CSAMT, AMT, and MT Overview

pyCSAMT works with several related electromagnetic (EM) sounding methods: magnetotellurics (MT), audio-magnetotellurics (AMT), controlled-source audio-frequency magnetotellurics (CSAMT), controlled-source EM (CSEM), and time-domain EM (TDEM). They share the same physical foundation: electrical conductivity controls how time-varying EM fields diffuse through the Earth. They differ mainly in source type, frequency band, acquisition geometry, and the assumptions that are safe during interpretation.

This page gives the conceptual background needed before reading the more specific pages on Impedance Tensor, Static Shift, and Inversion Concepts.

Why Resistivity Matters

Most pyCSAMT workflows are ultimately trying to estimate subsurface resistivity, commonly denoted \(\rho\), or its inverse conductivity, \(\sigma\):

\[\rho = \frac{1}{\sigma}.\]

In geophysical EM methods, resistivity is not measured directly. The field system measures electric and magnetic fields at the surface or near the surface. Those fields are then transformed into response functions such as impedance, apparent resistivity, phase, tipper, or transient decay curves. The interpreter uses those responses to infer geological structure.

Resistivity is useful because rocks, fluids, alteration zones, graphite, sulfides, clay, salinity, porosity, permeability, temperature, and fracture connectivity can all influence bulk electrical behavior. A resistivity model is therefore not a lithology map by itself; it is a physical property model that must be interpreted with geology, boreholes, geochemistry, hydrology, and survey context.

The Family Of Methods

The methods supported by pyCSAMT can be grouped by source.

Method	Source	Typical domain	Main interpretation concern
MT	Natural ionospheric and magnetospheric variations	Broad frequency band, often deep investigation	Assumes a plane-wave natural source at the survey scale.
AMT	Natural audio-frequency variations	Higher frequencies than long-period MT, shallower targets	Signal strength can be weak or culturally noisy in the audio band.
CSAMT	Controlled grounded electric dipole source	Audio-frequency controlled-source sounding	Must distinguish far-field behavior from near-field and transition-zone source effects.
CSEM	Controlled electric or magnetic source	Frequency-domain controlled-source EM	Source geometry and full transmitter-receiver coupling are part of the forward problem.
TDEM	Controlled transient source	Time-domain decay after source turn-off	Interpretation depends on transient diffusion and gate timing rather than steady harmonic impedance.

Frequency-domain methods use harmonic signals with angular frequency \(\omega\):

\[\omega = 2 \pi f,\]

where \(f\) is frequency in hertz. The period is:

\[T = \frac{1}{f}.\]

High frequencies generally sample shallower structure; low frequencies sample deeper structure. This is not a hard boundary, because sensitivity also depends on resistivity, dimensionality, noise, source geometry, and the inversion model.

Maxwell Equations In The Diffusive Regime

MT, AMT, CSAMT, and many CSEM workflows operate at frequencies where subsurface EM behavior is usually described by a diffusive approximation. Starting from Maxwell equations in the frequency domain:

\[\nabla \times \mathbf{E} = - i \omega \mu \mathbf{H},\]

\[\nabla \times \mathbf{H} = \mathbf{J}_s + \sigma \mathbf{E} + i \omega \epsilon \mathbf{E},\]

where \(\mathbf{E}\) is electric field, \(\mathbf{H}\) is magnetic field, \(\mathbf{J}_s\) is a source current density, \(\sigma\) is conductivity, \(\mu\) is magnetic permeability, and \(\epsilon\) is dielectric permittivity.

For many geophysical EM surveys in conductive Earth materials, the displacement current term \(i \omega \epsilon \mathbf{E}\) is small relative to the conduction current \(\sigma \mathbf{E}\). The working equation becomes approximately:

\[\nabla \times \mathbf{H} \approx \mathbf{J}_s + \sigma \mathbf{E}.\]

This is why EM sounding is often described as diffusion rather than wave propagation. EM energy diffuses downward and laterally, with a penetration scale controlled by resistivity and frequency.

