Modelling Grids and Variograms
Two tools take a model from a description of its surface towards a model of its volume. Variogram 3D measures how an attribute varies with distance and direction. Create Modelling Grid... builds a grid of cells over a model or between contact surfaces.
Variogram 3D
A variogram plots how different two values are, on average, against how far apart they are. Variogram 3D does this along three axes you can aim, as well as in all directions, and fits one model through them with a range for each axis.
Building one
- Colour the mesh or point cloud by the attribute to analyse: click its radio button.
- Right-click the object ▸ Attributes & Analysis ▸ Variogram 3D.
Each selected object gets its own variogram, named after the attribute and the object, under Variograms in the Interpretation tree. It computes at once. The properties of the last one open, and its chart appears in the Charts panel. An object with no attribute on display is refused, with a message in the messages panel, and so is one that is not loaded or is busy.
The samples are the points or vertices holding the attribute, or the centres of the visible triangles for a per-triangle layer. Elements with no value are left out, and so are those filtered out when the layer has Use Filter on.
Aiming the axes
The axes are a plane and a line in it: the major and intermediate axes lie in the plane and the minor axis is its pole. A new variogram starts on the source's best-fit plane with the major axis down dip.
Aim them by typing in the Axes group of the properties, or in the Vulkan view with the orientation gizmo: choose 3D Translate and click the knob at the centre of the ellipsoid, then drag the knobs for the plane and the major axis. They stay at right angles to each other, and the variogram recomputes when you release. Double-click the gizmo to move the ellipsoid instead. Tick Reset To Best-Fit Plane to go back to the starting axes.
Properties
| Group | Property | What it does | Default |
|---|---|---|---|
| Attribute | The layer analysed; a list of the source's layers. | The one on display | |
| Axes | Plane Dip, Plane Azimuth | The plane holding the major and intermediate axes. The azimuth is the direction its upward pole leans, as for orientation measurements. | Best-fit plane |
| Major Plunge, Major Trend | The major axis. It is kept in the plane: editing it tilts the plane as little as possible. | Down dip | |
| Lags | Lag Width | Width of each distance class, in project units. | Half the longest side of the source, divided by the number of lags |
| Number Of Lags | Number of distance classes. | 15 | |
| Max Lag Distance | The longest separation analysed: always the width times the number. Setting it changes the width. | ||
| Angle Tolerance | Half-angle, in degrees, of the cone of pair directions counted along each axis. | 22.5 | |
| Bandwidth | Largest distance a pair may lie off an axis and still count for it. 0 is no limit. | 0 | |
| Max Points | Larger sources are randomly subsampled to about this many points, the same ones each time; the number of pairs grows with its square. 0 uses all. | 20000 | |
| Min Pairs | A lag with fewer pairs is drawn hollow and left out of the fit. | 30 | |
| Standardise | Divide the semivariance by the sample variance, so the sill is near 1. | On | |
| Auto Recompute | Recompute after every edit and when an axis drag is released. | On | |
| Model | Type | Spherical, Exponential or Gaussian. | Spherical |
| Fit | Automatic fits the nugget, sill and ranges to the lags. Manual uses the values below; editing any of them switches to it. | Automatic | |
| Nugget, Sill | The semivariance at zero separation, and the level the model reaches. One of each for all axes. | ||
| Major Range, Intermediate Range, Minor Range | Distance along each axis at which the model reaches the sill. In a manual fit, 0 leaves the axis open. | ||
| Fit Quality | Major, Intermediate, Minor | How each range was arrived at, and its misfit to the reliable lags. Read-only. | |
| Points Used, Status | Points used of those carrying a value, and the result of the last computation. Read-only. | ||
| Open Report | Tick to write the chart and lag table to an analysis report and open it, in the project's Reports folder. | ||
| Display | Show Axes | Draw the three range axes through the ellipsoid. | On |
| Ellipsoid Opacity | 0 hides the ellipsoid, 1 is solid. | 0.3 | |
| Glyph Size | Length of the gizmo's arms, in project units. | About a third of the source's radius |
Reading the result
The Charts panel plots each axis and the fitted curves, with the sill and a legend giving each range. In the Vulkan view the model is a translucent range ellipsoid at the source's centroid. Only the small knob at its centre can be clicked, so the ellipsoid does not get in the way of picking on the mesh it describes.
An axis whose reliable lags never reach the sill is not given a guessed range. Fit Quality reports it as not resolved: at least the longest reliable lag, the legend marks it (unresolved), and the ellipsoid draws that axis at the lower bound in grey.
A mesh is a surface: its vertices barely separate along the normal, so the variogram along the minor axis has few pairs and short lags, and on a flat surface none at all. Expect that axis to be unresolved on an outcrop model.
