- [Lecturer] Let's study Indicator Kriging definition, input data for Indicator Kriging, steps of Indicator Kriging, go to the end let's make a summary. Journel defined it as that. It is a geo-statistical technique used to approximate our little conditional accommodate your distribution function at each point of a grid based on the correlation structure of indicator transformed data points. Input data, conditional data usually well log data, global facies proportions, indicator variogram parameters and the search parameters. They are following basic steps in the indicator process. One transform the original data into facies, two assign transformed data into grid, three prepare global facies proportion table, four apply binary indicator transform to each facies, five prepare variograms, six define search region, seven run Kriging for each undefined cell, eight check results. Indicator Kriging requires the equal data of this Kriger indicator variables. In this example original data set of net gross if threshold is 0.3 our net gross which is equal to or less than 0.3 will be transformed into shale that is zero. Please say 0.08 is transformed into zero, 0.12 is transformed into zero, 0.11 is transformed into zero, 0.23 is transformed into zero. And net to gross which is larger than 0.3 will be transformed to sand that is one. Please say 0.8 is transformed into one, 0.75 is transformed into one, 0.68 is transformed into one. This is an example of two indicators the procedures are similar for more than two facies. Assign transformed data into a simulation grid this may be used as conditioning data. Seven conditioning data are assigned to their nearest grid cell centers. When multiple data are assigned to the same cell we can take the maximum of current one or closest one to the cell center. In this example we do maximum occurrence for one, one and zero so it is one and one there has one data. Input data table is copied here this is a global facies proportion table. The facies counts of the input data are computed and show in this table. There are three zeros, there are two ones. The facies proportion values of the input data are computed and are shown in the table. Three divided by five is 0.6 two divided by five is 0.4. The facies proportion values are editable and are used as global facies proportions in simulation. When the variogram collision changes are short under the control data are scales. The final results much reach the input of the global facies proportions. Alright it is equal to one. And that is 100% in facies k present or the location mu a otherwise i is equal to zero if facies k that's not present at location mu a. This is to apply binary indicator transform to sand. Top is the assigned data map one is the sand, zero is shale. Wherever sand is present it's probability is about 100%, see two grey eclipses otherwise it is shale. It's probability is 0%, the two blue eclipses. The bottom is probability map of sand. This is to apply binary indicator transform to shale the top is the assigned data map one is sand, zero is shale. Wherever shale present it's probability is 100% see two blue eclipses. Otherwise it is sand it's probability is 0% see two grey eclipses. The bottom is the probability map of shale. Prepare indicator variogram for sand that is gamma one. Prepare indicator variogram for shale that is gamma zero. Define search region in 2D it is an eclipse select an undefined cell. Here we select i equal to two d equal to two as indicator Kriging. Only use it to input data. The order of the selecting and undefined cell doesn't matter. Well applying search region is to put eclipse center to the selective and estimating a cell center on probability map of sand under a quarter eclipse center to the selective undefined cell center on probability map of shale. Obtain data in search region in probability map of cell under obtain the i search region on probability map of shale. Let's work on that. Indicator Kriging gives us an estimate of mu for each facies. Which is the probability of this facies? Using conditional data, indicator variogram parameters and the search parameters and the global facies proportions thus then their activation is not in use. Run Kriging on probability map of sand and then run Kriging on probability map of shale. We get mean probability of sand is 18% mean probability of shale is 67%. Input global facies proportions are assigned to the cell where there are no conditional data obtained in the search area. Sorting mu sand equal to zero point about eight under mu shale equal to 0.67 from shale to sand that is the first step as mu shale equal to 0.67 and the second is mu sand equal to zero point about eight. Mu is mean under mu is probability. Then re-scale them into normalized zero to one cumulative probability space by simple normalization calculations shown here. Now we get to normalize the mu shale equal to 0.79 that is 79% and then normalize the mu sand equal to 0.21 that is 21%. update the re-scaled results the similar procedures as the first cell beta b conducted on all cells. Now we have finished all cells. Note these are not the real computed results we need to check if results are reasonable if results honor input conditional data if results honor the input global facies proportion if results honor the input variogram model. Let's make a summary. Indicator Kriging is a non-parametric method of interpolation. It generates deterministic results. It's based on data transformed from continuous values into categorical values or begin with the categorical data like facies. Indicator transform on categorical data is required. Indicator variogram for each categorical variable needs to be prepared. It uses the kriging mean to generate the probability distribution field of each categorical variable. It only uses input data when computing a value at an un-estimated grid cell. It provides the probability of the data value within some data range. It's used when interested in finding area with values within some data range but not the prediction of accurate data values. That's the end of the lecture.