Earthquake magnitude estimation using an optimized CNN-DNN-GRU model with binary differential evolution and firefly algorithm

Abstract

Accurate earthquake magnitude estimation is critical for mitigating seismic hazards; however, the inherently nonlinear and dynamic characteristics of geophysical data present persistent modeling challenges. To address this complexity, this study proposes a novel hybrid deep learning framework, CNN-DNN-GRU. This architecture synergizes Convolutional Neural Networks (CNNs) for spatial feature extraction, Deep Neural Networks (DNNs) for hierarchical data representation, and Gated Recurrent Units (GRUs) for capturing long-term temporal dependencies. The framework’s efficacy is further enhanced by integrating Binary Differential Evolution (BDE) for robust feature selection and the Firefly Algorithm (FA) for rigorous hyperparameter tuning. The model was trained and evaluated on a comprehensive tabular dataset comprising 3,500,000 seismic event instances—detailing parameters such as magnitude, depth, and geospatial coordinates—spanning from 1990 to 2023, utilizing a chronological 70%–15%–15% split for training, validation, and independent testing, respectively. Empirical evaluation demonstrates the proposed model’s high predictive accuracy, yielding a Mean Squared Error (MSE) of 0.0109, Root Mean Squared Error (RMSE) of 0.1048, Mean Absolute Error (MAE) of 0.0837, Median Absolute Error (MedAE) of 0.0709, Mean Absolute Percentage Error (MAPE) of 0.0230, and a Coefficient of Determination (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R^2$$\end{document}) of 0.9918. These findings validate the architecture’s superior generalization capabilities, establishing it as a highly reliable computational tool for a magnitude-estimation component that may support future early-warning-oriented systems when integrated with real-time waveform and station-level data.