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 from various fields of physics, connected with an estimation of the parameters of the physical objects by experimental data. The reader can also find many important topics, which are the basis for statistical methods of estimation and inverse problem solutions.

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. B…