Histograms and SGS Modeling Histograms are used daily for interpretation, quality control, and modeling in Petrel. This TIPS&TRICKS document briefly describes how histograms are built and used for QC but primarily focuses on their use in Petrophysical property modeling, specifically Sequential Gaussian Simulation (SGS). Porosity from the Gulfaks demo data distributed with each Petrel release will be used to demonstrate histogram input to SGS. We will demonstrate the dramatic impact these histograms have on property distribution in the model. Probably the most important point to learn from this paper is that histograms for each zone and facies of the model must be reviewed to ensure that the model is reasonable, represents the data, and matches the geologic interpretation.
Figure: Porosity histograms for one zone from: initial logs (top left) and up‐scaled cells (top center), and from models built using histogram input control: model–using up‐scaled cells (top right), model–using reasonable data analysis (bottom left), model–using mean and std dev (bottom center), and model–using extreme data analysis (bottom right). Note the amount of variation that can exist for the same rock unit.
Petrel has two methods for building histogram displays. The Settings Dialog histogram is quick and used for QC of a specific object. The Histogram Window is used for creating final displays, comparing several objects on the same histogram display, and for converting histograms to distribution functions (data).
Settings Dialog Histogram
The Histogram tab of an object’s Settings Dialog is second only to the Statistics tab as the most used tool in Petrel. The Statistics and Histogram tabs are the first line of attack for QC and should be checked for nearly every object that is built.
To view the Settings dialog’s Histogram double click on the object and go to the Histogram tab. The available parameters will vary slightly depending upon whether the object is an up‐scaled property or just an object. For all objects you have parameter control over:
Number of intervals (bins)
Display as percent or count (percent lets you compare objects with different counts)
Log or linear
Minimum value to display
Maximum value to display
Print histogram to a printer you select
Copy bitmap (allows copying to clipboard, then you paste to Input tab and display in other windows or to an external document)
When the histogram represents an up‐scaled property you have additional control over:
Which zone the histogram represents
What values are displayed: Log, Up‐scaled cells, all cells, or any combination
Use active filters
Volume weight the count (useful when cells of the model differ significantly in size)
You cannot control the colors of the bars on this type of histogram.
Figure: Histogram tab related to a general well log (left) and a property model (right).
The Histogram Window allows one or several objects to be displayed at the same time. This display has more versatility than the Dialog Histogram and is used more for analysis and final display than for QC.
To create a Histogram Window click on the Window button at the top of the Petrel window and select New histogram window. Resize the window and then check the button in front of the object or objects you want to display in the window. The parameter controls for this window are found in two places, some are accessed through the icons to the right of the display area and others using the Viewport Settings dialog for the histogram. This dialog
can be gotten to by clicking on the icon or by going to the Windows tab of the Petrel explorer Histogram window Histogram sub‐folder and double clicking on the sub‐folder. From this dialog you control most of the parameters you controlled in the Settings dialog Histogram. In addition you can link multiple histogram windows together in a coordinate group so that a change to one’s display form changes all. You can also link them to a visual group so that what is displayed (turned on or off) in one member of the group is adjusted similarly in all other members of that group.
Figure: Double click on the Histogram sub‐folder in the Windows tab of the Petrel exploer (left) to display the dialog for controlling the parameters of the Histogram window.
Icons to the right of the display area control a variety of things that are easily turned on and off to test. A few of interest are:
Select and edit or add points to a displayed function
Select and edit line of a displayed function
Display histogram as bars
Display histogram as a line
Show cdf (cumulative distribution frequency) curve
Display as percent
Volume weighting
Display histogram for all cells in selected property
Display histogram for up‐scaled cells in selected property
Display histogram for log values associated with up‐scaled cells in selected property
Range select points along the X‐axis (works but doesn’t seemed to be used for anything)
Create new distribution function
Smooth function when one is displayed
Use spline to connect points of a displayed function
One of the most frequently asked questions is: How do you change the colors of the bars on the histogram? This is done in three places.
Property: Double click on the Properties folder containing that property and go to the Style tab. Alter the parameters in the Histogram area of that dialog.
Well logs: Double click on the Wells folder and go to the Histogram tab. Alter parameters under the Histogram area of this dialog.
Objects: Double click on the object and go to the Style tab. Alter parameters under the Histogram area of this dialog.
Figure: Alter histogram bar colors and other data specific parameters using one of these three dialogs: Properties folder Settings (left), Wells folder Settings (center), and Object Settings (right).
Figure: Histogram window with a property and its three associated histograms displayed. The cdf for each is also displayed scaled to the histograms.
Subset Logs for Histogram Display
Well logs usually start out representing the entire well or significant portions of the well. However, sometimes it is desirable to display or analyze only a small portion of the log. For instance, you might want to analyze the portion of the log corresponding to only one zone or to only one facies in one zone. Histograms created for subsets of the entire log are often converted to distribution functions (discussed below) so that they can be both edited and used as input to the SGS modeling process (discussed below). The log calculator is used to output parts of logs that correspond to parts of other logs. Typical examples might be:
Output porosity where zone log is 2
Output porosity where facies is 3 and zone log is 2
Output porosity where the net non‐net log is 1
Each of these operations would create a new porosity log having values only in the portion of the well where the if statement was true. These new logs could then be displayed in a Histogram window and the data captured as a distribution function.
