Monte Carlo Methods · Inverse Problems

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Inverse Problems

Tikhonov regularization and practical inversion techniques

$ Regularization — The First RescueThe L-curve, Tikhonov penalty, and the art of balancing data fit against model simplicity $ Bayesian Inversion — Why Regularization WorksRegularization is a prior in disguise — the probabilistic viewpoint that unifies everything $ Big Problems Need Clever TricksSteepest descent, conjugate gradients, and iterative tricks for million-parameter problems $ Linear TomographyFrom seismic rays to Earth images — a complete tomographic inversion workflow $ Monte Carlo MethodsMCMC sampling — exploring the full posterior when formulas fail $ Geophysical Inversion ExamplesFault and glacier case studies where the answer is always a distribution $ How Much Did the Data Really Teach You?Shannon entropy and KL divergence — measuring what the data actually taught you

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