Statistic inversion of multi-zone transition probability models for aquifer characterization in alluvial fans

TL;DR

This paper introduces a statistical inverse framework using multi-zone transition probability models to characterize heterogeneity in alluvial fans, enabling detailed hydrofacies distribution simulation for flow and transport studies.

Contribution

It develops an analytical solution for multi-zone transition probability models and applies a statistical inversion method to accurately estimate model parameters with uncertainty quantification.

Findings

Successfully characterized heterogeneity of alluvial fan in Beijing Plain.

Demonstrated effective parameter estimation with uncertainty quantification.

Produced detailed hydrofacies distribution for flow and transport modeling.

Abstract

Understanding the heterogeneity arising from the complex architecture of sedimentary sequences in alluvial fans is challenging. This paper develops a statistical inverse framework in a multi-zone transition probability approach for characterizing the heterogeneity in alluvial fans. An analytical solution of the transition probability matrix is used to define the statistical relationships among different hydrofacies and their mean lengths, integral scales, and volumetric proportions. A statistical inversion is conducted to identify the multi-zone transition probability models and estimate the optimal statistical parameters using the modified Gauss-Newton-Levenberg-Marquardt method. The Jacobian matrix is computed by the sensitivity equation method, which results in an accurate inverse solution with quantification of parameter uncertainty. We use the Chaobai River alluvial fan in the Beijing Plain, China, as an example for elucidating the methodology of alluvial fan characterization. The alluvial fan is divided into three sediment zones. In each zone, the explicit mathematical formulations of the transition probability models are constructed with optimized different integral scales and volumetric proportions. The hydrofacies distributions in the three zones are simulated sequentially by the multi-zone transition probability-based indicator simulations. The result of this study provides the heterogeneous structure of the alluvial fan for further study of flow and transport simulations.