Fourier Analysis for Geophysics

The Fourier transform is the lens every geophysicist looks through. Build intuition slowly with interactive decompositions, then follow the idea into seismic spectra, filtering, and modern operator-learning methods that work in the frequency domain.

16 interactive sections across 4 books
Start here → The Fourier transform, slowly, from Seismic Data Processing

Seismic Data Processing

  1. The Fourier transform, slowly
  2. Z-transform & filter theory
  3. Bandwidth & spectral QC
  4. Noise attenuation suite

Physics-Informed Neural Networks for Exploration Seismology

  1. Fourier Neural Operators (FNO)
  2. Frequency-domain (Helmholtz) formulation
  3. Fourier feature embeddings
  4. Multi-scale and multi-resolution networks
  5. SIREN, sinusoidal representation networks
  6. Multi-scale failure modes in pure forward PINN
  7. Spectral bias and why physics needs it fixed

3D Seismic Interpretation

  1. Frequency attributes: spectral decomposition

A Mathematician's Survey

  1. The Fourier Transform on the Real Line
  2. Convergence Issues for Fourier Series
  3. Fourier Series Expansions
  4. The Heat Equation

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