Credits: 3

Prerequisite: Consent of Instructor

Time: TTH 12:00-1:15 PM

Place: Civil Bldg., Room 3201

COURSE OUTLINE

1) Introduction

Example using the earth’s magnetic field

2) Review of Vector Space Methods

Banach spaces/Hilbert spaces

Generalized Fourier Series

Adjoint theorems

3) Spectral and Singular Value Decompositions

4) Maximum Likelihood and Stochastic Inversion

5) Seismic Tomography as a Linearized Inverse Problem

6) Surface Wave Analysis of Dispersion

7) Linear Equality and Inequality Constraints

8) L1 Norm/Non-Gaussian Statistics

9) Iterative Steepest Descent and Conjugate Gradients

10) Monte Carlo Methods, Simulated Annealing and Genetic Algorithms

11) Kalman Filtering

12) Continuous Operators

The Green’s function as an inverse operator

Adjoint operators

Reciprocity

Functional derivatives

13) The Inverse Problem for Earthquake Source Parameters

14) Migration of Seismic Reflection Data

15) The Physics of Layered Media

Equations for acoustics and seismics

Layer matrices/matrizants

Exact inverse methods by layer-stripping

The Gelfand-Levitan method