Geophysical Inversion Theory and Global Optimization Methods

Geophysical inversion is an ill-posed problem. Classical local search method for inversion is depend on initial guess and easy to be trapped in local optimum. The global optimization is a group of novel methods to deal with the problems mentioned above.

The book introduces the geophysical inversion theory, including the classical solving approaches firstly. Then, it introduces several typical global inversion approaches including particle swarm optimization (PSO), differential evolution (DE), and multiobjective optimization methods, as well as some examples to inverse the geophysical data, such as gravity, MT sounding, well logging, self-potential, seismic data, using these global optimization approaches.
Components of the Book:
  • Front Matter
  • Chapter 1 Forward and inverse problem in geophysics
    • 1.1. Introduction
    • 1.2. Formulation of forward and inverse problem
    • 1.3. Existence and uniqueness of inversion problem solutions
    • References
  • Chapter 2 Foundation of Ill-posed problems and regularization methods
    • 2.1. Introduction
    • 2.2. Sensitivity and resolution of geophysical methods
    • 2.3. Formulation of well-posed and ill-posed problems
    • 2.4. Foundations of regularization methods of inverse problem solution
    • References
  • Chapter 3 Direct linear inverse methods
    • 3.1. Linear least-squares inversion
    • 3.2. Solution of the purely underdetermined problem
    • 3.3 Weighted least-squares method
    • 3.4 Regularization methods
    • References
  • Chapter 4 Iterative linear inverse methods
    • 4.1. Iterative method for linear equations
    • 4.2. A generalized minimal residual method
    • 4.3. The regularization method in linear inversion
    • References
  • Chapter 5 Nonlinear inverse methods
    • 5.1. Gradient-type methods
    • 5.2. Regularized gradient method
    • 5.3. Regularized nonlinear inversion method
    • References
  • Chapter 6 Particle Swarm Optimization methods
    • 6.1. Introduction
    • 6.2. PSO for MT data inversion
    • 6.3. PSO for Well logging data inversion
    • 6.4. PSO inversion for gravity data
    • 6.5. PSO inversion for self-potential data
    • 6.6. Parallel PSO inversion
    • 6.7. Uncertainty Assessment
    • References
  • Chapter 7 Differential Evolution methods
    • 7.1. Introduction
    • 7.2. DE for MT data inversion
    • 7.3. DE for Well logging data inversion
    • 7.4. DE for prestack seismic data inversion
    • 7.5. DE for geoelectircal data inversion
    • References
  • Chapter 8 Multiobjective Optimization methods
    • 8.1. Introduction
    • 8.2. Multiobjective regularization inversion
    • 8.3. Multiobjective joint inversion
    • 8.4. Cloud-based geophysical Inversion
    • References
Readership: Scientists and Researchers
1
Front Matter
Caiyun Liu, Jie Xiong
PDF (400 KB)
2
Chapter 1 Forward and inverse problem in geophysics
Caiyun Liu, Jie Xiong
PDF (267 KB)
7
Chapter 2 Foundation of Ill-posed problems and regularization methods
Caiyun Liu, Jie Xiong
PDF (315 KB)
23
Chapter 3 Direct linear inverse methods
Caiyun Liu, Jie Xiong
PDF (355 KB)
37
Chapter 4 Iterative linear inverse methods
Caiyun Liu, Jie Xiong
PDF (245 KB)
45
Chapter 5 Nonlinear inverse methods
Caiyun Liu, Jie Xiong
PDF (0 KB)
55
Chapter 6 Particle Swarm Optimization methods
Caiyun Liu, Jie Xiong
PDF (8730 KB)
105
Chapter 7 Differential Evolution methods
Caiyun Liu, Jie Xiong
PDF (5437 KB)
154
Chapter 8 Multiobjective Optimization methods
Caiyun Liu, Jie Xiong
PDF (3450 KB)
Caiyun Liu, Caiyun Liu received her B.S. degree of Applied Mathematics from Huazhong University of Science and Engineering, China, in 1998; M.S. degree of Applied Mathematics from Yangtze University, China, in 2008; and Ph.D. degree of Geophysics from China University of Geosciences, China, in 2014. From January 2016 to December 2016, she was a visiting professor of the Center for Computational Sciences at Mississippi State University, MS, USA. She is currently an associate professor in the School of Information and Mathematics, Yangtze University, China. Her research interests include geophysics, wavelet analysis, and artificial intelligence.

Jie Xiong, Jie Xiong received his B.S degree of Computer science and Telecommunication from Chongqing University of Post and Telecommunication, China, in 1998; M.S. degree of Computer Science and Application from Yangtze University, China, in 2005; and Ph.D. degree of Geophysics from China University of Geosciences, China, in 2012. From January 2016 to December 2016, he was a visiting professor of the Department of Computer Science and Engineering at Mississippi State University, MS, USA. He is currently an associate professor in the School of Electronics and Information, Yangtze University, China. His research interests include geophysics, cloud computing and big data analysis, and artificial intelligence.

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