Submitted:
31 July 2025
Posted:
01 August 2025
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Abstract
Keywords:
1. Introduction
1.1. Literature Review
1.1.1. Numerical Methods Approaches
1.1.2. Artificial Intelligence Methods
1.2. Aims and Objectives
- Recreate and evaluate baseline models to establish the relationship between seismic RMS amplitude and SWH, using comprehensive evaluation metrics for fair comparison.
- Develop a cost-effective modelling approach, deployable on consumer-grade hardware, promoting accessibility in resource-constrained settings and supporting ethical AI practices.
- Design an efficient and deployable data pipeline that minimises preprocessing to ensure practical real-time inference with low system complexity.
- Apply location-specific hyperparameter tuning to optimise model performance across varying environmental and geographical conditions.
- Prioritise high-integrity, real-world data over interpolated or gap-filled datasets to improve model reliability and generalisability.
1.3. Contributions
2. Materials and Methods
2.1. Exploratory Data Analysis
2.2. Model Selection
2.3. Creation of a Baseline
2.4. Experimental Setup and Hyperparameters
- Number of features considered when making a decision: This defines the feature subset to consider (50%, , or square root of total features) to decide how to split the data.
- Number of trees in the model: This refers to how many decision trees are combined to make predictions – 100, 200, or 300 trees.
- Maximum depth of each tree: Limits how many layers of decisions each tree can make, with common values being 10, 20, or 30 levels deep.
- Minimum number of data points at a final decision point: A tree will not make a decision (or `leaf’) unless it has at least 1, 3, or 5 data samples at that point.
- Minimum number of data points needed to split a branch: A decision within the tree requires at least 2, 5, or 10 samples to be considered.
2.5. Evaluation Metrics and Performance Analysis
3. Results
3.1. Baseline Model
3.2. Model Performance
3.2.1. Hyperparameter Tuning
3.2.2. K-Fold Cross Validation
4. Discussion
4.1. Comparison with Baseline Models
4.2. Summary of Key Findings
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
| AI | Artificial intelligence |
| CMEMS | Copernicus Marine Environment Monitoring Service |
| EIDA | European Integrated Data Archive |
| KNN | k-nearest neighbours |
| LGB | Light gradient boosting |
| MAE | Mean absolute error |
| MARE | Mean average relative error |
| MCMC | Markov chain Monte Carlo |
| ML | Machine learning |
| MSE | Mean squared error |
| PSD | Power spectral density |
| RF | Random forest |
| RMS | Root mean square |
| RMSE | Root mean squared error |
| SWH | Significant wave height |
References
- United Nations Department of Economic and Social Affairs. United Nations Sustainable Development Goals. 2015. https://sdgs.un.org/goals (accessed on 25 April 2025).
- Orós, J.; Montesdeoca, N.; Camacho, M.; Arencibia, A.; Calabuig, P. Causes of stranding and mortality, and final disposition of loggerhead sea turtles (*Caretta caretta*) admitted to a wildlife rehabilitation center in Gran Canaria Island, Spain (1998–2014): A long-term retrospective study. PLoS One 2016, 11(2), e0149398. [CrossRef]
- IOC-UNESCO. Global Ocean Science Report 2020—Charting Capacity for Ocean Sustainability; Isensee, K., Ed.; UNESCO Publishing: Paris, France, 2020.
- Ardhuin, F., Gualtieri, L. and Stutzmann, E. (2015). How ocean waves rock the Earth: Two mechanisms explain microseisms with periods 3 to 300 s. Geophysical Research Letters, 42(3), 765–772.
- Besedina, A.N. and Tubanov, Ts A. (2023). Microseisms as a tool for geophysical research. A review. Journal of Volcanology and Seismology, 17(2), 83–101.
- Ferretti, G.; Zunino, A.; Scafidi, D.; Barani, S.; Spallarossa, D. On microseisms recorded near the Ligurian coast (Italy) and their relationship with sea wave height. Geophys. J. Int. 2013, 194, 524–533. [CrossRef]
- Borzì, A. M.; Minio, V.; De Plaen, R.; Lecocq, T.; Alparone, S.; Aronica, S.; Cannavò, F.; Capodici, F.; Ciraolo, G.; D’Amico, S.; et al. Integration of microseism, wavemeter buoy, HF radar and hindcast data to analyze the Mediterranean cyclone Helios. Ocean Sci. 2024, 20(1), 1–20. [CrossRef]
- Sverdrup, H. U.; Munk, W. H.; Scripps Institution of Oceanography; United States Hydrographic Office. Wind, Sea and Swell: Theory of Relations for Forecasting; Hydrographic Office, 1947. https://books.google.com.mt/books?id=DvPyLfd1xdAC.
