New Variogram
Variogram analysis is a tool that is used in analysis of variability depending on distance and modelling. It is carried out within a composited data set. To add a new variogram; New Variogram option in Variogram tab is chosen.
For analysis, attribute to be analyzed is chosen from the top and bottom feature firstly.
- If top and bottom attributes are the same; program calculates the normal variogram.
If top and bottom attributes are different; cross variogram is calculated.
- When "z" values of lithologies are chosen as attribute values, two dimensional variogram modelling is allowed. Variogram is calculated for a unit distance and its layers.
- Number of steps; means how many of variogram values will be calculated and step interval means the unit distance, from which the variogram will be calculated. Practically variograms are calculated up to half length of the size of the area to be considered. In horizontal calculations, step interval can be taken as the average distance between drills. In vertical, i.e. along the drills, calculations, step interval can be chosen a little bigger than the composite length.
- Step tolerance means the distance that the step interval can be tolerated. Step tolerance can usually be taken as the half of the step interval or a little bigger.
| Description | Image |
|---|---|
Number of steps; means how many of variogram values will be calculated and step interval means the unit distance, from which the variogram will be calculated. Step tolerance means the distance that the step interval can be tolerated. Practically variograms are calculated up to half length of the size of the area to be considered. In horizontal calculations, step interval can be taken as the average distance between drills. In vertical, i.e. along the drills, calculations, step interval can be chosen a little bigger than the composite length. Step tolerance can usually be taken as the half of the step interval or a little bigger. Practical information given above relating to step interval, number and tolerance should be taken as analysis start values. In order to determine the optimal values relating to these parameters, it is required to consult a geostatistical expert. |
|
Variogram is calculated in specified directions for anisotropical research and modelling. Direction and angles used in NETPRO/Mine is explained with 3-D ellipsoid shown in the figure below. 3D ellipsoid is described with six parameters: sizes of three main axis of the ellipsoid (rmax, rmed and rmin) and three angles that position the ellipsoid (α, β, and Q). Let's say there are three perpendicular axis on X, Y, Z cartesian coordinat system. The position of the ellipsoid is achieved with three sequential rotational movement. It is assumed that all angles are measured counter-clockwise. Main axis, middle axis and small axis of the ellipsoid are position on X, Y and Z direction, respectively before any rotational operation. |  |
First rotation around Z axis: Ellipsoid is firstly rotated with α angle around Z axis (This is called direction (azimuth) angle). Let's say X', Y' and Z' are rotated coordinate system. Please pay attention that Z' is equal to Z. Azimuth takes a value between 0 and 360. Azimuth is 0 in the reference direction taken as North. |  |
Second rotation around Y axis:Ellipsoid is then rotated with β angle around Y' axis (β angle is called slope (base)). Let's say X", Y" and Z" are the second rotated coordinate system. Please pay attention that Y" is equal to Y'. |  |
Third rotation around X axis: Lastly, ellipsoid is rotated with Q angle around X". Q is called plunge or rake angle. X''', Y''' and Z''' final coordinat system is achieved with this last rotation. Please pay attention that the X''' is equal to X'' in this system. |  |
Last rotation matrix is achieved by multiplying matrixes that represent the three rotation. The order, in which the rotations take place is important. Six parameters that describe the ellipsoid given in Netpro/Mine parameter files should be entered in the specified order: r max, r med, r min, α, β, and Q. |  |
Nugget Effect (Co): It is obtained from the variograms calculated during the best drills. Variograms that are modelled with different directions should have the same Co (nugget effect) value. |  |
Variograms within a 3-D bed should be first calculated along drills. If all the drills are perpendicular, direction should be 0 and slope should be -90 degrees. Tolerance is the tolerance of inclination angle and bandwidth is the width that the variogram cone is limited. Bandwidth can be taken 4 or 5 times of step interval at first. If variograms will be calculated on a horizontal plane, they can be analyzed in four main directions (0, 45, 90 and 135 degrees). In this case, inclination angle tolerance can be taken 22.5 degrees. Practically angle tolerance should neither be chosen too high nor too low. When chosen too low, number of sample pairs and therefore the reliability of variograms are decreased. When chosen too high, however, experimental variogram comes close to average variogram and a bed that behaves anisotropically can be mistaken for an isotrope. When choosing both the angle tolerance and distance tolerance, it is suggested than a geostatistic expert is consulted.
Variograms that are modelled with different directions should have the same Co (nugget effect) value. Co is obtained from the variograms calculated during the best drills.
