DTM Polynomial Trends

You can use this function to fit a polynomial trend DTM surface to your string data. Analysing the polynomial trend can help you identify global trends in your data. For example, the dominant direction of the gold grade. The higher order the polynomial you fit to your data, the more global highs and lows you will be able to identify. However, the trend will not necessarily be a good fit to the individual input data points.

To run this function: Choose Surfaces > Advanced options > Polynomial trend analysis, or...

In the Function Chooser, type DTM POLYNOMIAL TRENDS, and press ENTER.

Tip: You will get better results from this function if your data is regularly spaced. You can use the create grid tools to force your data to be regularly spaced before running DTM POLYNOMIAL TRENDS.

Note: The higher (that is, quartic and higher) order polynomial surfaces generally give better fits to the data in the region of the data itself. However, extrapolations beyond the initial data boundary should be treated with caution for these polynomials. This is demonstrated in the following simple 2D example.

In this example, a polynomial (black line) has been fitted to some initial data (red crosses). The line fits very well to the data inside the region of the data, but continuing the line away from the data following the polynomial can lead to some values that are very different to the initial data. This difference is magnified as the order of the polynomial increases.

Fields on the Polynomial trends form

Field	Description
Input string file
Location	The name and location of the original string file.
ID number	The ID number of the original string file.
Projection plane
Create on	The projection plane. Options are: The XY plane: This creates the surface in plan view.Usually, you use this option for surfaces such as topography or pit designs. For any given (X, Y) coordinate, the surface will have a single Z value. The active plane: This creates the DTM as if looking directly at the active plane. Usually, you use this option for DTMs that overturn or dip steeply, such as faults or seams. The best-fit plane: This creates the DTM as if looking directly at the best-fit plane of the data points. If the data sits on a dipping plane or approximately on a plane (for example, as a result of digitizing on drillholes that are partially off-section) then you could use this option. The best-fit plane of the data will be calculated before creating the DTM while looking directly at that plane. Note: The plane used during DTM creation is stored with the DTM so that later commands (for example, BM MAKE CONSTRAINT or DRILL HOLE INTERSECT DTM) can correctly determine 'above' and 'below'. For a DTM created on the XY plane, the space considered 'above' a DTM is the portion physically above the DTM. The space considered 'below' a DTM is the portion physically below the DTM. For DTMs created on other planes, the space considered 'above' the DTM is in the 'towards' direction of the plane (along the section's Z-axis towards your viewpoint). For example, if a DTM was created using The active plane and the current view plane was: a vertical plane resulting from VERTICAL SECTION LOOKING EAST, then the 'towards' direction is to the West and the space towards the West of the DTM is considered 'above' the surface. a vertical plane resulting from VERTICAL SECTION LOOKING WEST, then the 'towards' direction is to the East and the space towards the East of the DTM is considered 'above' the surface. a vertical plane resulting from VERTICAL SECTION LOOKING NORTH, then the 'towards' direction is to the South and the space towards the South of the DTM is considered 'above' the surface. a vertical plane resulting from VERTICAL SECTION LOOKING SOUTH, then the 'towards' direction is to the North and the space towards the North of the DTM is considered 'above' the surface. For the plane of best fit, there are two possible directions that can be considered 'above' the surface (that is, the two normal vectors pointing directly away from either side of the plane). The direction considered 'above' the surface is determined by the following rules: For a horizontal plane of best fit, 'above' the surface is in the positive Z direction. For other non-vertical planes, 'above' the surface is in the direction with the positive Z component. For vertical planes that have an orientation (strike) closer to North-South than East-West, 'above' the surface is in the direction of the normal with the positive X component. For vertical planes that have an orientation (strike) closer to East-West than North-South, 'above' the surface is in the direction of the normal with the positive Y component. The edge case of a vertical, exactly SW-NE plane 'above' the surface is to the N-W.
