- [Voiceover] Let's study the background of declustering, the objective of declustering, polygonal declusterring cell declustering, comparisons of different methods. Then, we make a summary for this lecture. This is a porosity map. Nx equal to Ny equal to 101. The number of cells is 10,000. The number of porosity is 10,000. Mean is equal to 0.235. Standard deviation is equal to 0.114 Let's use this as the true distribution. Select 20 porosity values, make a histogram, calculate the mean and standard deviation of 20 porosity values, mean is equal to 0.253, that's overestimated, standard deviation is equal to 0.091, that's underestimated. Collected data are often not representative of the entire area of interest. Based on these data, histogram and statistics are biased. To adjust the histogram and statistics to be better representative of the entire area of interest by assigning each datum a weight. Wli, i is one, two, until n. Based on its closeness to surrounding data. Some of this is equal to one. Closely space the data. In form, fewer read notes. And hence, receive less weight. Widely space the data in for more great notes, and hence receive greater weight. Statistics that are being computed using weighted data mean understand the deviation are defined in the equations. Weights can be figured out by a polygonal declustering or cell declustering. The polygonal areas of influence are shown here in black lines. Many programs can generate this polygon around each datum and compute each area. I, I is equal to one, two, until N. Weight is defined as the area of the polygon divided by the total areas shown in the equation. Calculated the mean, under standard deviation of 20 weighted the property values. Weighted mean is 0.238. Standard deviation is 0.101. We'll compare this with two values. How to define the weights using cell declustering method. First, divide the area of interest into a number of cells, L, in this case L is equal to 16. Then count the occupied cells, Lo. For this case, Lo is equal to 15. Count the number of data in each occupied cell. Nlo lo is one, two, until lo. The total of nlo is the number of data. For this case, it is 20. Weight of each datum is defined inversely proportional to the number of data in a cell. Nlo the total weights is one. Let's make a look three examples. So weight is one datum in a cell, is one divided by 15. The weight is two data in data a cell, is one divided by two times 15, so weight if it's three data in a cell, is divided by three times 15. Calculated mean. Under standard deviation of 20 weighted porosity values. Weighted mean is equal to 0.239. Weighted standard deviation is equal to 0.104. We'll compare this with two values. Let's take a look as the numbers and the bar talks in the table. The statistics from polygonal and the cell declustering weighted are closer to two values than equal weighted ones. Let's make a summary. The statistics from polygonal and cell declustering weighted are closer to true ones than equal weighted ones. The examples shown in this lecture are 2D, but it can extend to 3D. For cell declustering method, the grid is different from geological model of flow simulation model grid. Choosing an optimal grid needs sensitivity studies. The declustered histogram which is representative of the entire area can be used as the target histogram in back normal score transformation of stochastic Gaussian simulation. This is the end of the lecture.