Gridding Surfaces from Polylines & Orientations
VRGS can interpolate a triangulated surface through your structural interpretation using kriging. Two kinds of interpretation data can drive the surface:
- Polylines — digitised bedding contacts, horizon traces, fault traces, or any other lines that lie on the surface you want to model.
- Orientation measurements — dip/dip-direction readings (bed attitudes, structural measurements). These act as gradient constraints: the surface is bent so that its local dip and dip direction honour each measurement.
The result is a regular grid converted to a triangulated mesh. The mesh stays linked to its source interpretation and regenerates automatically when the source polylines or orientations are edited.
In the Interpretation Tree, right-click a polyline group and choose Convert to Regular Grid (2.N D Grid). A new mesh named Grid is created in the project tree. To let dip measurements shape the surface as well, Ctrl-select an orientation group together with the polyline group before right-clicking.
Creating a surface
From polylines
Right-click a polyline group in the Interpretation Tree and choose Convert to Regular Grid (2.N D Grid). All visible polylines in the group are used as elevation control. Vertices are averaged per grid cell, then ordinary kriging interpolates between them.
From orientation measurements
Right-click an orientation group (bed attitudes / structural measurements) and choose Convert to Regular Grid (2.N D Grid). Each visible measurement contributes both its position (a point on the surface) and its dip/dip-direction (a gradient constraint).
The grid plane is automatically aligned with the mean orientation of the group, so consistently dipping successions grid correctly even at steep dips. Overturned geometry cannot be represented — the result is always a surface of the form z = f(x, y) in the (possibly tilted) grid frame.
Combining polylines and orientations
Ctrl-select an orientation group together with the polyline group, then right-click the polyline group and choose Convert to Regular Grid (2.N D Grid). The polylines fix the elevation of the surface; the orientation measurements constrain its dip between and beyond the lines.
In combined mode the orientation positions are deliberately not used as elevation control — only their dips matter — so measurements taken on nearby beds at a different stratigraphic level will still steer the shape of the surface without dragging it up or down.
This is particularly effective where a contact is only exposed in one part of an outcrop: a handful of dip readings lets the surface project the observed trend correctly instead of flattening away from the digitised lines. Dipping planar trends indicated by the orientation data are reproduced and extrapolated exactly.
The generated mesh
The surface appears as a triangulated mesh (named Grid) in the project tree. Because it carries a live generator:
- Automatic rebuild — editing, adding, or hiding source polylines or orientations regenerates the surface on the next redraw.
- Saved with the project — the link to the source groups and the gridding parameters are stored with the mesh, so automatic rebuilds and the Surface Generator submenu keep working after the project is closed and reopened. (If the source group is later deleted, the mesh simply becomes a static surface.)
- Surface Generator submenu — right-click the mesh in the project tree:
- Regenerate re-runs the gridding on demand.
- Paste Orientation re-orients the grid plane from an orientation on the clipboard (use Copy Orientation on any structural measurement first). Use this to tilt the grid frame when modelling a steeply dipping surface from polylines.
Gridding & variogram properties
Select the generated mesh to edit its gridding parameters in the Properties panel, then regenerate.
Gridding
| Property | Meaning |
|---|---|
| x / y spacing | Grid cell size. Defaults to about 1/100 of the data extent. Smaller cells give more detail and slower rebuilds. |
| Alpha | Strength of Laplacian smoothing applied after gridding (points-only surfaces). |
| Iterations | Number of smoothing passes (points-only surfaces). |
Laplacian smoothing is skipped when orientation constraints are present — it would flatten the dips the kriging has just honoured. Use the Nugget instead to smooth a noisy dip-constrained surface.
Variogram
| Property | Meaning |
|---|---|
| Sill | Total variance of the surface elevation. |
| Nugget | Measurement noise on the elevation data. 0 forces the surface exactly through the (cell-averaged) polyline data; larger values let it smooth through digitising noise. |
| Orientation Nugget | Noise on the dip data, as a fraction of the expected gradient variance (default 0.01). Larger values honour dip measurements more loosely — increase it if compass scatter makes the surface undulate. |
| Intermediate Axis Direction / Dip | Orientation of the grid plane (dip direction / dip). Set automatically for orientation-only grids; editable, or set via Paste Orientation. |
| Major Axis (strike) Range | Correlation length along the grid x-axis, in metres. Leave at 0 to fit automatically. |
| Intermediate Axis (dip) Range | Correlation length along the grid y-axis, in metres. |
| Minor Axis Range | Reserved; not used by the 2.5D grid. |
When the Major Axis Range is 0 the variogram is fitted automatically:
the sill comes from the variance of the elevation data, and — when
orientations are present — the range is chosen so that the model's expected
slope variability matches the spread of the measured dips.
How the interpolation works
Points-only surfaces use ordinary kriging with a spherical variogram. As soon as orientation constraints are involved, VRGS switches to a gradient-augmented kriging system (the same family of methods used by implicit structural modelling packages):
- A cubic covariance model carries the dip constraints — it is smooth enough to differentiate, and much better numerically conditioned than a Gaussian model for densely digitised lines.
- A linear drift term lets the surface follow and extrapolate dipping planar trends instead of reverting to a constant mean away from the data.
- Dip/dip-direction readings enter as exact surface-gradient constraints, relaxed by the Orientation Nugget.
Tips
- Surface undulates between measurements — increase the Orientation Nugget, and check for measurements with inconsistent dip directions (a single flipped reading bends the surface hard).
- Steeply dipping horizon digitised as polylines — copy a representative orientation and use Paste Orientation on the mesh so the grid plane dips with the structure; near-vertical surfaces cannot be represented by a horizontal height-field.
- Surface too spiky through noisy digitising — raise the Nugget slightly (a value around 5–10% of the Sill is a good start).
- Slow rebuilds on large interpretations — increase the grid spacing; kriging runs on per-cell averages, so the cell size is also the effective data resolution.