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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