Technical Notes - Helicopter Electromagnetics

HEM Apparent Conductivity and LIN Apparent Conductivity

Geophysical conductivity measurements, whether HEM, ground EM, or DC resistivity, all measure "apparent" conductivity, because all must make some assumptions about the geological conditions.

HEM apparent conductivity calculations make the following assumptions:

• The system altitude is significantly greater than the coil separation (it is approximately 4:1).
• The earth is a homogenous halfspace.

Some ground geophysical systems (e.g. EM31 and EM34) assume that the response is in the Low Induction

• Number (LIN) range. LIN systems make the following assumptions:
• The system height above ground is constant (it actually depends on the operator).
• The height is significantly less than the coil separation.
• The ground is a homogeneous halfspace.
• The conductivity and system parameters are in "low" induction numbers - meaning that the resistivity is linearly proportional to the measured quadrature-phase signal.

If you refer to Geonics Technical Note TN-6, "Electromagnetic Terrain Conductivity Measurement at Low Induction Numbers", you can find the theory for generating conductivity measurements from the EM31 or EM34. You will note that the calculation uses a linear approximation of the relationship between conductivity and EM response, namely that:

This linear approximation is valid only for low induction numbers. If you examine the standard response curve plotting quadrature against induction number, you will see why this must be so. As the graph in Figure 1 shows, the quadrature response rises with increasing conductivity in low induction numbers, and falls again as the induction number gets higher. Only by limiting the calculations to a low induction number range is the linear relationship between quadrature and conductivity useable.

While the first three assumptions listed above for LIN systems are generally valid, for some projects you will find that the last assumption is not valid, if the ground is relatively conductive. "Low" induction numbers are defined as significantly less than 1. For a frequency-domain ground EM system, the induction number is θ = √(μ * 2*π*frequency * conductivity * coil separation²).

If θ must be much less than 1, then one could use the value of <=0.3. Square both sides of the equation, rearrange, and conductivity <= 0.09 / (μ*2*π*frequency*coil separation²) for low induction number conditions. For the EM31, frequency is 9800Hz, the coil separation 3.66m. From this equation, EM31 apparent conductivity calculations are only valid if the true conductivity is less than about 90 mS/m.

The graph in figure 2 compares the true conductivity, the HEM derived apparent conductivity, and some LIN system conductivities calculated with the equation from Geonics TN-6. You can see that the LIN-derived conductivities diverge at about 100mS/m. By 300mS/m the longer spacing (EM34) systems cannot measure accurate conductivities, and by 1000mS/m even the shorter (EM31) systems are calculating a conductivity about 1/3 the actual value. (The "true" values were generated with both Fugro and MacQuarie University model algorithms, which agree to better than 0.1%). The HEM derived conductivities use the lowest frequency at the high conductivities, and the higher frequencies (which have more signal) at the lower conductivities.

The HEM system calculation uses an equation that employs both in-phase and quadrature components of the signal to fit the full range of induction numbers. RESOLVE HEM systems have an upper conductivity limit over 5000mS/m (tested over salt water against oceanographic conductivity meters) and a lower conductivity limit (dependent on frequency) below 0.02 mS/m.

Low Induction Number ground geophysical systems have a much smaller range than HEM. In higher conductivity environments, the LIN-system apparent conductivities will underestimate the true conductivity significantly.

Greg Hodges, Chief Geophysicist, October 2003