A 3D Geological Modeling Method Using the Transformer Model: A Solution for Sparse Borehole Data

Three-dimensional (3D) geological models are essential for geological analysis and mineral resource estimation. Although conventional on-site survey methods, such as boreholes, provide local engineering geological information for 3D geological modeling, accurately predicting strata in areas with sparse borehole data remains a challenge. This study proposes a 3D geological modeling method using the Transformer model under the conditions of sparse borehole data. First, a K-dimensional tree was used to identify boreholes adjacent to the target point, and a borehole context sequence was constructed using stratigraphic information from neighboring boreholes. Subsequently, the relationship between the target point and its adjacent borehole sequence was calculated using the multi-head attention mechanism of the Transformer model. Finally, trained Transformer encoders were used to predict the stratigraphic category of the target point, and the normalized information entropy was used to quantify uncertainty during the modeling process. Experimental results showed that the accuracy of the method was 0.86, outperforming the accuracy and uncertainty of a recurrent neural network. The root mean square error is smaller than the inverse distance weight and Kriging. Compared to other methods, the proposed method can more accurately describe the geometric shape and distribution of geological bodies and reveal the sedimentary laws of the study area.