Department
of Earth, Atmospheric and Planetary Sciences
EAPS
657 – Spring 2021
GEOPHYSICAL
INVERSE THEORY
Instructor: Robert Nowack,
494-5978
nowack@purdue.edu
Prerequisite:
Consent of Instructor
Time: TTH 12:00-1:20 PM
Place: Synchronous Online
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) 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)
11) Kalman Filtering and Data Assimilation
12) Continuous Operators
The Green’s function as an inverse operator
Adjoint operators
Reciprocity
Functional derivatives
13) Example of the Inverse Problem for Earthquake Source Parameters
14) Example of the Imaging and Migration of Seismic Reflection Data
15) The Physics of Layered Media
15) Brief Introduction to Neural Networks and Deep Learning