This course covers variety types of geophysical inversion method from linear to non-linear inversion and the course is fundamentally designed for graduate students. An introduction to linearized discretization method is provided. The fundamental objects of learning numerical analysis and inverse theory are studied such as vector spaces, matrix invertibility, singular value decompositions, Bayesian viewpoints, covariance and resolution matrices. Programming capability for the three assignments is required.

[Week 1] Introduction

[Week 2] Data analysis

[Week 3] Linear inversion : parameterization & covariance

[Week 4] Linear inversion : null space & regularization

[Week 5] HW #1 presentation

[Week 6] Non-linear inversion : steepest-descent method

[Week 7] Non-linear inversion : Quasi-Newton method & Conjugate-gradient method

[Week 8] Full waveform inversion at a glance (prestack seismic inversion)

[Week 9] HW #2 presentation

[Week 10] Non-linear inversion : Bayesian inversion

[Week 11] Non-linear inversion : Markov-chain Monte Carlo (McMC) method

[Week 12] Non-linear inversion : Neural-network (NN) methods

[Week 13] Stochastic impedance inversion (poststack seismic inversion)

[Week 14] HW #3 presentation

[Week 15] Final exam