Stochastic Modeling of Rock Heterogeneities Applying New Autocorrelation Estimators and Simulated Annealing

摘要

Two new integral estimators of spatial autocorrelation are putrnforward and studied. The first is LV (Local Variance), basedrnon the variance of the distribution. It is also an estimator of thernaverage value of the semivariogram within a region. Thernsecond, SLV (Semivariogram from the Local Variance), isrnrelated to the derivatives of the former. It is an estimator of thernsemivariogram itself. The behavior of these two estimators isrncompared to that of the classical semivariogram estimatorrn(CSV) using different data sets. SLV behavior is similar tornthat of CSV. Both are noisy and present fluctuations thatrnincrease with lag distance. Instead, LV is smoother and morernresistant to outliers, making it easier to be represented by arntheoretical model. Also, LV is less affected by individualrnvalues of samples, honoring the general statistics of data.rnAfterwards, the ability of the three estimators to model actualrnspatial variability is tested using the Simulated Annealingrnoptimization technique. This technique has a goodrnperformance when any of the three estimators is included inrnthe objective function. It is able to reproduce actual porosity orrnpermeability fields, even when there is a specific spatialrnstructure (such as cyclic, staircase-like, etc). However, LV hasrna main advantage: it still preserves the main features of thernspatial structure even though it is very smooth.