Skin Depth

A useful first-order scale is the skin depth \(\delta\), the distance over which a plane EM field decays by a factor of \(e^{-1}\) in a uniform half-space:

\[\delta = \sqrt{\frac{2 \rho}{\omega \mu}} = \sqrt{\frac{\rho}{\pi f \mu}}.\]

Assuming non-magnetic rocks with \(\mu \approx \mu_0\), a common field approximation is:

\[\delta \approx 503 \sqrt{\frac{\rho}{f}},\]

where \(\delta\) is in metres, \(\rho\) is in ohm-m, and \(f\) is in hertz.

Skin depth should not be read as “the investigation depth.” It is a scale for a uniform Earth. Real sensitivity depends on the full conductivity distribution and on the measured response. Still, it gives a useful intuition:

• decreasing frequency increases penetration;

• increasing resistivity increases penetration;

• conductive cover can strongly attenuate high-frequency fields;

• shallow conductors may screen deeper targets.

MT And AMT

MT uses naturally occurring EM fields. At suitable distances from source regions, these fields can be approximated as plane waves incident on the Earth. Under the plane-wave assumption, the horizontal electric and magnetic fields at a station are related by a complex impedance tensor:

\[\begin{split}\begin{bmatrix} E_x \\ E_y \end{bmatrix} = \begin{bmatrix} Z_{xx} & Z_{xy} \\ Z_{yx} & Z_{yy} \end{bmatrix} \begin{bmatrix} H_x \\ H_y \end{bmatrix}.\end{split}\]

The tensor components vary with frequency. From them, one computes apparent resistivity and phase. A common component-wise apparent resistivity is:

\[\rho_{a,ij} = \frac{1}{\mu_0 \omega} \left| Z_{ij} \right|^2,\]

and the impedance phase is:

\[\phi_{ij} = \tan^{-1} \left( \frac{\operatorname{Im}(Z_{ij})} {\operatorname{Re}(Z_{ij})} \right).\]

AMT is usually treated as the audio-frequency subset of MT. It is useful for shallower surveys because high frequencies have shorter skin depths. AMT surveys are often sensitive to:

• near-surface conductivity variations;

• cultural noise in the audio band;

• weak natural-field intervals;

• static shift of apparent resistivity;

• station-to-station consistency and frequency coverage.

pyCSAMT processing pages and pipeline steps often use MT/AMT language even when the same operation is useful for CSAMT impedance-like data. The important question is whether the response can be treated as an impedance response under the assumptions of the workflow.

CSAMT

CSAMT uses a controlled source, commonly a grounded electric dipole transmitter, and measures fields at receivers along one or more profiles. The controlled source improves signal repeatability and can be extremely useful when natural AMT signal levels are weak or cultural noise is high.

The price is that the source is no longer “infinitely far away.” Receiver responses may contain source-field geometry, near-field effects, transition zone behavior, source overprint, and shadow effects. These issues are central to CSAMT methodology and are discussed in references such as [Yan2004], [Chen2005], [Da2016], [WangLin2023], and [Zhang2021].

For a grounded electric dipole source, the source-receiver distance \(r\), transmitter length, Earth resistivity, frequency, and survey layout all affect whether a station behaves like a far-field MT-style measurement. In the far field, CSAMT responses can often be interpreted with MT-like apparent resistivity and phase concepts. In the near field or transition zone, direct MT-style interpretation can be misleading.

Field Zones In CSAMT

CSAMT interpretation often separates measurements into approximate field zones:

Zone	Qualitative behavior	Interpretation risk
Near field	Source geometry dominates part of the measured field.	MT-like apparent resistivity may reflect source coupling rather than subsurface layering alone.
Transition zone	Both source geometry and diffusive Earth response matter.	Apparent resistivity curves may show source overprint, shadow effects, or frequency-dependent distortion.
Far field	The source field approximates a plane-wave-like response at receivers.	MT-style impedance interpretation is more defensible, though noise, static shift, and dimensionality still matter.

