For example, you might have well data and wish to interpolate the water surface at depth, where the Z value is the depth of the water surface. In some wells, the depth to this surface is known. In other wells it might be unknown, but the minimum depths are known (e.g. the water surface depth is at least 25m, so Z>25).

In some cases, you may be able to simply use the minimum depths as the Z value for that point. You could grid the data and create your map. In other cases, you might not want to use the minimum depths as the Z value because the minimum depth value could be very different from the correct value for those points and you may not want the incorrect Z values influencing the interpolation of the known points. In these cases you can grid the known data and adjust the grid file so that it meets the criteria for the unknown conditional data. To apply the conditions to the grid file, you can use a combination of **Grids | Calculate | Residuals** and **Grids | Calculate | Math** by following these steps:

- These steps assume you have a data file of X, Y and Z data, where the known Z values are entered numerically (i.e. 25) and the unknown Z values are entered with a condition (i.e. >25).

*Create a data file of XYZ data, including the conditional data. There are four points in this data file with conditional Z values.*

- Either in the Surfer worksheet or in Excel, create a separate column where the conditional values are entered as a number without the conditional argument (<,<=, =>, > , etc).

Create a new column and enter just the conditional value as a number

without the argument.

- Open Surfer or go to
**File | New | Plot****Document**from within Surfer to open a plot window. - Grid the known XYZ data by going to
**Home | Grid Data | Grid Data**, selecting the data file of XYZ points and clicking*Open*. - In the
**Grid Data**dialog:- Select the appropriate X, Y and Z columns. Use the
*Water Depth*column (the known values) as your Z column. - Choose the gridding method and parameters you wish.
- Note the values in the
*Grid Line Geometry section.* - Click
*OK*. All the known points in the data file are gridded, the points with conditions in the Z column are ignored.

- Select the appropriate X, Y and Z columns. Use the

When just the known points are gridded, the point

locations with the conditional Z values may not meet the

conditional criteria. In this case, the conditions of three

of the four points are not met.

- Go to
**Grids | Calculate | Residuals**, select the grid file just created and click*Open*. - Select the data file you used to create the grid and click
*Open*. - In the
**Grid Residuals**dialog, select the appropriate X and Y columns. Choose the*Conditional Values*as the Z column, and select a column to save the residuals in.

Calculate the residuals between the conditional value

and the Z value in the grid file, storing the results in a

new column.

- Click
*OK*. The data file with the residuals column opens in the Surfer worksheet. Most likely, some of the residuals will be positive and some will be negative.

*The difference between the conditional value and the Z value in the grid file areentered in Column F. The *Residuals

*are the difference between the Z value in the data*

file (the conditional value) and the interpolated Z value for that location in the grid

file. If the residual value is negative, then that means that the interpolated Z value is

greater than the Z value in the data file. If the residual value is positive, then the

interpolated Z value is less than the Z value in the data file.

file (the conditional value) and the interpolated Z value for that location in the grid

file. If the residual value is negative, then that means that the interpolated Z value is

greater than the Z value in the data file. If the residual value is positive, then the

interpolated Z value is less than the Z value in the data file.

- Since the conditional data in our data file are all minimum values, we want the residuals to be negative (we want the interpolated value to be greater than the data value). Only one of the residuals in this example is already negative, so that is the only “good” residual value. The next step is to convert the “good” residuals to 0 and populate the empty cells with 0. Select the
*Residuals*column by clicking on the column header letter. - Go to
**Data | Data | Transform.** - In the Transform dialog, enter the function
*F= IF (F<0, 0, F)*(where F is the column letter of the Residuals column), you may need to change the*First row*value to 2.

Convert all the negative residuals to 0 using **Data | Data | Transform**.

- Click
*OK*. Now all the negative values are converted to 0. - Next we want to fill in all the empty cells with 0. Click in a cell in the
*Residuals*column - Go to
**Data | Find****| Replace**, leave the*Find*field empty, enter 0 for*Replace with*, and select*The column where the active cell is*for*In*.

*Populate all the empty cells in the *Residuals

*column with 0.*

- Click
*Replace All*and then*Close*. Now all the values are 0 except the positive residuals. The remaining positive residual values represent the difference between the Z value in the grid file and the minimum Z value requested. We want to add these values to the interpolated data in the grid file.

All the values are 0 except the positive residuals.

- Go to
**File | Save**to save the data file, and**File | Close**to close the worksheet. - Now we want to create the correcting grid based on the residual data. Go to
**Home |****Grid Data | Grid Data**, select the data file and click*Open*. - In the
**Grid Data**dialog:- Select the appropriate X and Y columns.
- For the Z column, choose to grid the new
*Residuals*column. - Choose
*Inverse Distance to a Power*as the*gridding method*. This will most closely honor the correcting residual values and still produce a nice looking map. - Enter the same
*Grid Line Geometry*options as the original grid file noted in Step 5 above. - Change the
*Output Grid File*to a new name by clicking on the yellow open folder icon, giving the file a new name or location and clicking*Save*. - Click
*OK*.

This residual map shows the distribution of the positive

residual data. This data will be added to the original

map so that all points meet their conditions. - Go to
**Grids | Calculate | Math.** - In the
**Grid Math**dialog:- Click the
*Add Grids*button. - Select the original grid created in Step 5 above, hold the CTRL button down, select the correcting grid created in Step 19 above, and click
*Open*. Both grids are added. - Enter the function
*A+B*to add the correcting grid to the original grid. - Change the
*Output Grid File*if desired by clicking on the yellow open folder icon, giving the file a new name or location and clicking*Save*. - Click
*OK*. This is the final grid with the conditions met.

- Click the
- Plot the newly created GRD as a contour layer.

Add the positive residuals grid file to the original grid file

to create the final grid, where all conditional points meet

their conditions.

*Acknowledgements go to Sergei Beda.*

*Updated November 9, 2018*

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