media. Convolutional Forsyte polynomial differentiator (CFPD) approach developed in this dissertation is robust and efficient, it shares some of the advantages of the high precision of generalized orthogonal polynomial and the high speed of the short operator finite-difference. By adjusting the operator length and optimizing the operator coefficient, the method can involve whole and local information of the wave-field. One of main tasks of the dissertation is to develop a creative, generalized and high precision method. The author introduce convolutional Forsyte polynomial differentiator to calculate the spatial derivative of seismic wave equation, and apply the time staggered grid finite-difference which can better meet the high precision of the convolutional differentiator to substitute the conventional finite-difference to calculate the time derivative of seismic wave equation, then creating a new forward method to modeling the wave-field in complex inhomogeneous media. Comparing with Fourier pseudo-spectral method, Chebyshev pseudo-spectral method, staggered- grid finite difference method and finite element method, convolutional Forsyte polynomial differentiator (CFPD) method has many advantages: 1. Comparing with Fourier pseudo-spectral method. Fourier pseudo-spectral method (FPS) is a local operator, its results have Gibbs effects when the media parameters change, then arose great errors. Therefore, Fourier pseudo-spectral method can not deal with special complex and random heterogeneous media. But convolutional Forsyte polynomial differentiator method can cover global and local information. So for complex inhomogeneous media, CFPD is more efficient. 2. Comparing with staggered-grid high-order finite-difference method, CFPD takes less dots than FD at single wave length, and the number does not increase with the widening of the studying area. 3. Comparing with Chebyshev pseudo-spectral method (CPS). The calculation region of Chebyshev pseudo-spectral method is fixed in , under the condition of unchangeable precision, the augmentation of calculation is unacceptable. Thus Chebyshev pseudo-spectral method is inapplicable to large area. CFPD method is more applicable to large area. 4. Comparing with finite element method (FE), CFPD can use lager grids. The other task of this dissertation is to study 2.5 dimension (2.5D) seismic wave-field. The author reviews the development and present situation of 2.5D problem, expatiates the essentiality of studying the 2.5D problem, apply CFPD method to simulate the seismic wave-field in 2.5D inhomogeneous media. The results indicate that 2.5D numerical modeling is efficient to simulate one of the sections of 3D media, 2.5D calculation is much less time-consuming than 3D calculation, and the wave dispersion of 2.5D modeling is obviously less than that of 3D modeling. Question on applying time staggered-grid convolutional differentiator based on CFPD to modeling 2.5D complex inhomogeneous media was not studied by any geophysicists before, it is a fire-new creation absolutely. The theory and practices prove that the new method can efficiently model the seismic wave-field in complex media. Proposing and developing this new method can provide more choices to study the seismic wave-field modeling, seismic wave migration, seismic inversion, and seismic wave imaging.

通过第一性原理计算研究内地核的结构与成分

The determination of the composition and structure of the Earth’s inner core has long been the major subject in the study of the Earth’s deep interior. It’s widely believed that the Earth’s core is formed by iron with a fraction of nickel. However, light elements must exist in the inner core because the earth core is less dense than pure iron-nickel alloy (~2-3% in the solid inner core and ~6-7% in the liquid outer core). The questions are what and how much light element is there in the iron-nickel alloy. Besides the composition, the crystal structure of the iron with or without light element is also not well known. According to the seismological observations, the sound waves propagate 3-4% faster along the spin axis than in the equatorial plane. That means the inner core is anisotropic. The densest structure of iron-nickel alloy should be h.c.p structure under the very high pressures. However, the h,c,p structure does not propagate waves anisotropic ally. Then what is the structure of the iron-nickel alloy or the iron-nickle-light element alloy. In this study, we tried to predict the composition and the structure of the inner core through ab initio calculation of the Gibbs free energy, which is a function of internal energy, density and entropy. We conclude that the h.c.p structure is more stable than the b.c.c structure under high pressure and 0 K, but with the increase of temperature, the free energy of the b.c.c structure is decreasing much faster than the h.c.p structure caused by the vibration of the atomics, so the b.c.c structure is more stable at high temperatures. With the addition of light elements (S or Si or both), the free energy of b.c.c. decreases even faster, about 3at% of Si not only explains why the inner core is about 2-3 % lighter than the iron-nickle alloy, but also reasons why the inner core is anisotropic, since the b.c.c. structure becomes more stable than the h.c.p structure at 5500-6000K and b.c.c. is anisotropic in propagating seismic waves. Therefore, we infer that the inner core of the earth is formed by b.c.c iron and a fraction of nickel plus ~3at.% Si, with a temperature higher than 5500K, which is consistent with the studies from other approaches.

