Scientific Background

This section explains the core electromagnetic and inversion concepts behind pyCSAMT workflows. The library is practical by design, but its outputs are only meaningful when the physical assumptions are understood — these pages cover the response functions, field-method differences, distortion effects, inversion ideas, and time-domain concepts that appear throughout the rest of the documentation.

Use this section when you need to understand why a workflow asks for a particular component, error floor, dimensionality, correction, or diagnostic plot.

• 1. Prerequisites
  • 1.1. Recommended Reading Paths
  • 1.2. Core Quantities
  • 1.3. Relationship To Other Sections
• 2. Physical And Geodetic Constants
  • 2.1. Electromagnetic Vacuum Constants
  • 2.2. Apparent Resistivity Factors
  • 2.3. Angles, Logarithms, And Tolerances
  • 2.4. Unit Conversion Scales
  • 2.5. Earth Radius And Geodesy Helpers
  • 2.6. UTM Zone Letters And Ellipsoids
  • 2.7. Where Each Constant Is Consumed
• 3. CSAMT, AMT, and MT Overview
  • 3.1. Why Resistivity Matters
  • 3.2. The Family Of Methods
  • 3.3. Maxwell Equations In The Diffusive Regime
  • 3.4. Skin Depth
  • 3.5. MT And AMT
  • 3.6. CSAMT
  • 3.7. Field Zones In CSAMT
  • 3.8. Apparent Resistivity Is Not True Resistivity
  • 3.9. Dimensionality: 1-D, 2-D, And 3-D Earth Assumptions
  • 3.10. Source Type And Data Interpretation
  • 3.11. Coordinate And Component Conventions
  • 3.12. Common Data Products
  • 3.13. How pyCSAMT Uses These Concepts
  • 3.14. Practical Reading Of A Survey
  • 3.15. Common Interpretation Pitfalls
  • 3.16. References
  • 3.17. Next Steps
• 4. Airborne Natural-Source EM: AFMAG, ZTEM, And MobileMT
  • 4.1. Why A Natural Source Can Be Flown
  • 4.2. From A Scalar Tilt Angle To A Tensor
  • 4.3. Why Attitude, Not Just Geology, Shows Up In The Data
  • 4.4. MobileMT: A Genuinely Different Physical Object
  • 4.5. Comparing The Three Systems
  • 4.6. Practical Implications
  • 4.7. Next Steps
  • 4.8. References
• 5. Field Zones: Near, Transition, And Far Field
  • 5.1. Why A Grounded Source Has Zones
  • 5.2. The Field-Zone Parameter
  • 5.3. Classifying Field Zones Across A Profile
  • 5.4. The Near-Field Correction Factor
  • 5.5. Applying – And Trusting – A Correction
  • 5.6. Source Overprint And The Shadow Effect
  • 5.7. A Second Convention: Wang & Lin (2023)
  • 5.8. Field Zones In Other Methods
  • 5.9. Practical Guidance
  • 5.10. Common Pitfalls
  • 5.11. Next Steps
  • 5.12. References
• 6. Impedance Tensor
  • 6.1. Role In MT, AMT, And CSAMT
  • 6.2. Coordinate Convention
  • 6.3. Complex Numbers And Phase
  • 6.4. Apparent Resistivity
  • 6.5. Diagonal And Off-Diagonal Components
  • 6.6. Tensor Rotation
  • 6.7. Strike, Principal Directions, And Ambiguity
  • 6.8. Phase Tensor
  • 6.9. Skew And Dimensionality
  • 6.10. Tipper And Vertical Magnetic Field
  • 6.11. Error Propagation
  • 6.12. Static Shift And Galvanic Distortion
  • 6.13. Determinant And Other Invariants
  • 6.14. Practical Component Choices
  • 6.15. pyCSAMT Containers And Utilities
  • 6.16. Quality Control Questions
  • 6.17. Interpretation Pitfalls
  • 6.18. Connection To Later Workflows
  • 6.19. References
• 7. Dimensionality, Distortion, And The Phase Tensor
  • 7.1. Alpha, Beta, And Ellipticity
  • 7.2. Classifying Dimensionality
  • 7.3. Groom-Bailey Galvanic Distortion
  • 7.4. Connection To Strike And Later Workflows
  • 7.5. Practical Guidance And Pitfalls
  • 7.6. References
• 8. Static Shift
  • 8.1. Why Static Shift Happens
  • 8.2. Scale Factor Notation
  • 8.3. Tensor View
  • 8.4. Why Phase Is Less Affected
  • 8.5. Static Shift Versus Near-Surface Effect
  • 8.6. How It Appears In Profiles
  • 8.7. CSAMT-Specific Cautions
  • 8.8. Correction Philosophy
  • 8.9. AMA Correction In pyCSAMT
  • 8.10. Choosing The Estimation Band
  • 8.11. LOESS, Reference Median, and Bilateral Options
  • 8.12. Stratagem Workflow
  • 8.13. Agent And Application Workflows
  • 8.14. Before/After Interpretation
  • 8.15. Effect On Inversion
  • 8.16. Common Mistakes
  • 8.17. Recommended Workflow
  • 8.18. Reporting Checklist
  • 8.19. Next Steps
  • 8.20. References
• 9. Maxwell Forward Modelling and Solver Contracts
  • 9.1. From Maxwell’s equations to an MT response
