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← Intelligent Geophysical Exploration College

Inversion & Modeling Department

The Inversion & Modeling Department grounds students in the mathematical foundations of inverse theory and forward modeling for geophysical parameter estimation. Students implement and validate algorithms that tackle ill-posed inverse problems using optimization, regularization, and probabilistic frameworks. Graduates leave able to face a new geophysical problem and both mathematically design and computationally implement an inversion algorithm for it.

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Seismic Exploration & Imaging DepartmentGravity & Magnetic Methods DepartmentElectromagnetic Methods DepartmentEarthquake Seismology DepartmentIntegrated Geophysics & Interpretation DepartmentInversion & Modeling DepartmentWell Logging & Petrophysics Department

Field-based Curriculum · 12

This department's curriculum is built directly on the GeoVerse Lab research fields its professors hold — click a field to see how it is taught.

Backus-Gilbert Inverse Theory & Model Resolution
Backus-Gilbert Inverse Theory & Model Resolution
Teaches Backus-Gilbert inverse theory — asking not for a best model but for what…
James Freeman Gilbert
Adjoint-State Method & PDE-Constrained Optimization
Adjoint-State Method & PDE-Constrained Optimization
Teaches the adjoint-state method — computing gradients with roughly two simulati…
Jacques-Louis Lions
Finite-Element Forward Modeling
Finite-Element Forward Modeling
Teaches finite-element modelling — locally refining resolution around complex ge…
Olgierd Zienkiewicz
Monte Carlo & MCMC Inversion
Monte Carlo & MCMC Inversion
Teaches Monte Carlo and MCMC inversion — sampling the full posterior distributio…
Nicholas Metropolis
Ill-Posed Problem Theory & Regularization Foundations
Ill-Posed Problem Theory & Regularization Foundations
Teaches, via Hadamard's criteria, why geophysical inverse problems are inherentl…
Jacques Hadamard
Bayesian Uncertainty Quantification & Maximum Entropy Inference
Bayesian Uncertainty Quantification & Maximum Entropy Inference
Teaches Bayesian uncertainty quantification — treating models as random variable…
Edwin Thompson Jaynes
Gradient-Based & Quasi-Newton Optimization
Gradient-Based & Quasi-Newton Optimization
Teaches the conjugate-gradient and quasi-Newton algorithms that turn gradients i…
Roger Fletcher
Finite-Difference Forward Modeling
Finite-Difference Forward Modeling
Teaches finite-difference solution of wave and diffusion equations — accuracy an…
Sven Treitel
High-Performance & Parallel Computing for Geophysical Inversion
High-Performance & Parallel Computing for Geophysical Inversion
Teaches designing parallel and GPU-accelerated architectures that make large 3D …
Gene Amdahl
Sequential/Recursive Bayesian Estimation
Sequential/Recursive Bayesian Estimation
Teaches sequential Bayesian inference — updating estimates as data arrive — and …
Rudolf E. Kálmán
Global & Evolutionary Optimization
Global & Evolutionary Optimization
Teaches evolutionary and stochastic global optimisation — strategies and limits …
John Henry Holland
Ray Theory & Traveltime Tomography
Ray Theory & Traveltime Tomography
Teaches ray theory and travel-time tomography — tracing high-frequency ray paths…
Vlastislav Červený