Voxel Math Expression Builder

Use the Voxel > Voxel Math menu option (geogxnet.dll(Geosoft.GX.MathExpressionBuilder.MathExpressionBuilder;RunVoxel)*) to create, save, load, and execute math expressions for your voxel data. This easy-to-use, standardised dialog provides all the math expression options on a single tabbed dialog.

See the Application Notes below for information on "master voxels" and how to use spatial coordinates (i.e., X,Y,Z) as voxel math variables.

Voxel Math dialog options

Step 1: Enter a mathematical expression, or alternatively, build the expression using the buttons and tabs located below the Expression box.
Expression	Enter the math expression in this box. The syntax is straightforward and based on the C programming language. The expression can contain any combination of functions and operators, absolute and/or variable voxel names, DUMMY values, and numbers, spanning multiple equations. The expression can either be directly typed in or built using the supplied Variables and Operators and Functions tabs. For further details see the Expression section under Application Notes.
	Click this button to expand and display the available Operators and Functions to build the Voxel Math expression. Use the keyboard to enter numerical values. For more detailed information about the operators and functions in this expanded section, click on the links below: Common Keys: Buttons consisting of the most commonly used operations and values, grouped along the left, right below Operators and Functions. Frequent Tab: Frequently used conditional and logarithmic operators and functions. Special Tab: Special limit and mathematical functions. Trig Tab: Trigonometry functions. Statistics Tab : Statistical properties of one or more lines. Surfaces Tab: Surfaces operators. Grids are now supported in the same manner as open surfaces and can similarly be used.
	Click this button to add a new grid variable at the cursor's location in the Expression box. The variable grid naming convention is G#, where # is the next available number.
	Click this button to add a voxel variable at the cursor's location in the Expression box. The variable voxel naming convention is V#, where the # is the next available number.
	Click this button to add a surface variable at the cursor's location in the Expression box. The variable surface naming convention is S#, where the # is the next available number. See Use Surfaces in Voxel Math Expressions for more information on using this feature.
Step 2: Assign grids, surfaces, voxels to the variable names used in the expression.
Assign voxels, grids, and surfaces:	This box is populated with all the variables present in the Expression box. Each variable can be set either by choosing a file from the drop-down list of the recently used files in the current project, or by using the browse button to navigate and select the appropriate file(s). The tool distinguishes between input and output xoxels. Input files must exist and are preceded by a character, while you can enter the output file name. To introduce a vector voxel in the math equation, proceed as with a voxel, but use the "Vector Voxel filter" to list the files of the desired type. For further details, see the Applications Notes below.
Common tasks	Use his drop-down list to select from the most common voxel math expressions: Add 2 voxels: V0 = V1 + V2; Divide 2 voxels: V0 = V1 / V2; Multiply 2 voxels: V0 = V1 * V2; Multiply voxel by factor 2: V0 = V1 * 2; Remove 5000 from voxel: V0 = V1 - 5000; Subtract 2 voxels: V0 = V1 - V2; True/False statement: V0 = (V1>5000) ? (V2) : (V3); You can select an expression from the list and, if needed, continue to further edit it.
Expression file	Once you have built the expression, you can save it to a file for future use. Similarly, if you have previously saved expressions, you can load them from the file. The expression files are simple ASCII text files and can be viewed outside of Oasis montaj using a text editor.
	Click on Clear to remove all entries, including the expression, grid assignment, and expression file.
	Click on Apply to apply the expression without exiting the dialog. This is useful when you intend to apply the same expression to multiple grids.

Applications Notes

If an equation yields a value outside the data range, the output is set to DUMMY.

In Geosoft convention, the DUMMY value depends on the data type:

For signed integer data types, the DUMMY value is set to the minimum value of the corresponding data range.
For unsigned integer data types, the DUMMY value is set to the maximum value of the corresponding data range.
The DUMMY values and data ranges for floating data types do not follow this convention. Instead, they are set to limits outside the data ranges you would typically handle in geophysical processing.

Click the link to expand and view the Geosoft data ranges and DUMMY values for the different data types.

Expression

Expressions are parsed from right to left. For example, in the conditional expression G0 = (condition)?G2:G3, the data type of the rightmost channel, G3, defines the data type of the output.

