Extrapolation: fantasy v. reality
Sir, Martin Geach (Soapbox, Geoscientist 26.5 June 2016) is raising an issue that was familiar to many petroleum geologists in the eighties: computer mapping of geological structures. This old chestnut seems to have echoed across the decades and still resonates today. I remember many a heated discussion about algorithms during interminable meetings to agree procedures for mapping oil and gas fields that crossed North Sea block boundaries and could vary in shape and volume distribution depending on which interpolation technique was used in CPS-1 or Zmap.
Data points (ie wells) were usually more than 200m apart, unlike Martin’s example. Although our volumes were measured from a surface down to a plane (eg the gas-water contact) the volumes, and the distribution of volumes by block, could vary widely between methods. Martin’s examples of Kriging and IDW methods are almost incredibly close in their volumetric results. However, the difference between them and the RBF/RST method is more than a factor of two - an intolerable outcome.
I suspect a wild over-extrapolation in the NE corner of the RBF/RST model where data are absent (as shown by the curious shape of contours in this area in the Kriging and IDW examples) and the algorithm has generated an unrealistically deep hole in the model. This also occurs in the SW, where it appears the depths are much greater (indigo colour) in the RBF/RST model than in the other two models. A rotation of the 3D view to show the depth axis, or a couple of cross-sections sliced across the model, would clearly reveal these reckless departures which, unless corroborated by real data points, should be eliminated by the geologist. At least, they should if these deep troughs lie on my side of the block boundary!
Chris Garland