Ellipsoid Visualiser
Many Surpac functions require you to define a search ellipsoid. This is made easier with the help of the Ellipsoid Visualiser. The Ellipsoid Visualiser is primarily a visualising tool aimed at assisting you to improve your search ellipsoid definition. The Visualiser is accessible on all forms used for defining a search ellipsoid via an Ellipsoid Visualiser Button. The Ellipsoid Visualiser can also be selected from the menu bar under Geostatistics
To run this function: Choose Block model > Geostatistics > Ellipsoid visualiser, or Block model > Estimation > Ellipsoid visualiser, or...
Procedure
- Choose Block modelling > Estimation > Ellipsoid visualiser to invoke the function.
- Enter values for anisotropy ratios and orientation.
Note: You can also invoke the function by clicking the Ellipsoid visualiser button on any form where search ellipsoid parameters are shown.
Note: The shape and orientation of the ellipsoid changes as you enter each value.
To save the ellipsoid as a string file,
- Enter values for Location, ID and String File Origin.
- Drag the Ellipsoid Detail slider to select a level of detail.
- Click the Save Now button.
A string file representing the ellipsoid, with centre at the specified String File Origin will be saved in the current working directory.
Open the string file in graphics to view the ellipsoid.
When used with the Save DTM Surface of Variogram Map function, the end result can display three dimensional anisotropy quite well:
Reference information
The Ellipsoid Visualiser form is divided into the Input Area (on the left) and the Display Area on the right.
The Display Area
You can rotate the ellipsoid and the axis by clicking and dragging anywhere on the ellipsoid display.
Ellipsoid
A three dimensional wire frame model is used to represent the ellipsoid and this is dynamically updated as you change the values in the various input fields. The major, semi-major and minor axis are labelled and coloured in order to distinguish them.
Axis
The x, y and z axis are also labelled and coloured. The orientation of the axis when the ellipsoid visualiser is first invoked is always plan view.
The Input Area
The ellipsoid in the display area is updated when focus is lost from an input field. Focus is lost by tabbing out of a field or by clicking in another part of the form. If the input you provide is valid for that field, then the ellipsoid model will reflect this information. Invalid entries will be replaced by the last valid entry.
Anisotropy Ratios
Enter your anisotropy ratios here and watch the visualiser in action. The axis of the ellipsoid change length, hence changing the shape of the model.
A maximum search radius can also be entered here, however this does not have any effect on the three dimensional model. Instead, this will be used in generating the string file.
Major/Semi-Major
This ratio must be greater than or equal to 1 AND less than the major/minor anisotropy ratio.
Major/Minor
This ratio must be greater than or equal to 1 AND greater than the major/semi-Major ratio.
Orientation
A ellipsoid can be defined by ZXY/ZYX (mathematical rotations) or by ZXZ/ZYZ (geological rotations). The choice of axes affects the order of data entry on the form.
| ZXY and ZYX Rotations | |
|---|---|
| Order of Rotation | Axis Name |
| 1st Axis | Bearing |
| 2nd Axis | Plunge |
| 3rd Axis | Dip |
| ZXZ and ZYZ Rotations | |
| Order of Rotation | Axis Name |
| 1st Axis | Bearing |
| 2nd Axis | Dip |
| 3rd Axis | Pitch |
Bearing
This is the azimuth of the major axis in the XY plane and is rotated about the minor axis.
The bearing must be between 0.0o and 360.0o inclusive in order to be valid.
Entering a value of 45o in the bearing text box will cause the ellipsoid to rotate 45o around the Z axis.
Pitch/Plunge
Valid axes are either X, Y or Z axis and is the semi-major axis. Valid entries are -90 to 90. If the rotation is about the Z axis then it is termed a pitch, if the rotation is about the X or Y axes it is termed a plunge.
Plunge (ZXY) is the rotation around the X axis by the Y (plunge) value.
Plunge (ZYX) is the rotation around the Y axis by the X (plunge) value.
Pitch (ZXZ or ZYZ) is the rotation around the 2nd Z value after the dip plane has been defined.
Adding the two Z bearings together will give an incorrect value, for example for a rotation convention of ZXZ, Z=30/X=40/Z=30 is not the same as Z=60/X=40/Z=0.
Dip
Dip (or tilt) is the vertical angle between a line and the horizontal and at right angles to the strike and can be positive or negative. If the rotation convention is ZXY or ZXZ, the dip is the line measured from the horizontal to the X axis while for a ZYX or ZYZ rotation convention, the dip is the line measured from the horizontal to the Y axis.
The dip can also be used to define a geological dip plane using a rotation convention of ZYZ (rotation around the Y axis) for a north/south striking plane or ZXZ for an east/west striking plane (rotation around the X axis). The final rotation using these conventions is a pitch defined by a rotation around the transformed minor z axis which is now perpendicular to the geological dipping plane.
ZXY is the rotation around the Y axis by the dip value.
ZYX is the rotation around the X axis by the dip value.
ZYZ is the rotation around the Y axis by the dip value.
A valid input is between -90.0o and 90.0o inclusive. Valid axes of rotation are the X, Y or Z axis.
The dip are best viewed in section (looking along the major axis).
Entering a value in the dip text box will cause a rotation around whichever axis (X, Y or Z) is selected in the third axis rotation panel.
Entering an invalid number in these text boxes will cause the text boxes to default back to the previous value.
Axes of Rotation
Axes rotation can be divided into two parts, selecting the axis of rotation and selecting rotation direction around each axis.
