Comparison of Spatial Interpolation Methods: Inverse Distance Weighted and Kriging for Earthquake Intensity Mapping in Aceh, Indonesia

Latifah Rahayu; Cut Chairilla Yolanda Utami; Rahmatul Fauzi; Novi Reandy Sasmita

doi:10.60084/ijds.v3i2.347

Authors

Latifah Rahayu Department of Statistics, Faculty of Mathematics and Natural Sciences, Universitas Syiah Kuala, Banda Aceh 23111, Indonesia
Cut Chairilla Yolanda Utami Department of Statistics, Faculty of Mathematics and Natural Sciences, Universitas Syiah Kuala, Banda Aceh 23111, Indonesia
Rahmatul Fauzi Department of Statistics, Faculty of Mathematics and Natural Sciences, Universitas Syiah Kuala, Banda Aceh 23111, Indonesia
Novi Reandy Sasmita Department of Statistics, Faculty of Mathematics and Natural Sciences, Universitas Syiah Kuala, Banda Aceh 23111, Indonesia

DOI:

https://doi.org/10.60084/ijds.v3i2.347

Keywords:

Spatial interpolation , Kriging , Inverse Distance Weighted (IDW), Earthquake intensity mapping , Geostatistical analysis

Abstract

Aceh Province, located in the Sumatra megathrust zone of Indonesia, is one of the most seismically active regions in Southeast Asia. Understanding the spatial distribution of earthquake magnitudes is essential for disaster mitigation and risk management. This study compares two spatial interpolation methods Inverse Distance Weighted (IDW) and Kriging to determine the most accurate approach for mapping earthquake intensity in Aceh Province. A total of 2,255 earthquake events with magnitudes of 2.5 M and above, recorded between 1990 and 2024 by the United States Geological Survey (USGS), were analyzed. IDW was tested using five power parameters (p = 1–5), while Kriging applied three semivariogram models (spherical, exponential, and Gaussian). The interpolation accuracy was assessed through Root Mean Square Error (RMSE), Mean Square Error (MSE), and Mean Absolute Percentage Error (MAPE). Results indicated that Kriging with the exponential semivariogram achieved the highest accuracy, with RMSE = 0.0848, MSE = 0.0072, and MAPE = 1.14%, outperforming IDW (RMSE = 0.2288, MSE = 0.0523, MAPE = 1.24%). The Kriging model effectively represented the gradual spatial decay of seismic energy, identifying Aceh Singkil and northern Simeulue as the most earthquake-prone zones, consistent with regional tectonic patterns. These findings confirm that incorporating spatial autocorrelation enhances interpolation accuracy and geophysical interpretation. The study establishes Kriging as a reliable tool for seismic hazard mapping and provides valuable insights for disaster preparedness, infrastructure planning, and future geostatistical applications in earthquake risk assessment.

Downloads

Download data is not yet available.

