Technical Notes - Helicopter Electromagnetics

Gridding of Resistivity Data

Often there are requests that apparent resistivity data be gridded with minimum curvature algorithms. For this discussion, minimum curvature is assumed to fit to the data a two-dimensional polynomial surface, shaped to have a minimum mathematical curvature (maximum radius curves). This algorithm is commonly used to grid magnetic data, for which it is assumed to provide the closest fit to the actual shape of the smoothly varying magnetic (potential) field. However, this mathematical shape is not the best fit to apparent resistivity data.

The difference lies in the fundamental difference in the parameter being displayed by gridding. Total magnetic field is a measure of the earth's magnetic field over the area that has been surveyed. It is not a direct measure of an actual rock parameter. Measured at any distance from the rock, the field will vary smoothly, with no step discontinuities. The measurement will vary with distance from the source of the anomaly, and with the shape of the inducing field (as magnetic anomalies change between the Arctic and equator).

Apparent resistivity, on the other hand, is an approximation of the actual physical property of the rock and it can change abruptly. For example, the apparent resistivity change at the interface between two rock types would form a step discontinuity. The measurement taken is, in theory, independent of the distance from which it is measured or the shape of the inducing field. In principle, the magnetic parameter most comparable to apparent resistivity is the magnetic susceptibility - a rock parameter that should not change with the measurement method.

Because the apparent resistivity can change abruptly, the profile or grid of the measurements can not be properly defined by a minimum curvature (smooth) profile or surface. Fugro normally uses an Akima spline, which fits closely to the data with roughly straight segments between data points, and short wavelength smooth curves between straight segments. The high sampling density along the survey lines relative to the cross-line spacing, allows us to employ linear splining to these data points.