Geophysical Inversion Theory and Global Optimization Methods
Caiyun Liu, Jie Xiong
(2018)
Geophysical Inversion Theory and Global Optimization Methods: pp.
7-22.
Chapter 2 Foundation of Ill-posed problems and regularization methods
The following sections are included:
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2.1. Introduction
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2.2. Sensitivity and resolution of geophysical methods
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2.2.1. Formulation inverse problem mathematically
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2.2.2. Sensitivity
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2.2.3. Resolution
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2.3. Formulation of well-posed and ill-posed problems
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2.3.1. Well-posed problems
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2.3.2. Conditionally well-posed problems
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2.3.3. Quasi-solution of the ill-posed problems
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2.4. Foundations of regularization methods of inverse problem solution
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2.4.1. Regularizing operators
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2.4.2. Stabilizing functionals
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2.4.3. Tikhonov parametric functional
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References