Figure: Well section showing the original porosity log, the logs used to subset porosity and the final porosity log (left) and the histogram for the new log (right).
Distribution Function from a Histogram
A distribution function is a series of X – Y pairs. When the function is built from a histogram the X represents the value at the center of a histogram bin and the Y is the count (number of values) in that bin. Once a function has been created it can be displayed, edited, exported, or used as data for property modeling.
Figure: Histogram (left), the distribution function built from it (center), and the X‐Y values defining the function (right).
Use the following steps to create a Distribution Function.
1. Display one data set on a Histogram window. (If you display more than one data set you cannot generate a function representing the data. You will be allowed to only generate a function as a constant value or as a normal distribution by specifying mean and standard deviation.)
2. Set the number of bins to your liking using the Settings dialog for the histogram window, reached using the icon and then altering the Number of intervals or the Increment parameter.
3. Create the Distribution Function by:
a. Clicking on the Create new distribution function icon. A Create distribution function dialog will appear
b. Entering the desired name
c. Un‐checking the Overwrite last parameter (This defaults to checked which 2 times out of 3 will cause you to wipe out the previous function you built and often wipe our many of the previous functions before you catch it, a problem that should be corrected in a coming release but… maybe not.)
d. Selecting the Fit distribution to Active histogram columns icon
e. Clicking Execute to build the function
4. Note that the function is displayed on the histogram
5. Go to the Input tab and see that the function has been placed at the bottom and has not overwritten an already existing function.
Figure: Create distribution function dialog (left), Histogram window with histogram and generated function displayed (center), and Input tab showing the resulting function after manually moving it into a folder (right).
Often the reason for creating a distribution function from logs already in Petrel is to alter the form of the function to better represent the interpretation. For example, there may be too little data to properly describe the porosity distribution of a particular facies or zone. In that case you would display a histogram of the data, create the distribution function, and then edit the function until it matches your interpretation of how the distribution really is in the rocks. Although it is possible to edit a function using its Settings dialog Function tab, it is best to edit using a Histogram window so that a background histogram can be displayed for reference while editing.
Figure: Histogram from Zone Ness 1 porosity log (left), Distribution function displayed on same histogram (center), and edited histogram with same histogram in background (right.
The steps used to edit a Distribution Function are:
1. Open a Histogram window
2. Display a background histogram from data to use as reference while editing (usually this is the histogram from which the function was derived)
3. Display the previously created distribution function that is to be edited.
4. Click on the Select and edit/add points icon
5. Edit the points
Move the existing points to desired locations
Touch a point and hit the delete key to remove it (often there are more points than needed)
Touch a line and move the cursor to create a new point
Histogram Control for SGS Modeling
Sequential Gaussian Simulation is a commonly used algorithm for building property models of continuous variables such as porosity. This algorithm uses as input a histogram of the data’s distribution. It assumes trends have been removed, the data are normally distributed, and that the distribution has a mean 0 and standard deviation 1. The Petrophysical modeling process has several ways to input histogram data: up‐scaled cells representing the log data, Data Analysis process results, mean and standard deviation values representing a normal distribution, and a Distribution function from the Input tab. Regardless of which method is used as input the program eventually applies a Normal Score transformation (derived from the histogram) to the data to convert the data from its input form to a normal distribution with mean zero and standard deviation 1. The normalized data are then modeled using parameters you specified for the SGS algorithm. The new model’s normalized cell values are then back transformed into porosity units with a distribution matching the input histogram.
Figure: Histogram portion of processing flow during SGS modeling. Blue represents input in original data units, light red represents internal Normal Score processing, green represents SGS modeling in mean 0 standard deviation 1 units, and yellow represents the output model in original data units.
Normal Score Transformation and Back Transformation
The normal score transformation involves four steps:
1. Build a cumulative distribution function (input cdf) for the input histogram.
2. Build a cumulative distribution function (normal cdf) for a mean 0 standard deviation 1 histogram
3. Map each input data value on the input cdf by noting its percentile position (Y axis) on the cdf curve
4. Extract a normalized value for each input data value by: locating its cdf percentile position on the normal cdf curve’s Y‐axis, going to that location on the curve, and reading off the normalized units value from the X‐axis.
The process is done for each up‐scaled cell in the property model. Once in normalized space, the SGS algorithm is applied using all other parameters you specified. This creates a model with cells having a mean 0 and standard deviation 1(if no special trends were applied). These modeled cell values are then back transformed by walking through the four steps above in reverse order. The resulting values are now in porosity units. Any other transforms (output truncation, log, trend, etc.) that you applied to the input data are reverse applied at this point to create the final porosity model. Note that the same input cdf curve is used in both transform directions. This means that the original histogram’s form will be reproduced in the output model unless special trends or other controls were applied during modeling that forced the resulting model to deviate from a normal distribution. Even then the results will be similar to the input histogram with minor distortions.