  • 9.2. Why diffusion controls the mesh scale
  • 9.3. The canonical mesh contract
  • 9.4. Building a solver mesh from geology
    • 9.4.1. What MeshDesign controls
    • 9.4.2. Topography is a physical region mask
    • 9.4.3. Reading mesh-quality diagnostics
  • 9.5. The solver-neutral Maxwell problem
    • 9.5.1. Problem hashes and provenance
  • 9.6. Backend capabilities are scientific claims
  • 9.7. The adapter lifecycle
    • 9.7.1. Adapting a trusted callable
  • 9.8. In-repository and external adapters
  • 9.9. Lazy backend registration
  • 9.10. Canonical results and diagnostics
  • 9.11. Analytic benchmarks before geological complexity
    • 9.11.1. Executable benchmark objects
  • 9.12. Mesh-convergence evidence
  • 9.13. Caching without confusing identity
  • 9.14. Batch solving and failure manifests
  • 9.15. Choosing a backend responsibly
  • 9.16. Common failure modes
  • 9.17. What reproducibility requires
  • 9.18. Relationship to inversion and AI datasets
  • 9.19. Reproduce the figures
• 10. Inversion Concepts
  • 10.1. The Forward and Inverse Problems
  • 10.2. Model Parameters
  • 10.3. Data Vectors
  • 10.4. Data Errors and Weights
    • 10.4.1. Error Floors
  • 10.5. Objective Function
  • 10.6. Regularization
  • 10.7. The Trade-Off Parameter
  • 10.8. RMS Misfit
  • 10.9. Dimensionality
  • 10.10. Meshes, Cells, and Padding
  • 10.11. Starting Models, Reference Models, and Bounds
  • 10.12. Backend Concepts in pyCSAMT
    • 10.12.1. Occam2D
    • 10.12.2. ModEM
    • 10.12.3. MARE2DEM
  • 10.13. Data Preparation Before Inversion
  • 10.14. Interpreting Residuals
  • 10.15. Uncertainty and Non-Uniqueness
  • 10.16. From Resistivity to Geology
  • 10.17. Practical pyCSAMT Workflow
  • 10.18. Common Pitfalls
  • 10.19. Pre-Inversion Checklist
  • 10.20. Post-Inversion Checklist
  • 10.21. Next Steps
  • 10.22. References
• 11. Foundations of AI Inversion
  • 11.1. What the network actually learns
  • 11.2. Learning from known earth models
    • 11.2.1. Choosing the model coordinates
    • 11.2.2. The prior is an executable scientific hypothesis
    • 11.2.3. Topography changes cells, not just plotting coordinates
    • 11.2.4. Sampling the prior without leaking the answer
  • 11.3. Maxwell physics belongs inside the evidence chain
    • 11.3.1. Discretization defines the physics that is learned
    • 11.3.2. Noise should resemble the survey, not decorate it
  • 11.4. Why the objective needs several terms
    • 11.4.1. Model-space losses answer different questions
    • 11.4.2. Depth weights change the estimand
    • 11.4.3. Smoothness and total variation encode structure
    • 11.4.4. Boundary losses make inactive regions explicit
    • 11.4.5. Response losses reconnect the proposal to observations
    • 11.4.6. Choosing the weights is an experiment
  • 11.5. Supervised, hybrid, and physics-informed routes
    • 11.5.1. Hybrid refinement
    • 11.5.2. Physics-informed neural networks
    • 11.5.3. Graph networks and irregular surveys
    • 11.5.4. Architectures should respect missingness
  • 11.6. The domain gap is a scientific variable
  • 11.7. Uncertainty must be calibrated against error
    • 11.7.1. Aleatoric and epistemic uncertainty
  • 11.8. Validation decides whether interpretation is allowed
    • 11.8.1. Structural recovery needs structural metrics
    • 11.8.2. Splits should test the intended claim
    • 11.8.3. Learning curves separate data and model limitations
    • 11.8.4. Baselines expose whether AI adds evidence
  • 11.9. Failure patterns and their interpretation
  • 11.10. What constitutes a reproducible claim
    • 11.10.1. Dimensional claims require special care
  • 11.11. Reproduce the figures
• 12. TDEM Basics
  • 12.1. Transient Diffusion
  • 12.2. What Is Measured
  • 12.3. Decay Curves
  • 12.4. Time Gates
  • 12.5. Waveforms
  • 12.6. Central-Loop and Offset Geometry
  • 12.7. Apparent Resistivity
  • 12.8. Pseudo-Frequency
  • 12.9. Late-Time Transform
  • 12.10. Fourier Transform
  • 12.11. pyCSAMT Data Flow
  • 12.12. Plotting and QC
  • 12.13. TDEM Inversion
  • 12.14. Combining TDEM With AMT, MT, or CSAMT
  • 12.15. Noise and Error Floors
  • 12.16. Depth of Investigation
  • 12.17. Common Mistakes
  • 12.18. Recommended Workflow
  • 12.19. Reporting Checklist
  • 12.20. Next Steps
  • 12.21. References