There is no universal single number that separates these zones for all surveys. A practical diagnostic uses the ratio between source-receiver distance and an EM length scale such as skin depth. Let:

\[\eta = \frac{r}{\delta}.\]

Large \(\eta\) values tend to be more far-field-like, while small \(\eta\) values tend to be more source-dominated. However, this is only a heuristic. Transmitter configuration, anisotropy, topography, 3-D geology, and local noise can change the practical interpretation.

In pyCSAMT, source-effect and field-zone tools should therefore be treated as diagnostics. They help identify where a conventional MT-style workflow may be safe, questionable, or inappropriate.

Apparent Resistivity Is Not True Resistivity

Apparent resistivity is the resistivity of a hypothetical uniform Earth that would produce the observed response at one frequency. It is not the actual resistivity at a single depth. For MT-like impedance data:

\[\rho_a(f) = \frac{|Z(f)|^2}{\mu_0 \omega}.\]

A pseudosection plots \(\rho_a\) or phase against station position and period/frequency. It is useful for quality control and qualitative geological inspection, but it is not a true cross-section. Main limitations include:

• depth is only indirectly related to period;

• apparent resistivity blends effects from a volume of Earth;

• conductive and resistive targets have different sensitivity footprints;

• topography, source effects, and static shift can distort patterns;

• 2-D and 3-D structures can produce responses that do not map vertically below each station.

For this reason, pyCSAMT documentation separates quick-look products from inversion products. Pseudosections are diagnostic and interpretive aids; resistivity models require a forward/inverse modelling step.

Dimensionality: 1-D, 2-D, And 3-D Earth Assumptions

The interpretation method must match the geology closely enough to be useful. Dimensionality describes how resistivity varies in space.

Assumption	Resistivity structure	Typical use
1-D	\(\rho = \rho(z)\)	Layered Earth sounding, first-pass modelling, station-by-station inversion, synthetic tests.
2-D	\(\rho = \rho(x,z)\) and approximately invariant along strike.	Profile interpretation when geological strike is stable and station spacing is along a crossing line.
3-D	\(\rho = \rho(x,y,z)\)	Complex geology, strong lateral changes, non-profile surveys, source and topographic complexity.

Many CSAMT/AMT field projects start with 1-D or 2-D thinking because it is fast and interpretable. That does not mean the Earth is actually 1-D or 2-D. Phase tensor analysis, skew, tipper behavior, induction arrows, strike estimates, and residual patterns help decide whether a simplified inversion is defensible.

Source Type And Data Interpretation

A useful way to think about method choice is to ask: “What source generated the field I am interpreting?”

Natural-source MT/AMT:

• source is not controlled by the operator;

• plane-wave assumption is central;

• impedance tensor is the primary response;

• remote reference and robust processing may be important;

• weak natural signal intervals can limit data quality.

Controlled-source CSAMT/CSEM:

• source location, orientation, waveform, and current are part of the experiment;

• signal strength can be high and repeatable;

• source geometry can contaminate MT-style apparent resistivity;

• near-field, transition-zone, and far-field behavior must be checked;

• full controlled-source modelling may be needed for rigorous inversion.

Time-domain TDEM:

• source is switched off or changed in time;

• measured response is a transient decay;

• time gates replace frequency samples;

• early times tend to sample shallower structure, later times deeper structure;

• receiver coupling, gate timing, and transmitter waveform are central.

The same field project may combine methods. For example, TDEM can constrain shallow structure or static shift, AMT/CSAMT can provide profile-scale coverage, and MT can extend depth of investigation.

Coordinate And Component Conventions

Most MT-style processing uses horizontal components:

• \(E_x\), \(E_y\): horizontal electric fields;

• \(H_x\), \(H_y\): horizontal magnetic fields;

• \(H_z\): vertical magnetic field, used in tipper analysis.

Coordinate conventions must be tracked carefully. Rotating data changes the impedance tensor:

\[\mathbf{Z}' = \mathbf{R}(\theta) \mathbf{Z} \mathbf{R}^{T}(\theta),\]

where \(\mathbf{R}(\theta)\) is a horizontal rotation matrix. The goal is often to align data with geological strike or profile orientation. The details are covered in Impedance Tensor, but the practical message is simple: component labels only have meaning relative to a coordinate system.

