저작근 근전도에 관한 정상교합자와 ii급 부정교합자의 비교 연구

Preface Bibliography 1. Interpolation. Introduction The Taylor expansion The finite Taylor series with the remainder term Interpolation by polynomials The remainder of Lagrangian interpolation formula Equidistant interpolation Local and global interpolation Interpolation by central differences Interpolation around the midpoint of the range The Laguerre polynomials Binomial expansions The decisive integral transform Binomial expansions of the hypergeometric type Recurrence relations The Laplace transform The Stirling expansion Operations with the Stirling functions An integral transform of the Fourier type Recurrence relations associated with the Stirling series Interpolation of the Fourier transform The general integral transform associated with the Stirling series Interpolation of the Bessel functions 2. Harmonic Analysis. Introduction The Fourier series for differentiable functions The remainder of the finite Fourier expansion Functions of higher differentiability An alternative method of estimation The Gibbs oscillations of the finite Fourier series The method of the Green's function Non-differentiable functions Dirac's delta function Smoothing of the Gibbs oscillations by Fejer's method The remainder of the arithmetic mean method Differentiation of the Fourier series The method of the sigma factors Local smoothing by integration Smoothing of the Gibbs oscillations by the sigma method Expansion of the delta function The triangular pulse Extension of the class of expandable functions Asymptotic relations for the sigma factors The method of trigonometric interpolation Error bounds for the trigonometric interpolation method Relation between equidistant trigonometric and polynomial interpolations The Fourier series in the curve fitting 3. Matrix Calculus. Introduction Rectangular matrices The basic rules of matrix calculus Principal axis transformation of a symmetric matrix Decomposition of a symmetric matrix Self-adjoint systems Arbitrary n x m systems Solvability of the general n x m system The fundamental decomposition theorem The natural inverse of a matrix General analysis of linear systems Error analysis of linear systems Classification of linear systems Solution of incomplete systems Over-determined systems The method of orthogonalisation The use of over-determined systems The method of successive orthogonalisation The bilinear identity Minimum property of the smallest eigenvalue 4. The Function Space. Introduction The viewpoint of pure and applied mathematics The language of geometry Metrical spaces of infinitely many dimensions The function as a vector The differential operator as a matrix The length of a vector The scalar product of two vectors The closeness of the algebraic approximation The adjoint operator The bilinear identity The extended Green's identity The adjoint boundary conditions Incomplete systems Over-determined systems Compatibility under inhomogeneous boundary conditions Green's identity in the realm of partial differential operators The fundamental field operations of vector analysis Solution of incomplete systems 5. The Green's Function. Introduction The role of the adjoint equation The role of Green's identity The delta function -- The existence of the Green's function Inhomogeneous boundary conditions The Green's vector Self-adjoint systems The calculus of variations The canonical equations of Hamilton The Hamiltonisation of partial operators The reciprocity theorem Self-adjoint problems Symmetry of the Green's function Reciprocity of the Green's vector The superposition principle of linear operators The Green's function in the realm of ordinary differential operators The change of boundary conditions The remainder of the Taylor series The remainder of the Lagrangian interpolation formula

Linear Differential Operators. By C. Lanczos. Pp. 580. 80s. 1961. (Van Nostrand, London)

Metamorphic chemical geodynamics in continental subduction zones

Today, surface-wave analysis is widely adopted for building near-surface S-wave velocity models. The surface-wave method is under continuous and rapid evolution, also thanks to the lively scientific debate among different disciplines, and interest in the technique has increased significantly during the last decade. A comprehensive review of the literature in the main scientific journals provides historical perspective, methodological issues, applications, and most-promising recent approaches. Higher modes in the inversion and retrieval of lateral variations are dealt with in great detail, and the current scientific debate on these topics is reported. A best-practices guideline is also outlined.

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Surface-wave analysis for building near-surface velocity models — Established approaches and new perspectives

The theory of the dynamic bulk modulus, K(ω), of a porous rock, whose saturation occurs in patches of 100% saturation each of two different fluids, is developed within the context of the quasi-static Biot theory. The theory describes the crossover from the Biot–Gassmann–Woods result at low frequencies to the Biot–Gassmann–Hill result at high. Exact results for the approach to the low and the high frequency limits are derived. A simple closed-form analytic model based on these exact results, as well as on the properties of K(ω) extended to the complex ω-plane, is presented. Comparison against the exact solution in simple geometries for the case of a gas and water saturated rock demonstrates that the analytic theory is extremely accurate over the entire frequency range. Aside from the usual parameters of the Biot theory, the model has two geometrical parameters, one of which is the specific surface area, S/V, of the patches. In the special case that one of the fluids is a gas, the second parameter is a different, but also simple, measure of the patch size of the stiff fluid. The theory, in conjunction with relevant experiments, would allow one to deduce information about the sizes and shapes of the patches or, conversely, to make an accurate sonic-to-seismic conversion if the size and saturation values are approximately known.

