Statistical methods of geophysical data processing /
This textbook contains a consideration of the wide field of problems connected with statistical methods of processing of observed data, with the main examples and considered models related to geophysics and seismic exploration. This textbook will be particularly helpful to students and professionals...
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| Format: | Electronic eBook |
| Language: | English |
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Singapore ; Hackensack, NJ ; London :
World Scientific,
©2010.
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| Online Access: | CONNECT |
Table of Contents:
- 1. Basic concepts of the probability theory. 1.1. The definition of probability. 1.2. Basic properties of probability. 1.3. Distribution functions. 1.4. The numerical characteristics of probability distributions. 1.5. Characteristic and generating functions. 1.6. The limit theorems. 1.7. Discrete distribution functions. 1.8. Continuous distributions. 1.9. Information and entropy. 1.10. Random functions and its properties
- 2. Elements of mathematical statistics. 2.1. The basic concepts of the decision theory. 2.2. Estimate properties
- 3. Models of measurement data. 3.1. Additive model. 3.2. Models of the quantitative interpretation. 3.3. Regression model. 3.4. The models of qualitative interpretation. 3.5. The models of qualitative-quantitative interpretation. 3.6. Random components of model and its properties. 3.7. Model with random parameters. 3.8. A priori information
- 4. The functional relationships of sounding signal fields and parameters of the medium. 4.1. Seismology and seismic prospecting. 4.2. Acoustics of the ocean. 4.3. Wave electromagnetic fields in geoelectrics and ionospheric sounding. 4.4. Atmospheric sounding
- 5. Ray theory of wave field propagation. 5.1. Basis of the Ray theory. 5.2. Ray method for the scalar wave equation. 5.3. Shortwave asymptotic form of the solution of the one-dimensional Helmholtz equation (WKB approximation). 5.4. The elements of elastic wave Ray theory. 5.5. The Ray description of almost-stratified medium. 5.6. Surface wave in vertically inhomogeneous medium. 5.7. Ray approximation of electromagnetic fields. 5.8. Statement of problem of the Ray kinematic tomography
- 6. Methods for parameter estimation of geophysical objects. 6.1. The method of moments. 6.2. Maximum likelihood method. 6.3. The Newton-Le Cam method. 6.4. The least squares method. 6.5. LSM
- nonlinear model. 6.6. LSM
- orthogonal polynomials (Chebyshev polynomials). 6.7. LSM
- case of linear constraints. 6.8. Linear estimation
- case of nonstationary model. 6.9. Bayes' criterion and method of statistical regularization. 6.10. Method of maximum a posteriori probability. 6.11. The recursion algorithm of MAP. 6.12. Singular analysis and least squares method. 6.13. The method of least modulus. 6.14. Robust methods of estimation. 6.15. Interval estimation. 6.16. The method of Backus and Gilbert of the linear inverse problem solution. 6.17. Genetic algorithm
- 7. Statistical criteria for choice of model. 7.1. Test of parametric hypothesis. 7.2. Criterion of a posteriori probability ratio. 7.3. The signal resolution problem. 7.4. Information criterion for the choice of the model. 7.5. The method of the separation of interfering signals
- 8. Algorithms of approximation of geophysical data. 8.1. The algorithm of univariate approximation by cubic splines. 8.2. Periodic and parametric spline functions. 8.3. Application of the spline functions for histogram smoothing. 8.4. Algorithms for approximation of seismic horizon subject to borehole observations. 8.5. Algorithm of approximation of formation velocity with the use of areal observations with borehole data
- 9. Elements of applied functional analysis for problem of estimation of the parameters of geophysical objects. 9.1. Elements of applied functional analysis. 9.2. Ill-posed problems. 9.3. Statistical estimation in the terms of the functional analysis. 9.4. Elements of the mathematical design of experiment
- 10. Construction and interpretation of tomographic functionals. 10.1. Construction of the model of measurements. 10.2. Tomographic functional. 10.3. Examples of construction and interpretation of tomographic functionals. 10.4. Ray tomographic functional in the dynamic and kinematic interpretation of the remote sounding data. 10.5. Construction of incident and reversed wave fields in layered reference medium
- 11. Tomography methods of recovering the image of medium. 11.1. Elements of linear tomography. 11.2. Connection of radon inversion with diffraction tomography. 11.3. Construction of algorithms of reconstruction tomography. 11.4. Errors of recovery, resolving length and backus and Gilbert method. 11.5. Back projection in diffraction tomography. 11.6. Regularization problems in 3-D ray tomography. 11.7. Construction of green function for some type of sounding signals. 11.8. Examples of the recovery of the local inhomogeneity parameters by the diffraction tomography method
- 12. Methods of transforms and analysis of the geophysical data. 12.1. Fourier transform. 12.2. Laplace transform. 12.3. Z-transform. 12.4. Radon transform for seismogram processing. 12.5. Gilbert transform and analytical signal. 12.6. Cepstral transform. 12.7. Bispectral analysis. 12.8. Kalman filtering. 12.9. Multifactor analysis and processing of time series. 12.10. Weiner filter. 12.11. Predictive-error filter and maximum entropy principle.