Rotation around the axis
An easy way to visualise Z axis rotation is to place a map flat on a desk and look down at it in plan view. Turn the map clockwise and you are rotating the X and Y axes about the Z axis to the left (based on the left hand rule below).
ZXY rotation.
Dip is the rotating around the Y axis (causes the X axis to dip).
Plunge is the rotation around the X axis.
ZYZ rotation.
Dip is the rotation around the Y axis.
Pitch the rotation within the dip plane, in this case the second rotation around the z axis after the dip plane has been established.
If the pitch is 0o, then the structure is horizontal.If the pitch is not 0o then the two Z values can not be added together. That is, Z(20)Y(45)Z(60) is not equal to Z(80)Y(60)Z(0) or Z(0)Y(60)Z(80) and Z(80)Y(60)Z(0) is not equal to Z(0)Y(60)Z(80).
The best way to visualise rotations is to get 3 toothpicks and colour code them to the axis on the Ellipsoid Visualiser form (blue - major axis (Y), red - semi-major axis (X) and green - minor (Z).
Join the toothpicks to form the 3 axis with the toothpick points indicating the positive direction for each axis.
Enter values in the Ellipsoid Visualiser and compare the rotated toothpicks with what is on the screen.
Rotation Direction
Selecting the rotation direction is as important as selecting the axis of rotation and can be compared to giving someone instruction to turn without telling them to turn left or right.
Rotation direction has been defined using the left (L) or right (R) hand rule.
The left hand rule is best visualised by holding an axis you wish to rotate in your left hand with your thumb parallel to the axis and pointing in the direction of increasing values. The fingers then curl around the axis in the direction of a positive left hand rotation.
The right hand rule is similar except you use your right hand with the thumb pointing towards the increasing values.
A left rotation is the same as a negative right rotation.
Notation used to describe the rotation convention is the rotation order and then the rotation around each axis. For example ZXY LRL indicates that the Z axis is a left rotation (first axis, first rotation), the X axis is a right rotation (second axis, second rotation) and the Y axis is a left rotation (third axis, third rotation).
The rotations are ZXY LRR verses ZXY LRL (Surpac rotation convention).
A variety of rotation conventions can be selected from the drop down box. Selecting "Other" in this box allows the user to create their own convention by selecting the axis and rotation directions.
The rotation convention is recorded in any saved ellipsoid string files.
View
By simply clicking one of the three view ports, the ellipsoid and the axis will be positioned in the corresponding plane.
Plan
The models will be aligned to look at the XY plane.
Section
The models will be aligned to look at the XZ plane.
Long Section
The models will be aligned to look at the YZ plane.
Appearance
Toggle the displaying of the ellipsoid axis labels with the show labels check box.
Alter the level of detail of the ellipsoid using the slider.
A value of 4 will smooth the surface of the ellipsoid, allowing the model to closely resemble a solid, where as a value of 1 will give less detail to the model and give the appearance of a squared surface.
Origin
Use these input fields to specify an origin of your search ellipsoid. This origin is used to create a string file. The default origin is 0,0,0.
Using the maximum search radius, the anisotropy ratios, the origin, and the orientation, a string file of your ellipsoid can be generated. Specify a file name and simply press the SAVE NOW button. You can create as many ellipsoids as you like while the form is open. Change the details, change the file name and press SAVE NOW. If you select the apply button on the form and have not selected the SAVE NOW button, the string ellipsoid will not be saved.
Having your ellipsoid saved as a string file opens all sorts of possibilities, as immediately all the graphics functions become available. For example, you could open the search ellipsoid string file with your block model, or create a solid ellipsoid using SOLIDS - TRIANGULATE - MANY SEGMENTS or SOLIDS - TRIANGULATE - CONNECTED SEGMENTS - ALL (after removing X, Y and Z axis).
An audit trail is maintained when saving a string file.
An example of a string file audit trail with axis ZXY or ZYX is shown below.
| 1, -3.471, 1.397, 3.317, Semi-Major, 60.00, YL 0, 0.000, 0.000, 0.000, 1, -7.198, -2.620, -6.428, 1, 7.198, 2.620, 6.428, Major, 40.00, XR, Search Radius 10.00,Maj:Semi ratio 2.00, Maj:min ratio 3.00 0, 0.000, 0.000, 0.000, 1, 0.019, 3.079, -1.277, 1, -0.019, -3.079, 1.277, Minor, 20.00, ZL, Surpac ZXY LRL |
Semi-Major, 60.00, YL
- the Semi-major axis was the Y axis
- the ellipsoid was rotated 60 degrees around this axis with a left rotation.
Major, 40.00, XR, Search Radius 10.00,Maj:Semi ratio 2.00, Maj:min ratio 3.00 - the Major axis was X
- rotation was 40 degrees with a right rotation.
- the other values are the search radius, major/semi-major and major/minor values
Minor, 20.00, ZL, Surpac ZXY LRL - the minor axis was the Z axis
- rotation was 20 degrees with a left rotation.
- the rotation convention as selected from the dropdown box in the Ellipsoid Visualiser form.
If the axis of rotation is ZXZ or ZYZ, the string file has minor differences as shown below.
| 1, -1.584, 1.787, 0.740, Geology ZYZ LLL 0, 0.000, 0.000, 0.000, 1, -7.713, -6.131, -1.710, 1, 7.713, 6.131, 1.710, Major, 20.00, YL, Search Radius 10.00, Maj:Semi ratio 4.00, Maj:min ratio 9.00 0, 0.000, 0.000, 0.000, 1, -0.066, 0.374, -1.044, 1, 0.066, -0.374, 1.044, Minor, 10.00, ZL, Semi-Major, 30.00, ZL |