Technical Notes - Helicopter Electromagnetics

The DIGHEM Resistivity Algorithm

In order to provide a measure of ground resistivity using an efficient and robust algorithm, airborne electromagnetic (AEM) survey data processing generally employs a "homogeneous halfspace" algorithm. This type of calculation is based on the assumption that the earth has uniform resistivity. If this ideal geological case is true, the algorithm will return an apparent resistivity very close to the actual resistivity of the earth. However it generally is not true. The earth is commonly layered, or has other changes in resistivity locally. An important difference between apparent resistivity algorithms is how they handle the response when the earth is not homogeneous.

Apparent resistivity calculation with a specific frequency domain AEM system can use any two of three potential input parameters - signal phase, signal amplitude, and system altitude. The calculation will output the resistivity, and an "apparent" version of the third parameter. Fugro Airborne Surveys uses the "pseudo-layer" version of a homogeneous halfspace algorithm to calculate apparent resistivity from Dighem helicopter electromagnetic (HEM) data. This algorithm uses the phase and amplitude as input, and outputs an apparent altitude above the halfspace. The difference between the apparent altitude and the true altitude is called the pseudo-layer, and reflects the difference between the real geology and a homogeneous halfspace.

This algorithm was chosen because the phase angle is most sensitive to conductive signals from deep (weak response) targets. Amplitude-altitude algorithms are less sensitive to the deeper targets, because they can miss the weak in-phase response of a deep target relative to strong quadrature of the host rock. While amplitude-altitude algorithms were more forgiving of phase drift and low in-phase signals, by the early 1990's all the reputable contractors had changed to the more accurate pseudo-layer method.

The original publication on the different HEM algorithms was "Resistivity Mapping with an Airborne Multi-Coil Electromagnetic System", by Doug Fraser in Geophysics, Vol43, No.1 in 1978.

Apparent Depths
As was stated above, the use of signal phase and amplitude in the apparent resistivity calculation produces an "apparent altitude", which may not be equal to the altimeter measurement, or even to the actual system altitude. In normal HEM processing, the measured altitude is subtracted from the apparent altitude, resulting in an "apparent depth". If the measured altitude is too low because the altimeter does not penetrate the tree cover, the calculated altitude will be greater than the measured altitude, and the apparent depth will be positive, indicating that the ground is farther from the system than the altimeter indicates. However, even with a correct altitude measurement, the apparent depth can be non-zero, positive or negative, if the geology is not approximately a homogeneous halfspace like the model used in calculating the apparent resistivity.

The simplest non-halfspace model to consider is that of a thin, highly resistive layer (for example, sand) over a conductive earth (clay-rich soil). In this case the "halfspace" to which the system will respond is that of the conductive clay, and the response of the sand will have very little effect on the EM system. In such a case, the apparent altitude will seem to be greater than the measured altitude, because the response is coming from the buried halfspace. A positive apparent depth will be measured. In cases of high contrast between the layers, and a thin, highly resistive upper layer, the apparent depth can be a good approximation of the upper layer thickness.

If the upper layer is more conductive than the halfspace, but thin enough to have only a small effect on the total signal received, the apparent resistivity measured will be closer to that of the halfspace. The effect of the upper layer, however, will be to boost the signal measured, making the system appear to be closer to the halfspace than it actually is, and the algorithm will produce a negative apparent depth. This negative value is not an "error" - it is an indication that the signal is stronger than would be generated by a homogeneous halfspace of the calculated apparent resistivity. To an experienced interpreter it indicates a thin, conductive layer at surface. The (negative) apparent depth calculated when there is a conductive layer at surface does not correlate directly to the thickness of the conductive layer. More complex methods of resistivity calculation are used to resolve the thickness of the layer in this situation.

Appendix: Apparent Thickness Examples

Figure 1: shows an example of the calculated apparent depth versus the true thickness, of a resistive upper layer for each of three frequencies. The apparent depth is approximately equal to the layer thickness, until the upper layer becomes electrically thick enough to interact significantly with the electromagnetic field at each frequency. Lower frequencies penetrate deeper, and so their apparent depths are a valid measurement of the layer to slightly greater thickness.

Figure 2: shows a similar graph, for a conductive layer at surface. As the top layer thickness becomes significant, it interacts with the electromagnetic field, so the apparent depth never becomes a reasonable approximation of the thickness.

Greg Hodges, Chief Geophysicist, 2002