After creating the surface, change the current plane to the best-fit plane	Selected: After the DTM is created, the plane becomes the best-fit plane. Cleared: After the DTM is created, the plane remains the same as it was before running this function.
Boundary limit string
Location	The name and location of the boundary limit string file.
ID number	The ID number of the boundary limit string file.
String No	The string number of the boundary limit string in the string file.
Segment No	The segment number of the boundary limit string in the string file.
Output DTM
Location	The name and location of the output DTM.
ID number	The ID number of the output DTM.
Object ID	The object ID of the output DTM.
Object name	The name of the object for the output DTM.
Polynomial surface
Surface to fit	The type of polynomial surface to fit to your data. Options are: PLANAR: z = A + Bx + Cy QUADRATIC: z = A + Bx + Cy + Dx² + Exy + Fy² CUBIC: z = A + Bx + Cy + Dx² + Exy + Fy² + Gx³ + Hx²y + Ixy² + Jy³ QUARTIC: z = A + Bx + Cy + Dx² + Exy + Fy² + Gx³ + Hx²y + Ixy² + Jy³ + Kx⁴ + Lx³y + Mx²y² + Nxy³ + Oy⁴ QUINTIC: z = A + Bx + Cy + Dx² + Exy + Fy² + Gx³ + Hx²y + Ixy² + Jy³ + Kx⁴ + Lx³y + Mx²y² + Nxy³ + Oy⁴ + Px⁵ + Qx⁴y + Rx³y² + Sx²y³ + Txy⁴ + Uy⁵ USER DEFINED: For this type you enter the maximum x power, maximum y power, and maximum total power. The maximum total power defines the general order of the polynomial, while varying the maximum x and y powers allow you to exclude a range of terms from the full polynomial. For example: maximum total power = 2, maximum x power = 2, maximum y power = 2 defines a full quadratic polynomial (which is equivalent to you choosing the QUARTIC type), and maximum total power = 3, maximum x power = 3, maximum y power = 3 defines a full cubic polynomial (which is equivalent to you choosing the CUBIC type). However, maximum total power = 3, maximum x power = 3, maximum y power = 1 limits the terms to give the following polynomial: z = A + Bx + Cy + Dx² + Exy + Fx³ + Gx²y (that is, the full CUBIC polynomial without some of the terms). If you choose maximum total power = 8, maximum x power = 8, maximum y power = 8, you will get a full eighth order polynomial with no terms missing.
Maximum x power	The integer value, between 0 and 10, that defines the maximum x power for the user-defined polynomial. This field is active only if you selected USER DEFINED for the Surface to fit.
Maximum y power	The integer value, between 0 and 10, that defines the maximum y power for the user-defined polynomial. This field is active only if you selected USER DEFINED for the Surface to fit.
Maximum total power	The integer value, between 0 and 10, that defines the maximum total power for the user-defined polynomial. This field is active only if you selected USER DEFINED for the Surface to fit.
Trend surface based on	Z values: The trend surface data is based on the Z values (elevation). D fields: The trend data is based on the D fields. When you select this option the field becomes active for you to enter the number of the D field.
X resolution	The X resolution for the output DTM. This resolution determines the grid pattern that new points will be inserted in the new boundary.
Y resolution	The Y resolution for the output DTM. This resolution determines the grid pattern that new points will be inserted in the new boundary.

Output

The new polynomial trend surface DTM is created and saved.

Trouble shooting

Message	Description
`The defined boundary segment cannot be found in the string file`	Check that the new boundary does indeed exist in the defined file.
`The boundary segment is open, the new boundary must be closed`	Check that the new boundary is closed.
`Duplicate points have been found in the boundary segment (search distance = 0.05)`	Filter duplicate points from the new boundary and re-apply the function.
`Invalid D field for point x= xxx y= yyy z= zzz, calculations will continue ignoring this point`	Invalid D field found in the initial string data, this point will be ignored.
`Insufficient data points present for calculations to proceed`	There are not enough initial data points present to accurately fit the required polynomial.