Output

In addition to generating a contour grid, the Trend Surface analysis process will generate a Stats file and an output Data file. You must enter suitable names for these files. When you run the analysis, data will be written to these files.

Stats file

The Stats file is a report file (*.RPT). Once you have run Trend Surfaces you can open this file and check its contents.

Its major components are:

• The solutions to the Linear, Quadratic and Cubic equations.
• An Analysis of Variance table.
• Percentage of the Total sum of the Squares for the Linear, Quadratic and Cubic components.

The three equations are fitted to the data using the Least Squares method. The quality of the fit between the original data and the trend surface is calculated on the differences between what the trend says there is and the actual value. Both the Percentage of Total Sum of the Squares and the Analysis of Variance Table are presented to enable you to get a feel for which surface may be best.

The most important column in the Analysis of Variance table is that showing the F-ratio. If the residuals follow a normal distribution and are independent of one another, the statistics shown in this column would follow the F distribution.

The first number compares the variation of the original set of sample data with that which remains after fitting the corresponding trend surface. In simple terms, the reported value indicates the factor by which fitting the trend surface has reduced the variation among the sample values.

In the F-ratio column for the quadratic and cubic surfaces an additional value is reported. This is generated to allow the linear surface to be compared with the quadratic surface and the quadratic surface compared with the linear surface. The quadratic F-ratio will be lower than the linear F-ratio either, because more coefficients are used in the calculation, or because the quadratic surface does not describe the trend as well as the linear surface. The second value describes how much more variation is explained by the quadratic than was already explained by the linear equation.

The corresponding additional value in the cubic F-ratio cell is used to compare the cubic F-ratio with the quadratic F-ratio in the same way.

The percentage of the Total Sum of the Squares is the ratio of the sum of the squares explained by a trend surface compared with the total sum of the squares before the trend surface is fitted.

Another way to compare surfaces is to calculate experimental variograms from the residuals of each equation. When a sufficient order of trend is observed, the parabolic rise seen in data with a trend will disappear. If too high an order is selected, the semi variogram will turn downward.

To determine if the residuals are random, independent, and have a Normal distribution, use the Histogram or Probability plot options in Distribution Stats to examine the residual values of each equation.

While the Analysis of Variance statistical procedure requires that the residuals of the data values should be independent of one another, it is anticipated this is not the cases for a geostatistical analysis. The ability to predict point and block values relies on an expectation of geological continuity.

Data file

• The original input data on which the calculations are based, that is, the contents of the Easting, Northing, Z, and Analysis fields.
• For each record, the trend and residual, for the linear, quadratic, and cubic analysis. The residuals describe the differences between the trend equation value for a point and the measured value. The variable names and file structure are determined by the program.

You will use the residual values in this file when calculating semi variograms.