Applied Seismic Wave Theory
Applied Seismic Wave Theory
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发表时间：
1987
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通讯作者：
A. Berkhout
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作者：
A. Berkhout
导论. I. Capita Selecta来自Vector Analysis。标量积，梯度，旋度和散度。斯托克斯定理、高斯定理和绿色定理。二.一维离散谱分析。δ脉冲和离散函数。周期时间函数的傅里叶级数。瞬态的傅里叶积分。离散性与周期性的关系。时间和频率的采样和混叠。基质制剂。将宽带实验分解为单色模拟。三.多维离散谱分析基本理论。空间混叠。二维谱分析与平面波分解。扩展到三个维度。四.震动基本概念。自由振动。强迫振动。耦合系统。从振动到波动。五、声波。声波方程的推导。声波方程的单向形式。平面波。球面波柱面波。声波方程数值模拟原理。六.弹性波均匀各向同性固体中的压缩波。均匀各向同性固体中的剪切波。弹性波方程的推导。弹性波方程的单向形式。弹性波动方程数值模拟原理。七.边界条件声学边界的反射和透射系数。卷积中的反射。流体-固体边界。弹性边界的反射和透射系数。摘要八.基尔霍夫和瑞利积分均匀介质基尔霍夫积分的推导。均匀介质瑞利积分的推导。卷积形式的瑞利积分。Rayleigh积分到波数域的变换。非均匀类流体介质的基尔霍夫和瑞利积分。瑞利积分作为基尔霍夫积分的单向版本。基尔霍夫积分的离散形式。离散形式的瑞利积分。摘要九.波场的方向性。傅立叶积分的夫琅和费近似。方向性模式。散射波场的远场表达式。摘要X.正问题和逆问题。波场单程正演延拓原理单向逆波场外推原理双向技术原则。Example.摘要(Each第一章包括导言和参考文献）。附录。主题索引。
Introduction. I. Capita Selecta from Vector Analysis. Scalar product, gradient, curl and divergence. Theorem of Stokes, theorem of Gauss and Green's theorem. II. One-Dimensional Discrete Spectral Analysis. The delta pulse and discrete functions. Fourier series of periodic time functions. Fourier integral of transients. Relationship between the discrete property and periodicity. Sampling and aliasing in time and frequency. Matrix formulations. Decomposition of a broad band experiment into monochromatic simulations. III. Multi-Dimensional Discrete Spectral Analysis. Basic theory. Spatial aliasing. Two-dimensional spectral analysis and plane wave decomposition. Extensions to three dimensions. IV. Vibrations. Basic concepts. Free vibrations. Forced vibrations. Coupled systems. From vibrations to waves. V. Acoustic Waves. Derivation of the acoustic wave equation. One-way versions of the acoustic wave equation. Plane waves. Spherical waves. Cylindrical waves. Principle of numerical modeling with the acoustic wave equation. VI. Elastic Waves. Compressional waves in homogeneous isotropic solids. Shear waves in homogeneous isotropic solids. Derivation of the elastic wave equation. One-way versions of the elastic wave equation. Principle of numerical modeling with the elastic wave equation. VII. Boundary Conditions. Reflection and transmission coefficients for acoustic boundaries. Reflection in terms of convolution. The fluid-solid boundary. Reflection and transmission coefficients for elastic boundaries. Summary. VIII. Kirchhoff and Rayleigh Integrals. Derivation of the Kirchhoff integral for homogeneous media. Derivation of the Rayleigh integrals for homogeneous media. Rayleigh integrals in terms of convolution. Transformation of Rayleigh integrals to the wave number domain. Kirchhoff and Rayleigh integrals for inhomogeneous fluid-like media. Rayleigh integrals as one-way versions of the Kirchhoff integral. Discrete version of the Kirchhoff integral. Discrete versions of the Rayleigh integrals. Summary. IX. Directivity Properties of Wave Fields. Fraunhofer approximations in terms of the Fourier integral. Directivity patterns. Far field expressions of scattered wave fields. Summary. X. Forward and Inverse Problems. Principle of one-way forward wave field extrapolation. Principle of one-way inverse wave field extrapolation. Principle of two-way techniques. Example. Summary. (Each chapter includes an introduction and references). Appendices. Subject Index.