Common Data Products

pyCSAMT workflows commonly create or consume the following products.

Product	What it shows	How to use it
Apparent resistivity curve	\(\rho_a\) versus frequency or period at one station.	Inspect shifts, slopes, outliers, and frequency coverage.
Phase curve	Impedance phase versus frequency or period.	Identify conductive/resistive trends and dimensionality issues.
Pseudosection	Response plotted by station and period/frequency.	Quick-look lateral continuity and QC; not a true depth section.
Phase tensor plot	Distortion-resistant tensor geometry.	Dimensionality, strike, skew, and structural complexity.
Tipper/induction vectors	Vertical magnetic response to horizontal magnetic fields.	Lateral conductivity contrasts and 3-D effects.
Inversion model	Resistivity distribution produced by fitting data with a forward model.	Main quantitative interpretation product, subject to uncertainty.
Residual or misfit map	Difference between observed and predicted data.	Diagnose poor fits, noisy stations, model inadequacy, or source issues.

How pyCSAMT Uses These Concepts

The theory pages are not isolated from the software. They explain why the workflow is organized the way it is.

pyCSAMT area	Theoretical connection
pycsamt.seg and pycsamt.site	Store station data, fields, impedance tensors, coordinates, and survey context.
pycsamt.emtools	Implements processing and diagnostic operations such as frequency editing, tensor analysis, static shift handling, source-effect diagnostics, and QC plots.
pycsamt.pipeline	Chains theory-aware processing steps into reproducible workflows.
pycsamt.models and pycsamt.inversion	Prepare and interpret model-based inversion workflows such as Occam2D and ModEM.
pycsamt.agents	Help translate user requests into workflow plans, run diagnostics, and explain output products.
pycsamt.app	Provides desktop and web interfaces for the same processing concepts.

Practical Reading Of A Survey

When approaching a new MT/AMT/CSAMT survey, a robust interpretation sequence is:

1. Confirm survey type, source type, coordinate system, station spacing, frequency/period band, and file format.

2. Inspect station metadata and frequency coverage before interpreting any pseudosection.

3. Check apparent resistivity and phase curves station by station.

4. For CSAMT, inspect field-zone and source-effect diagnostics before treating the data as MT-like impedance data.

5. Check static shift risk, especially in rugged near-surface geology or resistive/conductive shallow cover.

6. Evaluate dimensionality with phase tensors, skew, strike, tipper, and profile consistency.

7. Choose a model class: 1-D, 2-D, 3-D, or controlled-source forward/inverse modelling as required.

8. Interpret inversion results with residuals, uncertainty, geology, and independent constraints.

This sequence is deliberately conservative. EM responses are non-unique, and many different subsurface models can explain similar data. Good workflows make assumptions explicit and preserve enough QC information to revisit those assumptions later.

Common Interpretation Pitfalls

The most common mistakes are conceptual rather than computational:

• treating a pseudosection as a true geological section;

• ignoring source effects in CSAMT data;

• interpreting shifted apparent resistivity as a real layer without checking static shift;

• assuming high-frequency data always mean shallow depth in every resistivity environment;

• using a 2-D inversion when the data show strong 3-D behavior;

• comparing stations without checking coordinate rotation and component convention;

• trusting a low RMS inversion without inspecting residual distribution and geological plausibility.

The purpose of pyCSAMT’s processing, pipeline, and agent layers is to make these checks repeatable.

References

This overview is consistent with standard EM theory and MT/CSAMT practice, including the methodology references collected in References. Especially relevant entries include [WardHohmann1988], [Yan2004], [Chen2005], [Da2016], [WangLin2023], [Zhang2021], [deGrootHedlin1990], and [Kelbert2014].

Next Steps

Continue with:

• Impedance Tensor for tensor notation, apparent resistivity, phase, rotations, strike, and tipper;

• Static Shift for near-surface galvanic distortion and correction strategies;

• Inversion Concepts for model fitting, regularization, misfit, and non-uniqueness;

• TDEM Basics for time-domain EM concepts.