Geophysical Inversion Theory and Global Optimization Methods
Caiyun Liu, Jie Xiong
(2018)
Geophysical Inversion Theory and Global Optimization Methods: pp.
23-36.
Chapter 3 Direct linear inverse methods
The following sections are included:
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3.1. Linear least-squares inversion
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3.1.1. The linear discrete inverse problem
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3.1.2. General solution for the linear equations
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3.1.3. The data resolution matrix
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3.2. Solution of the purely underdetermined problem
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3.2.1. Underdetermined system of linear equations
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3.2.2. The model resolution matrix
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3.3 Weighted least-squares method
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3.4 Regularization methods
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3.4.1. The Tikhonov regularization method
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3.4.2. Solving regularized linear inverse with SLDM method
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3.4.3 Weighting matrices for the model parameters and data
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References