#
Sesimic Tomography Short Course

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Professor Gerard T. Schuster

Department of Geology and Geophysics

University of Utah

**OBJECTIVE**
The objective of the tomography short course is to familiarize
exploration seismologists about the
theory and practice of seismic tomography. The prerequisite is
a basic knowledge of matrices and vectors, with some
familiarity of the CDP seismic method.
The course will consist of both lectures and in-class exercises.
We will also have an exercise where participants design
a seismic field experiment, pick traveltimes,
and invert data for subsurface velocity.
MATLAB exercises will be conducted to reinforce lecture material, including
simple exercises with steepest descent, conjugate gradient, forming
traveltime normal equations, forming resolution matrices and kernels,
and carrying out refraction and reflection tomography exercises.

**OUTLINE**

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- Day 1: Basics of Seismic Traveltime Tomography

- Least Squares Fundamentals: Gradient, Hessian, normal equations, damping, ill-conditioning
and src-rec geometry
- Traveltime Equations
- Inverting the Traveltime Equation
- Resolution and Experiment Design
- Refraction Tomography Case Histories
- VSP Tomography Case Histories
- MATLAB Exercise: Normal Equations and Least Squares Inversion
- MATLAB Exercise: Traveltime Picking
- MATLAB Exercise: Assessing Quality of Data

- Day 2: Exercises in Traveltime Tomography

- Resolution and Experiment Design
- Assessing Quality of Data and Solution
- Inverting Refraction Data Exercise
- Reflection Tomography Case Histories
- MATLAB Exercise: Inverting your Traveltime Picks
- MATLAB Exercise: Assessing Quality of Solution

- Day 3: Advanced Concepts

- Iterative Solution Methods
- Regularization Methods: Reweighted Least Squares, Damping, Multigrid
- Regularization Methods: Constraints
- Interferometric Tomography
- Wavepath Traveltime Tomography
- MATLAB Exercise: Regularization
- MATLAB Exercise: Steepest Descent and Conjugate Gradient

- Day 4: Deconvolution

- Deterministic Deconvolution
- 1-D Predictive Deconvolution
- 2-D FX Deconvolution
- 3-D FXY Deconvolution
- MATLAB Exercise: 1-D Deconvolution of Data
- MATLAB Exercise: 1-D Prediction and Prediction Error Filtering
- MATLAB Exercise: 2-D FX Prediction Deconvolution of Data