Physics-Informed Neural Networks for Exploration Seismology

Seismic Series
By OgbonLab

Where deep learning meets the wave equation, and both come out stronger.

From "what is a neuron?" to confident, working expert in PINN methods for seismic inverse problems.

13 parts 92 sections Free, browser-native
Start reading → First up: What is a neuron?

Table of contents

Every section is a working session: text, math, code, interactive widgets. Click any title to jump in.

Part 1: Part 0: Neural networks from absolute zero

  1. What is a neuron?
  2. Layers, depth, and universal approximation
  3. Activation functions and inductive bias
  4. Loss functions and the loss landscape
  5. Gradient descent by hand
  6. The chain rule and backpropagation
  7. Auto-differentiation as a computational graph
  8. Training loops and optimisers
  9. Spectral bias and why physics needs it fixed
  10. A geophysics primer for ML readers

Part 2: Part 1: The PINN formulation

  1. Why supervised ML alone cannot solve PDEs
  2. The PINN idea: PDE residual as a loss term
  3. 1D Burgers’ equation, end to end
  4. Boundary and initial conditions: soft enforcement
  5. Hard-constraint enforcement via reparameterisation
  6. The forward problem vs the inverse problem
  7. The canonical PINN gallery

Part 3: Part 2: Architectures for PINNs

  1. Vanilla MLPs and their limits
  2. Fourier feature embeddings
  3. SIREN, sinusoidal representation networks
  4. Hard-constrained architectures
  5. Multi-scale and multi-resolution networks
  6. Picking an architecture: a decision tree

Part 4: Part 3: Training pathologies and remedies

  1. Why most beginner PINNs do not converge
  2. The loss-balance crisis: data + PDE + BC weights
  3. NTK-balanced weighting
  4. Gradient pathologies and adaptive weights
  5. Causality weighting for time-domain PINNs
  6. Curriculum and multi-stage training
  7. Adaptive collocation point sampling (RAR/RAD)
  8. Domain decomposition: XPINN, cPINN, FBPINN

Part 5: Part 4: Wave equations in PINN form

  1. The 1D acoustic wave equation
  2. The 2D acoustic wave equation
  3. Frequency-domain (Helmholtz) formulation
  4. Anisotropy: VTI and TTI media
  5. Free-surface boundary conditions
  6. Absorbing boundary conditions (ABC)
  7. Perfectly matched layers (PML)
  8. Picking a formulation: time vs frequency

Part 6: Part 5: Forward modelling and where PINNs fall short

  1. 1D layered medium: PINN vs analytic
  2. 2D smooth velocity: PINN vs FDTD
  3. The cost-vs-accuracy front
  4. Multi-scale failure modes in pure forward PINN
  5. When forward PINN earns its keep

Part 7: Part 6: Velocity inversion with PINNs

  1. The classical FWI loss vs the PINN-FWI loss
  2. 1D velocity inversion end-to-end
  3. 2D Marmousi-class inversion: setup
  4. Multi-scale frequency continuation
  5. Cycle skipping: detection and remedies
  6. Multi-parameter inversion (vp, vs, rho)
  7. Source-encoded FWI-PINN
  8. Loss-weight sensitivity in FWI-PINN
  9. Defending an inversion run: convergence diagnostics

Part 8: Part 7: Travel-time, surface-wave, and joint inversion

  1. The eikonal equation and why PINNs love it
  2. EikoNet: from clicked source to travel-time field
  3. Factored eikonal: removing the source singularity
  4. Travel-time tomography
  5. Microseismic event location
  6. Dispersion-curve and joint inversion

Part 9: Part 8: Operator learning for seismology

  1. From per-instance solvers to operator learners
  2. DeepONet: branch and trunk networks
  3. Fourier Neural Operators (FNO)
  4. Learned propagators for fast forward modelling
  5. Parametric PDE explorers in real time
  6. When operator learning beats per-instance training

Part 10: Part 9: Hybrid PINN + classical, with uncertainty

  1. PINN as regulariser, initialiser, or solver
  2. PINN-augmented classical FWI
  3. Learned regularisers and ML priors
  4. Generative priors for velocity models
  5. Bayesian PINNs and ensemble PINNs
  6. Uncertainty-aware velocity inversion

Part 11: Part 10: Field and benchmark capstones

  1. Marmousi velocity inversion (the field-standard testbed)
  2. Microseismic monitoring of a Marcellus frac stage
  3. USArray surface-wave tomography of the western US
  4. AVO from PINN-augmented FWI
  5. Sub-salt imaging at a Gulf-of-Mexico class target
  6. 4D time-lapse monitoring at a Sleipner CO2-injection target
  7. Eikonal basin tomography
  8. Reproducing a current arXiv PINN paper end-to-end

Part 12: Part 11: Self-assessment quizzes

  1. Quiz: Part 0: Neural networks from zero
  2. Quiz: Part 1: PINN formulation
  3. Quiz: Part 2: Architectures
  4. Quiz: Part 3: Training pathologies
  5. Quiz: Part 4: Wave equations
  6. Quiz: Part 5: Forward modelling
  7. Quiz: Part 6: Velocity inversion
  8. Quiz: Part 7: Travel-time and joint inversion
  9. Quiz: Part 8: Operator learning
  10. Quiz: Part 9: Hybrid PINN and uncertainty
  11. Quiz: Part 10: Capstones
  12. Final exam, integrated assessment

Part 13: Part 12: Master PINN-for-seismology workflow

  1. Master PINN-for-seismology workflow card

This page is prerendered for SEO and accessibility. The book hydrates on JavaScript load with progress tracking, bookmarks, and the AI tutor.