References

Rizal, J., Yodi Gunawan, A., W. Indratno, S., and Meilano, I. (2023). Seismic Activity Analysis of Five Major Earthquake Source Segments in the Sumatra Megathrust Zone, Bulletin of the New Zealand Society for Earthquake Engineering, Vol. 56, No. 2, 55–70. doi:10.5459/bnzsee.1555.
U.S. Geological Survey. (2004). M 9.1 - 2004 Sumatra - Andaman Islands Earthquake, USGS Earthquake Hazards Program.
Bilham, R. (2005). A Flying Start, Then a Slow Slip, Science, Vol. 308, No. 5725, 1126–1127. doi:10.1126/science.1113363.
Synolakis, C., Okal, E., and Bernard, E. (2005). The Megatsunami of December 26, 2004, Bridge, National Academy of Engineering, Vol. 32, No. 2, 25–35.
Alavi, S. H., Bahrami, A., Mashayekhi, M., and Zolfaghari, M. (2024). Optimizing Interpolation Methods and Point Distances for Accurate Earthquake Hazard Mapping, Buildings, Vol. 14, No. 6, 1823. doi:10.3390/buildings14061823.
U.S. Geological Survey. (n.d.). ANSS Comprehensive Earthquake Catalog (ComCat) and Earthquake Hazards Program: Catalog Documentation and Search Interface, USGS Earthquake Hazards Program.
Mase, L. Z. (2022). Local Seismic Hazard Map Based on the Response Spectra of Stiff and Very Dense Soils in Bengkulu City, Indonesia, Geodesy and Geodynamics, Vol. 13, No. 6, 573–584. doi:10.1016/j.geog.2022.05.003.
Swita, B., Astuti, M., Faisal, F., and Nuryaman, A. (2025). Mapping Earthquake Magnitudes In Bengkulu Province And Surrounding Areas Using Robust Ordinary Kriging, BAREKENG: Jurnal Ilmu Matematika Dan Terapan, Vol. 19, No. 3, 1537–1552. doi:10.30598/barekengvol19iss3pp1537-1552.
Hutchings, S. J., and Mooney, W. D. (2021). The Seismicity of Indonesia and Tectonic Implications, Geochemistry, Geophysics, Geosystems, Vol. 22, No. 9. doi:10.1029/2021GC009812.
Azhar, R., Rusdi, M., Irham, M., and Fuadi, A. (2021). Spatial Distribution of Mangrove Using a Geographic Information System in Aceh Besar, IOP Conference Series: Earth and Environmental Science, Vol. 674, No. 1, 012024. doi:10.1088/1755-1315/674/1/012024.
Nabila Azzahra Haris Putri, and Fauzan, A. (2024). Comparison of Inverse Distance Weighted and Thin Plate Spline Interpolation Methods in Projecting the Strength of the West Sumatra Earthquake, EKSAKTA: Journal of Sciences and Data Analysis, 185–193. doi:10.20885/EKSAKTA.vol5.iss2.art9.
AbdelRahman, M. A. E., Zakarya, Y. M., Metwaly, M. M., and Koubouris, G. (2020). Deciphering Soil Spatial Variability through Geostatistics and Interpolation Techniques, Sustainability, Vol. 13, No. 1, 194. doi:10.3390/su13010194.
Fatmawati, A. I., and Lubis, R. S. (2024). Estimated Sulfur Dioxide Pollutant Concentrations In Medan City Using Ordinary Kriging and Inverse Distance Weighting Approaches, Mathline : Jurnal Matematika Dan Pendidikan Matematika, Vol. 9, No. 1, 13–30. doi:10.31943/mathline.v9i1.548.
Wahid, M. A., and Winarno, E. (2024). Bauxite Resource Estimation Analysis Using Ordinary Kriging and Inverse Distance Weighting in West Kalimantan, Journal of Earth and Marine Technology (JEMT), Vol. 4, No. 2, 255–264. doi:10.31284/j.jemt.2024.v4i2.5340.
Ananias, D. R. S., Liska, G. R., Beijo, L. A., Liska, G. J. R., and de Menezes, F. S. (2021). The Assessment of Annual Rainfall Field by Applying Different Interpolation Methods in the State of Rio Grande Do Sul, Brazil, SN Applied Sciences, Vol. 3, No. 7, 687. doi:10.1007/s42452-021-04679-1.
Guédé, K. G., Yu, Z., Hofmeister, F., Gu, H., Mohammadi, B., Chen, X., Lin, H., Shen, T., and Gouertoumbo, W. F. (2024). Geostatistical Interpolation Approach for Improving Flood Simulation Within a Data‐Scarce Region in the Tibetan Plateau, Hydrological Processes, Vol. 38, No. 11. doi:10.1002/hyp.15336.
Aparecido, L. E. de O., Moraes, J. R. da S. C. de, Lima, R. F. de, and Torsoni, G. B. (2022). Spatial Interpolation Techniques to Map Rainfall in Southeast Brazil, Revista Brasileira de Meteorologia, Vol. 37, No. 1, 141–155. doi:10.1590/0102-77863710015.
Workneh, H. T., Chen, X., Ma, Y., Bayable, E., and Dash, A. (2024). Comparison of IDW, Kriging and Orographic Based Linear Interpolations of Rainfall in Six Rainfall Regimes of Ethiopia, Journal of Hydrology: Regional Studies, Vol. 52, 101696. doi:10.1016/j.ejrh.2024.101696.
Sawires, R., Santoyo, M. A., Peláez, J. A., and Corona Fernández, R. D. (2019). An Updated and Unified Earthquake Catalog from 1787 to 2018 for Seismic Hazard Assessment Studies in Mexico, Scientific Data, Vol. 6, No. 1, 241. doi:10.1038/s41597-019-0234-z.
Vorobieva, I. A., Gvishiani, A. D., Shebalin, P. N., Dzeboev, B. A., Dzeranov, B. V., Skorkina, A. A., Sergeeva, N. A., and Fomenko, N. A. (2023). Integrated Earthquake Catalog II: The Western Sector of the Russian Arctic, Applied Sciences, Vol. 13, No. 12, 7084. doi:10.3390/app13127084.
Maiti, S. K., and Kim, B. (2025). An Updated, Homogeneous, and Declustered Earthquake Catalog for South Korea and Neighboring Regions, Natural Hazards and Earth System Sciences, Vol. 25, No. 10, 4021–4041. doi:10.5194/nhess-25-4021-2025.
Pradhan, A., Adams, K. H., Chandrasekaran, V., Liu, Z., Reager, J. T., Stuart, A. M., and Turmon, M. J. (2024). Modeling Groundwater Levels in California’s Central Valley by Hierarchical Gaussian Process and Neural Network Regression, Journal of Geophysical Research: Machine Learning and Computation, Vol. 1, No. 4. doi:10.1029/2024JH000322.
Healy, D., Tawn, J., Thorne, P., and Parnell, A. (2025). Inference for Extreme Spatial Temperature Events in a Changing Climate with Application to Ireland, Journal of the Royal Statistical Society Series C: Applied Statistics, Vol. 74, No. 2, 275–299. doi:10.1093/jrsssc/qlae047.
Li, J., and Heap, A. D. (2008). A Review of Spatial Interpolation Methods for Environmental Scientists, Australian Geological Survey Organisation, Vol. GeoCat# 68, No. 2008/23, 154. doi:http://www.ga.gov.au/image_cache/GA12526.pdf.
Webster, R., and Oliver, M. A. (2008). Geostatistics for Environmental Scientists: Second Edition, Geostatistics for Environmental Scientists: Second Edition, 1–315. doi:10.1002/9780470517277.
Li, J., and Heap, A. D. (2011). A Review of Comparative Studies of Spatial Interpolation Methods in Environmental Sciences: Performance and Impact Factors, Ecological Informatics, Vol. 6, Nos. 3–4, 228–241. doi:10.1016/j.ecoinf.2010.12.003.