Ellipsoids

Search ellipsoids are required for estimation and can also be used for classification. This page explains how to define, manage, display, and validate ellipsoids in GENESIS, including variable ellipsoids.

Defining a search ellipsoid

GENESIS uses the same rotation convention for ellipsoids and anisotropic variograms as earlier SGS software.

By convention, the unrotated primary ellipsoid is aligned as follows:

• the long axis points toward Y
• the medium axis points toward X
• the short axis points toward Z

The ellipsoid is then rotated into its final orientation using the standard GENESIS angles:

• Azimuth
• Dip
• Spin

A fourth angle, Azimuth2, is also available to match other software conventions. In practice, the two most common angle sets are:

• Azimuth, Dip, Spin
• Azimuth, Dip, Azimuth2

Rotation angles

Let X, Y, Z be the original Cartesian axes, and X’, Y’, Z’ the rotated axes.

Azimuth

Azimuth is the first rotation. It rotates the ellipsoid clockwise in plan view. For example, an azimuth of 30° points the long axis toward the north-northeast.

Dip

Dip is the second rotation. It rotates the ellipsoid around the X’ axis according to the right-hand rule. A negative dip makes the long axis point downward. For example, a dip of -20° with an azimuth of 30° points the long axis downward at 20 degrees toward the north-northeast.

Spin

Spin is the third rotation. It rotates the ellipsoid around the Y’ axis according to the right-hand rule. A positive spin rotates the ellipsoid clockwise when looking in the Y’ direction.

Azimuth2

Azimuth2 is an alternate fourth rotation. It rotates the ellipsoid around the Z’ axis according to the left-hand rule. A positive Azimuth2 rotates the ellipsoid clockwise when looking in the -Z’ direction.

GSLIB uses the same angle convention.

The Ellipsoid list

The Ellipsoid list is the main place for creating and managing ellipsoids.

The list shows the main ellipsoid properties, including:

• visibility
• color
• shading
• transparency
• azimuth
• dip
• spin
• Azimuth2
• major axis
• median axis
• minor axis
• comments

You can edit values directly in the list for many of these fields.

Create menu

• New - creates a new ellipsoid by entering its parameters.
• From bm… - creates one or more ellipsoids from the overall orientation of selected block models. You choose the major, median, and minor axis lengths.

Edit menu

• Find And Replace… - updates matching text-based values in the selected ellipsoids.
• Modify - opens the selected ellipsoid for detailed editing.
• Remove - deletes the selected ellipsoid.
• Copy - creates a duplicate of the selected ellipsoid.
• Create Envelope - converts the selected ellipsoid into an envelope.
• Create All Orthogonal - creates additional orthogonal ellipsoids based on the selected ellipsoid.
• Convert Azi2 to Spin - creates a new ellipsoid using the same orientation expressed with Spin instead of Azimuth2.
• Convert Spin to Azi2 - creates a new ellipsoid using the same orientation expressed with Azimuth2 instead of Spin.

File menu

• Import… - imports ellipsoids from a file containing Name, Azimuth, Dip, Spin, Azimuth2, Major, Median, Minor, and Comment.
• Export… - exports the selected ellipsoids using the same fields.

Display menu

• Set to Centroid - places the selected ellipsoid at the current centroid so it can be displayed at that location.

Editing rules

When editing ellipsoids, the following value ranges are enforced:

• Azimuth: 0 to 360
• Dip: -90 to 90
• Spin: -180 to 360
• Azimuth2: -90 to 90
• Major, Median, Minor: must be greater than 0

Creating an ellipsoid interactively

You can also create an ellipsoid directly in the graphics window.

Start ellipsoid creation from the normal create workflow, then draw the ellipsoid in two stages:

1. draw the first axis on screen
2. draw the second axis to define the remaining shape

During creation, GENESIS asks whether the axes you drew represent:

• the long and median axes, or
• the median and short axes

You are then prompted for the missing axis length, and the new ellipsoid is added to the ellipsoid set. Press Esc to leave the creation mode.

Displaying an ellipsoid on a block

To display an ellipsoid on a specific block:

1. double-click the block
2. choose Set Ellipsoid center to this block
3. select the ellipsoid to display

This is useful for checking which samples or blocks may be included or excluded for the selected block location.

Variable ellipsoid

GENESIS can estimate and classify block models using variable ellipsoid technology. Instead of using a single fixed orientation everywhere, the search direction can vary from block to block. This is especially useful for thin, folded, or rapidly changing structures.

A major advantage of this workflow is that the orientation can follow the trend and is easy to validate and visualize.

How variable ellipsoid information is stored

Variable ellipsoid directions are stored in block model variables named:

• Azimuth
• Dip
• Spin
• Azimuth2

These variables define the local orientation of the ellipsoid for each block.

Validating a variable ellipsoid

When a block model contains variable-ellipsoid orientation fields, additional validation commands are available from the block context menu.

To validate variable ellipsoid directions on a block model:

• double-click a block and choose Set Variable Ellipsoid center to this block to place a selected ellipsoid on that block using the block’s stored orientation
• double-click a block and choose View Variable Ellipsoid Interactive to inspect the orientation continuously while moving the mouse across blocks

Interactive view updates the ellipsoid as you move from block to block. Press Esc to leave the interactive mode.

Defining a variable ellipsoid with geolines

You can generate variable ellipsoid directions from geolines.

General principle

Create geolines that follow the structural direction you want the ellipsoid to honor.

• Geolines used for azimuth and dip do not need a special tag.
• If you also want to define spin, create another set of geolines, usually perpendicular to the first set, and assign them the tag spin.
• If you want to generate Azimuth2 by continuity instead of Spin, use geolines tagged azi2.

The number of lines required depends on the complexity of the structure. More complex geometry generally requires more control lines.

Workflow

1. create the geolines that describe the orientation of the mineralized structure
2. assign tags where needed:
   • leave azimuth/dip geolines untagged
   • tag spin-control geolines as spin
   • tag Azimuth2-control geolines as azi2 if that workflow is required
3. open the geoline list
4. select the geolines
5. choose Operation / Generate Variable Ellipsoid
6. select the target block model

The resulting orientation values are written into the block model as predefined variable-ellipsoid fields.

Note

The number of lines you need depends on the complexity of the structure. The orientation of the ellipsoid for each block is calculated using inverse square distance on the nearest lines. For example, if you have a simple planar structure, a few lines may be sufficient. If the structure is folded or rapidly changing, more lines are usually required to capture the local orientation accurately.

Defining a variable ellipsoid from a block model

Variable ellipsoid directions can also be generated directly from the block model.

To do this:

1. open the block model list
2. select the block model
3. choose Operation / Generate Variable Ellipsoid…
4. choose the method you want:
   • By Block Model - generates directions automatically from the selected block model topology
   • By Geoline - generates directions from selected geolines
   • All Angles By Continuity - generates azimuth, dip, and spin by best continuity
   • Azimuth2 By Continuity - generates a local Azimuth2 by best continuity

The block-model method is simple and fast because it does not require geolines.

Important note

When generated directly from the block model topology, the result is based on the overall local geometry of the block model. If you need tighter control over Spin or another specific orientation component, the geoline-based method is usually more appropriate.

If you are working with a multifolder block model view, make sure the parent block model already contains the variable ellipsoid fields before generating directions.