No abstract

In the past two decades, algorithms for multiple‐point statistics (MPS) have been applied in many fields. However, 3D training datum or data (TD) is difficult to be obtained. Two‐dimensional geological cross‐sections from boreholes or geophysical data with high reliability are usually used to explain geological phenomena and are relatively easier to be acquired. In this study, a step‐wise algorithm that combines sequential process and global optimization is presented. Constructing 3D TD set and corresponding pattern databases that extended from 2D cross‐sections at each scale is one of the key steps after presetting the simulation parameters. The following step is constructing an initial model at the coarsest scale with the pattern databases. The iterative Expectation Maximum‐like (EM‐like) optimization process is implemented to obtain the final realization. Each iteration is conducted with a multiscale strategy. Simulation examples of the regional geological structures show that the stratigraphic sequence can be reasonably kept and reproduced. Also, the randomness and effectiveness of the microstructure model are verified by calculating the proportion of grains, fractal dimension and the curve of two‐point connectivity probability function.