1. Prerequisites

Before working through the response functions, distortion effects, and inversion ideas in the rest of this section, it helps to know which page answers which question and to share a common notation for the handful of quantities that recur on nearly every page. This page is that map: a reading order depending on the field method in use, and the small vocabulary of symbols assumed everywhere else.

1.1. Recommended Reading Paths

For MT, AMT, or CSAMT impedance workflows:

1. Start with CSAMT, AMT, and MT Overview.

2. Read Impedance Tensor.

3. Read Static Shift if apparent resistivity curves are shifted between nearby stations or if near-surface heterogeneity is expected.

4. Read Inversion Concepts before running Occam2D, ModEM, or MARE2DEM.

For TDEM workflows:

1. Start with TDEM Basics.

2. Read Inversion Concepts to understand how transient data become an inversion data vector.

3. Read CSAMT, AMT, and MT Overview if TDEM products are being compared with frequency-domain EM results.

For model-backend decisions:

1. Read CSAMT, AMT, and MT Overview to understand method assumptions.

2. Read Inversion Concepts to understand regularization and dimensionality.

3. Continue to Choosing A Model Backend.

1.2. Core Quantities

Many pyCSAMT workflows revolve around a small set of physical quantities, each with a notation kept consistent across every theory page:

Quantity	Typical notation	Why it matters
Resistivity	\(\rho\)	The main interpreted property in most EM inversions.
Conductivity	\(\sigma = 1 / \rho\)	Controls EM diffusion and current concentration.
Angular frequency	\(\omega = 2 \pi f\)	Links harmonic fields, impedance, skin depth, and phase.
Impedance tensor	\(\mathbf{Z}\)	Relates horizontal electric and magnetic fields in MT, AMT, and CSAMT style workflows.
Apparent resistivity	\(\rho_a\)	A frequency-dependent response estimate, not a direct layer resistivity.
Phase	\(\phi\)	Measures phase lag between field components and helps identify conductive or resistive structure.
RMS misfit	\(RMS\)	Summarizes data fit relative to assigned uncertainties.

These are notation, not numbers – the actual constants and unit factors behind \(\omega=2\pi f\) or \(\rho_a\)’s conversion factors live in Physical And Geodetic Constants, which is where to look when a page’s formula needs a concrete value rather than a symbol.

1.3. Relationship To Other Sections

Theory pages connect directly to the applied documentation:

• Identify your data format explains how field data enter pyCSAMT.

• Classical model integrations explains how physical assumptions map to external modelling backends.

• Pipeline System explains how repeated processing and inversion workflows are organized.

• Tutorials gives worked examples that apply these concepts.