Figure: Normal score transform of up‐scaled cell values from porosity units to mean 0 standard deviation 1 units (left), SGS modeling in normalized units (left middle), Normal score transform of all cell values back from normalized units to porosity units (right middle), and final model in porosity units (right).
Histogram from Up‐scaled Logs
If you have a large number of wells with log data which create a histogram(s) you feel is representative of the property’s distribution then you can use the up‐scaled values from those wells to define the histogram input for SGS modeling. When defining the Petrophysical modeling parameters you will use the Distribution tab to point to the up‐scaled logs. In this tab you will want to check several parameters since they have an affect on the input histogram or output values. These parameters include:
Is logarithmic: Checking this would remove a log trend (common for permeability data) from the data. This removal is done before the up‐scaled cell values are used to build a histogram.
Output data range: The cell values of the final model will be checked against these numbers and clipped to them if they are violated. You usually want to click on the Estimate button to make these match the up‐scaled cell values.
Distribution method: Standard means you are using this property’s data and histogram to control its distribution. Bivariate means you are using another property’s cell values to guide this property’s distribution.
Distribution: From upscaled logs means you want to use the histogram built from the up‐scaled cells as input to SGS modeling.
[Note: Even if data are sufficient to define an input histogram from up‐scaled cells, you may wish to use Data Analysis rather than the Distribution tab to input the histogram. You would do this when log form, skewness, X‐ Y‐ Z trends, etc. need to be removed from the data and that functionality is not available in the Distribution tab.]
Figure: Distribution parameters set to use the up‐scaled cell values to build the histogram input for SGS.
Figure: Zone Ness1 Porosity histogram just for the up‐scaled cells (left) and for all cells (right). Note how the property distribution for the entire model matches the original input data’s distribution.
Histogram from Data Analysis
If you know you do not have enough well data to define histograms that correctly represent the property’s distribution then you should use the Data Analysis process to edit the histogram to match your interpretation of the distribution and use that for SGS modeling. Data analysis allows trends to be removed from the data and property distribution trends to be put into the data (via the histogram). Although Data Analysis has many parts, this discussion focuses only on editing the Normal Score histogram.
To edit the Normal Score input histogram:
1. Go to the Data Analysis process and select the up‐scaled property you are modeling, the associated facies model (if used), the zone, and the facies (if used).
2. Go to the Transformations tab and highlight Normal score in the right selection area.
3. Click on the Define curve radio button and you will see the Normal Score curve defined as three points.
4. Click on the Fit the distribution curve to the transformed property values icon. This essentially converts the curve to a distribution function that fits the histogram.
5. Use the cursor to edit the curve by moving, adding, and deleting points.
6. Click Apply to save the changes and move on to the next facies or zone.
Note that you can use original log values as the background histogram rather than up‐scaled cells by clicking on the
Use logs icon. This may give you more insight into the distribution. Sometimes a facies or zone will have no log data. Go to a zone that has a similar distribution, copy that transformation, and paste it into the one that is missing
data ( ). You can then use the transform as it is or alter it to fit your interpretation.
Once all histograms are edited you are ready for SGS modeling. In the SGS dialog, click on the Use the
transformations made in data analysis icon just above the Variogram tab to force SGS to use the edited histograms from Data Analysis. This also causes all parameters except Seed to be cleared off the Distribution tab.
Figure: Data Analysis dialog for one zone showing the Normal Score as it first appears (left) and after checking the Define curve radio buttion (right).
Figure: Data Analysis dialog for one zone showing the Normal score curve fit to the data’s histogram (left) and after editing (right).
Figure: Zone Ness1 Porosity histogram just for the up‐scaled cells (left) and for all modeled cells (right). Note how the property distribution for the entire model matches the edited Data Analysis curve in the figure above.
If you have little or no log data for a particular property and want a histogram based on statistics derived from neighboring fields or the literature, then you can enter the Mean and Standard deviation you want the property to have for SGS modeling. To specify this style of distribution check the radio button in front of Normal distribution and enter the Mean and Std. If there is some data you can press the Estimate button to insert the mean and standard deviation of that data.
Figure: The Distribution tab of the SGS dialog with the mean and standard deviation specified.
Figure: Zone Ness1 Porosity histogram just for the up‐scaled cells (left) and for all modeled cells (right). Note how the modeled histogram matches the defined normal distribution.
Histogram from Distribution Function (Input Tab)
If you have too little log data in the model area but have other wells outside the model area that, if combined would create histograms representative of the property’s distribution, then you can create a histogram using all well data, extract the distribution function, and use that function for SGS modeling. We have already discussed how to subset a log, build a histogram of that data, and extract a distribution function from the histogram. Given that you have a distribution function ready to submit to the SGS algorithm, all you have to do is check the radio button in front of General distribution and use the blue arrow to insert the name of the distribution. Note that the Log and Output data range parameters are still available for adjustment using this approach.
Figure: The Distribution tab of the SGS dialog with a Distribution function specified.
Figure: Zone Ness1 Porosity histogram just for the up‐scaled cells (left), the distribution function input to SGS (center), and the histogram for all modeled cells (right). Note how the modeled histogram matches the distribution function.
