SIO 230 Geophysical Inverse Theory 2009

Possible Topics:

• Introduction to functional analysis up to the Projection Theorem for Hilbert spaces.
• Linear inverse problems with exact and uncertain data; model construction; regularization as the minimization of model complexity.
• Numerical methods for practical solutions, including Conjugate Gradients.
• Resolution: Backus-Gilbert theory.
• Inference: bounding functionals; ideal body theory.
• Other constraints; linear and quadratic programming.
• Nonlinear inverse problems solved by linearization; Frechet and Gateaux derivatives.
• Iterative optimization: Occam's method.
• 1-D MT sounding, an exactly soluble nonlinear problem.