## GG 542/CAAM 592 Seismology II

**Instructor:** Colin A. Zelt

Department of Earth Science, Rice University

P.O. Box 1892, Houston, Texas, 77251-1892, USA

I teach approximately one-third (4 weeks) of this course on traveltime
inversion and tomography using the following outline.

**1. Introduction**

Inverse theory
Discrete inverse theory
Main parts of tomography problem
Glossary
Tomography problems
Central slice theorem
**2. Linear Inverse Theory**

Formulating inverse problems
Solutions to inverse problems
Noise, random variables and probability distributions
Solution of linear, Gaussian inverse problem using least-squares
Least-squares solution
Classification of inverse problems
Prior information
Solution of purely underdetermined problem using a priori information
Solution of mixed-determined problem
Solutions using weighted measures of length as a priori information
Singular value decomposition
**3. Traveltime Inversion**

Linearization
1. slowness formulation
2. velocity formulation
Interface inversion
Objective functions: regularization, creeping and jumping
**4. Back Projection Tomography**

Back projection algorithms
1. Simple back projection
2. ART
3. SIRT
**5. Model Assessment**

Resolution and errors
Direct testing methods
Non-uniqueness
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