Description
Divide each impedance component by sqrt(permeability) × sqrt(angularFrequency), square their hypotenuse for apparentResistivity, and return atan2 phase.
Electrical geophysical responses combine measured fields with a geometric or electromagnetic model. Apparent resistivity is a response-derived quantity; interpreting it as subsurface material properties requires additional assumptions and usually inversion.
Divide each impedance component by sqrt(permeability) × sqrt(angularFrequency), square their hypotenuse for apparentResistivity, and return atan2 phase.
When to use this tool
Use Magnetotelluric Apparent Resistivity Term when you need one electrical-response conversion under an explicit field and unit convention.
How to use the tool and how it works
- Enter impedanceReal, impedanceImaginary, angularFrequency, permeability. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read apparentResistivity, phaseRadians. Use the output convention below.
Require positive angularFrequency and permeability and nonzero complex impedance. Divide each impedance component by sqrt(permeability) × sqrt(angularFrequency), square their hypotenuse for apparentResistivity, and return atan2 phase.1
For E/H impedance, apparent resistivity is |Z|²/(μω). Using E/B or frequency in hertz without conversion changes the required formula.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| impedanceReal | Real E/H impedance component in ohms, not E/B. | Required. Finite number. |
| impedanceImaginary | Imaginary E/H impedance component in ohms. | Required. Finite number. |
| angularFrequency | Positive angular frequency in rad/s, not hertz. | Required. Finite number; strictly above 0. |
| permeability | Positive supplied magnetic permeability in H/m. | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| apparentResistivity | Scalar apparent resistivity in Ω·m; not an inverted Earth material resistivity. Unit: ohm*m. | Required. Finite number. |
| phaseRadians | Phase Radians Unit: rad. | Required. Finite number. |
{
"input": {
"impedanceReal": 0.01,
"impedanceImaginary": 0.01,
"angularFrequency": 6.283185307179586,
"permeability": 0.0000012566370614359173
},
"output": {
"apparentResistivity": 25.330295910584454,
"phaseRadians": 0.7853981633974483
}
}Limitations and assumptions
- For Ω·m output use E/H impedance in ohms, angular frequency in rad/s, and permeability in H/m; E/B impedance requires a different convention. This one scalar mode does not invert an earth model or validate tensor orientation and instrument calibration.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Apply the appropriate survey geometry and inversion method to the full data. Verify calibration, units, field convention, and dimensionality before interpreting apparent quantities as Earth properties.
References
-
Calculation and input contract: geophysics/magnetotelluric-apparent-resistivity-term — tool.io
-
Electromagnetic Methods: magnetotelluric impedance and apparent resistivity — Scripps Institution of Oceanography, UC San Diego
Similar or alternative tools
- Electrical Resistivity Array Geometric Factor
Return voltage/current as resistance and multiply by geometricFactor for apparentResistivity.
- Geophysical Spatial Sampling Nyquist Margin Tool
Ideal band-limited Nyquist spacing condition; the equality boundary does not guarantee recovery of an unknown phase.