A variogram and its last result are saved with the project.
Modelling grids
Modelling grids are experimental and are not switched on in a standard session. While they are off, the Interpretation tree has no Modelling Grids branch and Create Modelling Grid... on the right-click menus has no effect.
Creating a grid
Select what the grid is to cover and right-click ▸ Create Modelling Grid..., on a mesh or point cloud in the Data tree or a polyline in the Interpretation tree. A selected folder brings its members. There is no dialog: the grid is built at once, as Modelling Grid and a number under Modelling Grids in the Interpretation tree, and its properties open.
| Selection | The grid |
|---|---|
| One mesh, or point clouds, or both | A box over the selection, with a flat top and base at its highest and lowest points, layered evenly. |
| Two or more meshes | The meshes are contacts, stacked by their mean elevation, so one stray vertex cannot change the order. The unit between each pair is layered on its own. Point clouds in the selection only widen the extent. |
| Polylines | A flat box over their extent. |
A new grid has square cells, 25 along its longer side, and 5 layers. A point cloud that is not loaded does not count towards the extent, and the messages panel says so. A grid can have at most 4 million cells; beyond that its Status asks for bigger cells.
Where two contacts cross, the upper cuts into the lower, as at an unconformity: the lower contact is pushed down to meet it, the units below are truncated, and the cells there pinch out.
The model and the grid
The Model group describes the volume of interest, and the Grid group the cells that fill it. They have separate orientations, so a grid can follow a palaeocurrent or a foreset inside a regionally dipping model. Editing any of these rebuilds the grid.
| Group | Property | What it does |
|---|---|---|
| Model | Centre X, Centre Y, Centre Z | The centre of the box. The model and the grid turn and tilt about it. |
| Length, Width, Thickness | The box's size along its strike, along its azimuth, and through its layers. | |
| Azimuth, Dip | Clockwise from north, the dip direction of the box, and its dip. | |
| Grid | Cell size I, Cell size J, Cell size K | Cell size along the strike of the layers, along the grid's azimuth, and through the layers. |
| Azimuth, Dip | Clockwise from north, the dip direction of the layers, and their dip. Independent of the model's. | |
| Cells I, Cells J, Cells K | Read-only: enough cells to enclose the model, rounded up. | |
| Layers K | On a grid between contacts, the number of layers in each unit. | |
| Outside the model, Cut by the model | Read-only: cells with nothing inside the box, which take no part, and cells the box cuts. |
Centre Z, Thickness, Cell size K, Cells K and both Dip rows are on flat grids only. Between contacts, the top and base come from the surfaces, the cells follow them, and the box cuts the cells on its vertical sides only.
Cells at the edge are cut flat on the faces of the box rather than left as a staircase of whole cells. Only the part inside the box is drawn and measured, so a flat grid's volume is exactly the box's.
Recalculate Size on the grid's right-click menu fits the box to its source meshes and point clouds in the model's current orientation, so turning the model and recalculating gives the tightest box that way. A grid made from polylines has no sources to fit to, and the messages panel says so.
The Volumetrics group gives the Gross rock volume, Active cells, Excluded cells, Pinched out and Status of the last build. The Layering group shows the layering Mode and Reference, which are read-only.
Looking inside a grid
The grid draws as a mesh named after it with (cells) on the end, listed under its row in the tree. Deleting the grid deletes this mesh too.
- Slicing. The Slice group's I from, I to, J from, J to, K from and K to set the range of cells shown, with K counted down from the top. The cells at the cut are drawn, so you see into the grid. Slicing changes the display only; the volumes are always of the whole grid.
- Cell attributes. The Attributes row under the grid holds Cell I, Cell J, Cell K, Unit, Active, Cell Volume, Thickness and Centre Elevation, recomputed by each build. Click a layer's radio button to colour the cells. The layers and their display settings are saved with the project.
- Contains Data. A cell is 1 when a point of the source clouds or meshes lies in it or one of their triangles passes through it, and 0 otherwise. Data outside the box does not count. A grid made from polylines has no such layer.
- Filtering. Tick Use Filter on any cell layer to hide the cells outside its window, for example to keep only the cells that contain data. Filters can hide every cell, which turns the mesh off until a cell passes again.
- Inspecting a cell. In the Vulkan view, click a cell to highlight its faces and write its I, J and K, its status, its centre and the value of every layer to the messages panel. A click elsewhere clears the highlight. Interrogate mode gives the same answer in either view. The first click after reopening a project refreshes the mesh, and the messages panel asks you to click again.
See also
- Attributes — the layers these tools read.
- Charts, Histograms and Filtering — the variogram chart.
- Analysis Reports — where Open Report writes.