Missing Data Imputation Method for Seabed Terrain and Strata Deformation Monitoring Utilizing Spatiotemporal Correlation

The accurate recording of terrain and strata deformation time series is vital for geodesy and geophysical studies. However, missing values often occur due to various reasons, necessitating robust imputation methods to utilize all available data effectively. In this study, a novel missing data imputation method is proposed based on the in situ long-term monitoring data obtained from micro-electro-mechanical system (MEMS) sensor arrays deployed in the Beilun Port, Ningbo, China. We investigate the spatiotemporal correlation between different sensor nodes (SNs) and employ separate fitting of deformation data from highly correlated sensors during high-tide and low-tide times for imputation. The analysis indicates that simple regression imputation achieves relative error (RE) of approximately 2% when the correlation coefficient exceeds 0.90 for a single node. However, for multiple regression, the RE does not significantly decrease with an increasing number of independent variables beyond three. To validate the accuracy of the proposed imputation method, the simulations using four baseline methods and four correlation-iterative (CI) models are conducted, which include four different missing patterns and missing rates ranging from 5% to 40%. The results demonstrate that the CI random forest regression (CI-RFR) model outperforms other methods across various missing patterns and rates, particularly in the in-row pattern.