3. NeurISIS FRACTURE SETS ANALYSIS

3.1 Algorithm
3.2 NeurISIS User Interface
3.3 Verification Case

3. NeurISIS FRACTURE SETS ANALYSIS

NeurISIS uses a probabilistic neural network (PNN ) for fracture set identification. The algorithm offers the following advantages over conventional approaches:

• It takes advantage of the geologist's ability to define prior assumptions based on visual inspection of the data
• It can define sets based on any combination of fracture attributes
• It allows user control of the relative weightings of different fracture attributes
• It provides reproducible, defensible set classifications
• It provides robust set definitions, even for extensivity overlapping sets

This section presents the algorithms implemented, the user interface, and a verification test case.

3.1 Algorithm

The probabilistic neural network (Specht, 1990) used by NeurISIS is based on a combination of probability theory and Bayesian statistics, and was developed primarily for solving multivariate classification problems (Masters, 1993).

The algorithm for the implemented probabilistic neural network is illustrated in Figure 3-1. The algorithm proceeds as follows:

1. The user evaluates the data to define the variables to be considered in set classification.
2. The user evaluates the data to define prior distributions for each of the sets. Fractures with these distributions of properties are then generated to constitute the "training set".
3. The user specifies weightings w_i for each of the classification variables, for use in the utility function for evaluation of set classification.
   
   V(c) =
   
   where V(c) is the utility for classification c, W_i is the weighting for variable i, and D_i(j|c) is the Euclidian distance from the data point j for its classification c,
4. The neural network algorithm uses the minimum distance V(c) for each data point to determine which set it should be assigned to. Each fracture is evaluated for its probability of membership in each of the defined sets, and is assigned to those sets.
5. The statistics for each set are reported based on the fractures assigned to each set.
6. Set statistics and graphical displays are provided.

The classes of fracture properties which can be used in this algorithm are provided in Table 3-1.

Table 3-1 Fracture Property Classes

3.2 NeurISIS User Interface

The user interface for NeurISIS is illustrated in Figure 3-2. The user interface is designed based on an "object oriented" tree structure (Figure 3-3). Each fracture can have any number of properties, defined according to the class-types of Table 3-1. The procedure for set definition is described in the bulleted list below. The menu options are listed in Table 3-2.

• Dataset: Define the fracture data in the required format. The .ISI and .SAM formats required are illustrated in Tables 3-3 and 3-4. This file includes a definition of each of the fields in the file, and the data in tabular form.
• File/Open: Open the .ISI data file and the .SAM file describing the orientation and geometry of the fractures.
• Neural Net/Select Dataset: Choose a subset to analyze (if desired).
• Edit/Terzaghi: Apply the Terzaghi correction to the selected data. A warning will be issued if the data has already been Terzaghi corrected.
• View/Stereoplot: Produce stereoplots of the current data, with Terzaghi corrections (if selected) (Figure 3-4).
• Edit/Define New Set: Based on the visual analysis of the data, and statistical analysis of the data files, select properties to be used in the set assignments for the first set. Provide a weighting (0 to 1) for each of the available properties, and the initial distribution assumptions for each property. Distributions are specified by a distributional form (e.g., normal or log-normal), and moments (e.g., mean and standard deviation or dispersion) (Figure 3-5).
• Repeat the Edit/Define New Set for each set to be generated for the training set.
• Neural Net/Generate: Generate training sets according to the statistical descriptions provided using Edit/Define New Set. Specify the number of fractures to be generated for each set.
• Neural Net/Train: Use the probabilistic neural network algorithm to generate a neural network based on the assumed fracture set definitions.
• Neural Net/Classify: Use the neural network generated in the previous step to classify every fracture into one of the sets. Calculate the statistics of each set based on the fractures assigned to the sets (Figure 3-6).
• View/Stereoplot: Produce stereoplots of the fracture sets as assigned by the neural network.
• File/Save As: Save statistical reports and files containing the individual fracture sets.

Table 3-2 NeurISIS User Interface

Table 3-3 NeurISIS Data Format (.ISI)

# Any line beginning with a # symbol is a comment.

BEGIN FIELDS

Count = 3

# Count is the number of fields.

BEGIN FIELD

Name = "Orientation"

Type = ORIENTATION

# data type orientation is expressed as two real values

# theta (trend) and phi (plunge)

Pole = TRUE

# Pole = TRUE if data is pole trend, plunge, FALSE if data is dip-dir,dip

Corrected = TRUE

# Corrected = TRUE if a Terzaghi correction has been made

END

BEGIN FIELD

Name = "Survey ID"

# Files can be linked to borehole and traceplanes through

# an integer Survey ID in the .SAM file to facilitate Terzaghi correction.

Type = INTEGER

END

BEGIN FIELD

Name = "Tracelength"

Type = REAL

END

END

#now the data

#TREND PLUNGE SID TRACELENGTH

BEGIN DATA

Count = 200

211 29 1 3.96

224 34 1 7.05

201 13 1 2.22

<<additional data records>>

341 36 1 4.73

314 31 1 7.73

END

Table 3-4 Borehole Data Format (.SAM)

# Any record beginning with a # is a comment

#Borehole

BEGIN borehole

name = "Borehole NE-1X"

survey_id = 1

origin = 80 -80 0

scan_trend = 0

scan_plunge = 0

scan_length = 160

radius = 0.12

END

#Traceplane

BEGIN traceplane

name = "Tracemap XJX-43-2K"

survey_id = 2

origin = 80 80 0

scan_trend = 0

scan_plunge = 0

scan_length = 160

tran_trend = 0

tran_plunge = 90

tran_width = 160

END

3.3 Verification Case

The verification case was defined by generating two overlapping Fisher distributed fracture sets using the statistics given in Table 3-5. The stereoplot before fracture separation by NeurISIS is provided in Figure 3-7. The statistics for the fracture sets following neural network analysis, and the stereoplots for the fractures assigned to the sets are provided in Figure 3-8.

Table 3-5 NeurISIS Verification Case