WD-HMSTL: A Wavelet-Driven Hybrid Multi-Scale Temporal Learning Framework for Earthquake Precursor Groundwater Level Anomaly Detection

Groundwater level anomalies are considered important indicators of earthquake precursors; however, minute-level groundwater level time series often contain both long-term trends and short-term disturbances, which increases the difficulty of anomaly identification. To address this issue, a Wavelet-Driven Hybrid Multi-Scale Temporal Learning Framework (WD-HMSTL) is proposed for earthquake precursor groundwater level anomaly detection. The framework first applies discrete wavelet transform using the Daubechies4 wavelet to decompose the original groundwater level series into high-frequency and low-frequency components. The high-frequency component, representing short-term fluctuations and abnormal disturbances, is modeled using an improved xLSTM-Dyt network with dynamic Tanh activation and a residual stacked structure of sLSTM and mLSTM to enhance nonlinear representation ability. The low-frequency component, describing long-term trend evolution, is modeled using an Autoregressive Integrated Moving Average Model (ARIMA)-Transformer hybrid structure, where the Transformer learns the residuals of the ARIMA model to compensate prediction errors. The high-frequency and low-frequency predictions are then integrated through linear regression, and anomaly detection is performed based on the distribution of prediction residuals using a high-quantile threshold combined with a sliding window strategy. Experimental results show that the proposed WD-HMSTL framework achieves stable prediction performance with an R2 of 0.9654 and an RMSE of 0.2483 on the test set, while exhibiting strong sensitivity to abnormal disturbances. These results demonstrate that WD-HMSTL effectively separates multi-scale features and improves the detection of earthquake precursor groundwater level anomalies.