Theory of Frequency Dependent Acoustics in Patchy-Saturated Porous Media

Multichannel Analysis of Surface Waves (MASW) analysis is an efficient tool to obtain the vertical shear-wave profile. One of the key steps in the MASW method is to generate an image of dispersive energy in the frequency-velocity domain, so dispersion curves can be determined by picking peaks of dispersion energy. In this paper, we propose to image Rayleigh-wave dispersive energy by high-resolution linear Radon transform (LRT). The shot gather is first transformed along the time direction to the frequency domain and then the Rayleigh-wave dispersive energy can be imaged by high-resolution LRT using a weighted preconditioned conjugate gradient algorithm. Synthetic data with a set of linear events are presented to show the process of generating dispersive energy. Results of synthetic and real-world examples demonstrate that, compared with the slant stacking algorithm, high-resolution LRT can improve the resolution of images of dispersion energy by more than 50%.

Rayleigh-wave dispersive energy imaging using a high-resolution linear radon transform

Quantitative estimation of minimum offset for multichannel surface-wave survey with actively exciting source

We present a new algorithm for calculating an image of dispersive energy in the frequency-velocity (f-v) domain. The frequency decomposition is first applied to a shot gather in the offset-time domain to stretch impulsive data into pseudo-vibroseis data or frequency-swept data. Because there is a deterministic relationship between frequency and time in a sweep used in the frequency decomposition, the first step theoretically completes the transform from time to frequency. The slant stacking is then performed on the frequency-swept data to complete the transform from offset to velocity. This simple two-step algorithm generates an image of dispersive energy in the f-v domain. The straightforward transform only uses offset information of data so that this algorithm can be applied to data acquired with arbitrary geophone-acquisition geometry. Examples of synthetic and real-world data demonstrate that this algorithm generates accurate images of dispersive energy of the fundamental as well as higher modes.

Generating an image of dispersive energy by frequency decomposition and slant stacking

Yinhe Luo,1,2 Yingjie Yang,3 Yixian Xu,1,2 Hongrui Xu,1 Kaifeng Zhao1 and Kai Wang1 1Hubei Subsurface Multi-scale Imaging Lab (SMIL), Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan, Hubei 430074, China. E-mail: luoyinhe@cug.edu.cn 2State Key Laboratory of Geological Processes and Mineral Resources, China University of Geosciences, Wuhan, Hubei 430074, China 3ARC Centre of Excellence for Core to Crust Fluid Systems (CCFS)/GEMOC, Department of Earth and Planetary Sciences, Macquarie University, North Ryde, NSW 2109, Australia

On the limitations of interstation distances in ambient noise tomography

As theory dictates, for a series of horizontal layers, a pure, plane, horizontally polarized shear (SH) wave refracts and reflects only SH waves and does not undergo wave-type conversion as do incident P or Sv waves. This is one reason the shallow SH-wave refraction method is popular. SH-wave refraction method usually works well defining near-surface shear-wave velocities. Only first arrival information is used in the SH-wave refraction method. Most SH-wave data contain a strong component of Love-wave energy. Love waves are surface waves that are formed from the constructive interference of multiple reflections of SH waves in the shallow subsurface. Unlike Rayleigh waves, the dispersive nature of Love waves is independent of P-wave velocity. Love-wave phase velocities of a layered earth model are a function of frequency and three groups of earth properties: SH-wave velocity, density, and thickness of layers. In theory, a fewer parameters make the inversion of Love waves more stable and reduce the degree of nonuniqueness. Approximating SH-wave velocity using Love-wave inversion for near-surface applications may become more appealing than Rayleigh-wave inversion because it possesses the following three advantages. (1) Numerical modeling results suggest the independence of P-wave velocity makes Love-wave dispersion curves simpler than Rayleigh waves. A complication of “Mode kissing” is an undesired and frequently occurring phenomenon in Rayleigh-wave analysis that causes mode misidentification. This phenomenon is less common in dispersion images of Love-wave energy. (2) Real-world examples demonstrated that dispersion images of Love-wave energy have a higher signal-to-noise ratio and more focus than those generated from Rayleigh waves. This advantage is related to the long geophone spreads commonly used for SH-wave refraction surveys, images of Love-wave energy from longer offsets are much cleaner and sharper than for closer offsets, which makes picking phase velocities of Love waves easier and more accurate. (3) Real-world examples demonstrated that inversion of Love-wave dispersion curves is less dependent on initial models and more stable than Rayleigh waves. This is due to Love-wave’s independence of P-wave velocity, which results in fewer unknowns in the MALW method compared to inversion methods of Rayleigh waves. This characteristic not only makes Love-wave dispersion curves simpler but also reduces the degree of nonuniqueness leading to more stable inversion of Love-wave dispersion curves.

Yixian Xu

Papers

Rayleigh-wave dispersive energy imaging using a high-resolution linear radon transform

Quantitative estimation of minimum offset for multichannel surface-wave survey with actively exciting source

Generating an image of dispersive energy by frequency decomposition and slant stacking

On the limitations of interstation distances in ambient noise tomography

Advantages of Using Multichannel Analysis of Love Waves (MALW) to Estimate Near-Surface Shear-Wave Velocity