Lithological identification with probabilistic distribution by the modified compositional Kriging

Lithological distribution, as a direct geological reflection, has been widely used in petroleum and geological projects. It is a challenging task to obtain a probabilistic map of lithology by compositional Kriging (CK) with limited logging core data. The predictions are usually affected by local high or low values, resulting in discontinuous boundaries and abnormal data fluctuation. To address the problem of local instability, we proposed the modified compositional Kriging (MCK) with a regulating factor, for adjusting the influence of core data to increase the accuracy and continuity of lithological probabilistic map. To obtain a reasonable result, we determined the hyper-parameter in the regulating factor's function and a kind of seismic attribute highly correlated with logging data. The examples and the cross validation showed the effectiveness of Kriging method, and then proved the outstanding achievement of MCK through the comparison of field data's predictions. After direct demonstration, we extracted the correlation coefficients and the regulating factor in our method to reveal more details inside the calculation. The correlation coefficients showed the variation of logging's influence and illustrated the phenomenon that lacking of loggings can lead to deviations in the probability map. The regulating factor's distribution showed the extra effect of MCK to increase the stability by its controlling effect. Hence, the proposed MCK method can provide a stable distribution of lithology when a suitable regulating factor has been chosen. This method is an effective tool for estimating lithological probabilistic map with limited wells.