- Cannata, A.; Cannavò, F.; Moschella, S.; Di Grazia, G.; Nardone, G.; Orasi, A.; Picone, M.; Ferla, M.; Gresta, S. Unravelling the relationship between microseisms and spatial distribution of sea wave height by statistical and machine learning approaches. Remote Sens. 2020, 12(5), 761. [CrossRef]
- Minio, V.; Borzì, A. M.; Saitta, S.; Alparone, S.; Cannata, A.; Ciraolo, G.; Contrafatto, D.; D’Amico, S.; Di Grazia, G.; Larocca, G.; Cannavò, F. Towards a monitoring system of the sea state based on microseism and machine learning. Environ. Model. Softw. 2023, 167, 105781. [CrossRef]
- Istituto Nazionale di Geofisica e Vulcanologia (INGV). Rete Sismica Nazionale (RSN) [Data set]; Istituto Nazionale di Geofisica e Vulcanologia (INGV): Rome, Italy, 2005. (accessed on 23 November 2024). [CrossRef]
- E.U. Copernicus Marine Service Information (CMEMS). Mediterranean Sea Waves Reanalysis [Data set]; Marine Data Store (MDS). (accessed on 31 March 2025). [CrossRef]
- Khan, A.A.; Chaudhari, O.; Chandra, R. A review of ensemble learning and data augmentation models for class imbalanced problems: Combination, implementation and evaluation. Expert Syst. Appl. 2024, 244, 122778. [CrossRef]
- Guo, Y.; Fu, L.; Li, H. Seismic data interpolation based on multi-scale transformer. IEEE Geosci. Remote Sens. Lett. 2023, 20, 1–5. [CrossRef]
- Kaur, H.; Pham, N.; Fomel, S. Seismic data interpolation using CycleGAN. In SEG Tech. Program Expanded Abstracts 2019, 2202–2206.
- Baranbooei, S.; Bean, C.J.; Rezaeifar, M.; Donne, S.E. Determining offshore ocean significant wave height (SWH) using continuous land-recorded seismic data: an example from the northeast Atlantic. J. Mar. Sci. Eng. 2025, 13(4), 807. https://www.mdpi.com/2077-1312/13/4/807.
- Breiman, L. Random forests. Mach. Learn. 2001, 45, 5–32. [CrossRef]
- Moni, A.; Craig, D.; Bean, C.J. Separation and location of microseism sources. Geophys. Res. Lett. 2013, 40(12), 3118–3122. [CrossRef]
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| Replicated Baseline Performance | Final Model Performance | |||||||
| Station | R² | MSE | MAE | RMSE | R² | MSE | MAE | RMSE |
| AIO | 0.350 | 0.089 | 0.209 | 0.298 | 0.607 | 0.071 | 0.182 | 0.267 |
| CAVT | - | - | - | - | 0.892 | 0.023 | 0.101 | 0.151 |
| CSLB | 0.868 | 0.044 | 0.137 | 0.210 | 0.881 | 0.055 | 0.143 | 0.235 |
| HAGA | 0.639 | 0.065 | 0.156 | 0.255 | 0.784 | 0.064 | 0.153 | 0.252 |
| MMGO | 0.330 | 0.252 | 0.243 | 0.502 | - | - | - | - |
| MPNC | 0.861 | 0.030 | 0.109 | 0.174 | - | - | - | - |
| MSDA | 0.843 | 0.056 | 0.147 | 0.237 | 0.862 | 0.033 | 0.122 | 0.182 |
| MUCR | 0.840 | 0.052 | 0.156 | 0.228 | 0.862 | 0.041 | 0.141 | 0.202 |
| SOLUN | 0.698 | 0.054 | 0.135 | 0.233 | - | - | - | - |
| WDD | 0.841 | 0.067 | 0.157 | 0.258 | 0.921 | 0.021 | 0.102 | 0.144 |
| AIO | CAVT | CSLB | HAGA | MSDA | MUCR | WDD | |
| RF_max_depth | 30 | 30 | 10 | 20 | 30 | 30 | 10 |
| RF_n_estimators | 200 | 200 | 200 | 100 | 100 | 100 | 100 |
| RF_max_features | sqrt | sqrt | 0.5 | ||||
| RF_min_samples_split | 2 | 2 | 5 | 2 | 10 | 10 | 5 |
| RF_min_samples_leaf | 1 | 1 | 3 | 1 | 1 | 1 | 3 |
| MAE | 0.18243 | 0.10066 | 0.14298 | 0.15251 | 0.12207 | 0.14089 | 0.10175 |
| MSE | 0.07107 | 0.02291 | 0.05519 | 0.06361 | 0.03282 | 0.04067 | 0.02073 |
| RMSE | 0.26659 | 0.15137 | 0.23492 | 0.25221 | 0.18116 | 0.20166 | 0.14398 |
| R² | 0.60686 | 0.89238 | 0.88108 | 0.78357 | 0.86198 | 0.86200 | 0.92060 |
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