Nearest neighbor multiple-point statistics method for fast Earth surface process modeling

Abstract:

Generating numerical models is important to understand Earth surface system associated with autogenic dynamics. Many Earth surface processes investigated by field and experimental data only represent a small subset of possible outcomes observed in nature. Therefore, it is necessary to generate a set of realistic models to simulate spatial and temporal variability. As an emerging stochastic modeling framework, multiple-point statistics (MPS) is widely applied to model geological structures such as bedrock topography and morphodynamic system. Given a training image, MPS extracts spatial patterns and reproduces suitable structures in a simulation grid. However, running speed is a key limitation. MPS investigates spatially and temporally complex dynamics at the cost of a growing simulation time.

In this work, we present a nearest neighbor simulation (NNSIM) method for fast categorical geological modeling. The main idea is to incorporate k-nearest neighbor classifiers into MPS framework. The point simulation program is treated as a classification problem. First, we applied the fast condensed nearest neighbor method to select important patterns. Second, a teacher-student architecture is proposed to extend pattern subset and improve classification accuracy. Third, we employ the ball-tree strategy to accelerate the searching program.

We tested the proposed method by modeling a channel system. Compared with existing programs, our NNSIM exhibits a better performance in terms of running time. Essential structures of the channel system are properly preserved. Further application focuses on a single flume experiment of braided river channels evolving under steady water and sediment discharges. Our method creates an ensemble of morphodynamic models to quantify spatial and temporal uncertainty. The experimental results show that the autogenic dynamics are suitably reproduced in the simulated realizations. The proposed NNSIM can accurately simulate the variability of the delta system for the given measures.