Longer, more complex expressions spanning multiple lines remain visible as you work. When new rows are added to the Expression box, its height automatically expands to display up to 12 lines. Beyond this, a scroll bar appears along the right margin for navigation.

To further increase the vertical height of the box, while the focus is on the Expression box, hover the cursor over the top or bottom edge of the dialog until the double arrow appears. Click and drag the edge of the dialog to resize the box accordingly.

When working with long expressions, the dialog can also be widened. Hover the cursor over the left or right edge of the dialog until the double arrow appears, then click and drag to adjust the width as needed.

Assign Voxels, Grids, and Surfaces

To further increase the vertical height of the Assign voxels, grids, and surfaces box, focus on it, then hover the cursor over the top or bottom edge of the dialog until the double arrow appears. Click and drag the edge of the dialog to resize the box accordingly.

You will not see the temporary variable listed in this window.

Voxel Math Example

The nested equation below results in the output voxel VO, where all elements that intercept the five section grids are set to 1, while all other voxels are set to DUMMY. Such an equation could be used to generate VOXI constraint models.

VO=(G1.intersect)?1:

((G2.intersect)?1:

((G3.intersect)?1:

((G4.intersect)?1:

((G5.intersect)?1:

((G6.intersect)?1:

((G7.intersect)?1:0))))));

Input Section Grids and Overlapping Voxel

Output Voxel Intersection with Section Grids

Master Voxel

The "Master Voxel" is required and is used to determine the geometry (size, projection and data type) of the output voxel. All other input voxels, grids and/or surfaces will be sampled and reprojected if they do not match the Master Voxel. The Master Voxel is typically the first input Voxel and can be identified as bolded (e.g. V1) in the Assign voxels, grids and surfaces window. When you mouse over the bolded variable the popup message, "This input is the master input" appears.

For example:

Special Case:

If you do not want the first input Voxel to be the Master you can specify a separate Master Voxel by appending its name to the end of the expression. For example, if you have the Voxel expression, V0 = V1 + V2; then V1 will typically be the Master Voxel (bolded). However, if you want to specify your own Master Voxel you can specify, V0 = V1 + V2; VM; and the VM will be your new Master Voxel (bolded).

Only certain operations are logically possible on vector voxels. If you attempt to perform an impermissible operation on a vector voxel, you will receive a message indicating it and the operation will not be performed.

The permissible operations are:

VV0 = C * VV1

VV0 = VV1 /C

VV0 = C1 * VV1 + C2 * VV2

VV0 = C1 * VV1 - C2 * VV2

VV0 = VV1 * VV2  (dot product = VV1x*VV2x+VV1y*VV2y+VV1z*VV2z)

VV0 =V1 * VV1   (multiply all 3 components by V1)

VV0 = in (VV1, S)?VV1:VV2

Where:

C --> constant

G --> grid

S --> surface

VV --> vector voxel

V --> voxel

An expression similar to the one below is not supported:

VV0 = VV1 / VV2

Using Spatial Coordinates (X, Y, Z) as Voxel Math Variables

The following Voxel Math Expression generates a Voxel (3D grid) that tapers linearly from a value of 3 in the center (0, 25000, -7350) to values of zero at the edges of the Voxel. The image below shows the resulting Voxel. You can use similar expressions to edit the values in a Voxel or to smoothly merge two voxels.

//V0=.\demo2.geosoft_voxel

//vm=.\top_salt.geosoft_voxel

V0 = 3*(1-abs(x)/25000)*(1-abs(y-25000)/25000)*(1-abs(z+7350)/7300);

vm;

Temporary Variable Definition

Temporary variables can be defined in a math expression. These variables exist only during the computation stage and are not saved in the output. To define a temporary variable, precede it with the "@" symbol (e.g., @Var1). Multiple temporary variables can be included in an expression.

*The GX.NET tools are embedded in the geogxnet.dll file located in the "...\Geosoft\Desktop Applications \bin" folder. If running this GX interactively, bypassing the menu, first change the folder to point to the "bin" directory, then supply the GX.NET tool in the specified format. See the topic Run GX for more details on running a GX.NET interactively.