Gridding: turning picks into a map
Learning objectives
- Explain why inverse distance weighting produces bullseyes and cannot extrapolate a trend
- Use minimum curvature and describe what the tension parameter changes
- Recognise when the error in a map is set by pick density rather than by the algorithm
- Read a residual map and say where the interpretation is unconstrained
You pick every eighth line, because picking every line on a survey this size would take a week. That gives you a few hundred points on a surface with sixteen thousand bins. The other fifteen thousand seven hundred are invented by an algorithm, and the map you hand over, the volume you compute, and the well you propose all rest on that invention.
The two algorithms behave completely differently
Inverse distance weighting takes an average of nearby picks, weighted by distance. It is easy to explain and visibly wrong. Because it is an average, it can never produce a value outside the range of the data, so it cannot extrapolate a trend; and because the weight goes to infinity at a control point, every pick becomes a small bullseye. Between picks the surface decays toward the mean.
Minimum curvature solves a different problem: find the smoothest surface that passes through every pick. That is what a geologist does with a pencil, and it extrapolates trends because smoothness, not proximity, is the constraint.
The tension parameter interpolates between two physical models. At zero the relaxation is biharmonic and minimises curvature, giving a surface that behaves like a thin elastic plate. At one it is harmonic and minimises area, giving a surface that behaves like a soap film pulled taut over the picks. Real gridding packages expose exactly this knob, usually without saying what it does.
The error you cannot see on real data
Every map in this section is compared against the true surface, which is the one thing no interpreter can ever do. Two results are worth carrying away.
At a coarse line spacing the error stops depending on the algorithm at all. No method recovers structure that was never sampled, so a map built on a 500 metre grid over a 300 metre feature is wrong in a way no amount of clever interpolation can repair. The fix is more picks, not a better gridder.
And the residual map shows you where. Error concentrates between the picked lines and at the edges of the survey, which is exactly where an interpreter has the least evidence and where a prospect is most likely to be quietly invented or destroyed.