超参数控制下的波阻抗约束反演

The seismic survey is the most effective geophysical method during exploration and development of oil/gas. As a main means in processing and interpreting seismic data, impedance inversion takes up a special position in seismic survey. This is because the impedance parameter is a ligament which connects seismic data with well-logging and geological information, while it is also essential in predicting reservoir properties and sand-body. In fact, the result of traditional impedance inversion is not ideal. This is because the mathematical inverse problem of impedance is poor-pose so that the inverse result has instability and multi-result, so it is necessary to introduce regularization. Most simple regularizations are presented in existent literature, there is a premise that the image(or model) is globally smooth. In fact, as an actual geological model, it not only has made of smooth region but also be separated by the obvious edge, the edge is very important attribute of geological model. It's difficult to preserve these characteristics of the model and to avoid an edge too smooth to clear. Thereby, in this paper, we propose a impedance inverse method controlled by hyperparameters with edge-preserving regularization, the inverse convergence speed and result would be improved. In order to preserve the edge, the potential function of regularization should satisfy nine conditions such as basic assumptions edge preservation and convergence assumptions etc. Eventually, a model with clear background and edge-abnormity can be acquired. The several potential functions and the corresponding weight functions are presented in this paper. The potential functionφLφHL andφGM can meet the need of inverse precision by calculating the models. For the local constant planar and quadric models, we respectively present the neighborhood system of Markov random field corresponding to the regularization term. We linearity nonlinear regularization by using half-quadratic regularization, it not only preserve the edge, and but also simplify the inversion, and can use some linear methods. We introduced two regularization parameters (or hyperparameters) λ2 and δ in the regularization term. λ2 is used to balance the influence between the data term and the transcendental term; δ is a calibrating parameter used to adjust the gradient value at the discontinuous position(or formation interface). Meanwhile, in the inverse procedure, it is important to select the initial value of hyperparameters and to change hyperparameters, these will then have influence on convergence speed and inverse effect. In this paper, we roughly give the initial value of hyperparameters by using a trend- curve of φ-(λ2, δ) and by a method of calculating the upper limit value of hyperparameters. At one time, we change hyperparameters by using a certain coefficient or Maximum Likelihood method, this can be simultaneously fulfilled with the inverse procedure. Actually, we used the Fast Simulated Annealing algorithm in the inverse procedure. This method overcame restrictions from the local extremum without depending on the initial value, and got a global optimal result. Meanwhile, we expound in detail the convergence condition of FSA, the metropolis receiving probability form Metropolis-Hasting, the thermal procession based on the Gibbs sample and other methods integrated with FSA. These content can help us to understand and improve FSA. Through calculating in the theoretic model and applying it to the field data, it is proved that the impedance inverse method in this paper has the advantage of high precision practicability and obvious effect.

Heat capacity enhancement and thermodynamic properties of nanostructured amorphous SiO2

The heat capacity of nanostructured amorphous SiO2 (na-SiO2) has been measured by adiabatic calorimetric method over the temperature range 9-354 K. TG and differential scanning calorimeter (DSC) were also employed to determine the thermal stability. Glass transition temperature (T-g) for the two same grain sizes with different specific surface of naSiO(2) samples and one coarse-grained amorphous SiO2 (ca-SiO2) sample were determined to be 1377, 1397 and 1320 K, respectively. The low temperature experimental results show that there are significant heat capacity (C-P) enhancements among na-SiO2 samples and ca-SiO2. Entropy, enthalpy, Gibbs free energy and Debye temperature (theta (D)) were obtained based on the low temperature heat capacity measurement of na-SiO2. The Cp enhancements of na-SiO2 were discussed in terms of configurational and vibrational entropy. (C) 2001 Elsevier Science B.V. All rights reserved.