Quantifying Rotation-Induced Errors in Near-Field Seismic Recordings: Assessing Impact on Rotation and Acceleration Measurements.
DOI:
https://doi.org/10.26443/seismica.v4i1.1444Keywords:
rotational seismology, rotation errors, 2024 Hualien earthquake, Volcanic Seismicity, attitude correction, Euler anglesAbstract
Understanding the full wave field is imperative for seismic data analysis, as the different components induce errors in the sensors. Recent development of rotational seismometers allows for detailed measurements of the wave field gradients. Providing additional information that was previously unattained. However, it is well-known from navigation solutions that rotational data requires proper processing to be physically meaningful. In this study, we focus on investigating and quantifying two errors affecting recording of rotations: 1) misorientation of sensor to local system called misorientation of rotations and 2) changing projection of the Earth's spin in the recordings - Earth spin leakage. Using 6-component datasets, including 3C translation and 3C rotation, from near-field events at the Kilauea Caldera in Hawai' i and the Mw 7.4 Hualien event on 2024-04-02, we find that the Earth spin leakage is negligible, while the misorientation of the rotations increases with ground motion amplitude, potentially becoming significant for large earthquakes in the near-field. While these errors do not significantly affect acceleration corrections in our dataset, they may be relevant for high-amplitudes or in highly sensitive applications. This work offers the first quantification of these errors in seismology and provides guidance for assessing the need for corrections in future studies.
References
Bernauer, F., Behnen, K., Wassermann, J., Egdorf, S., Igel, H., Donner, S., Stammler, K., Hoffmann, M., Edme, P., Sollberger, D., Schmelzbach, C., Robertsson, J., Paitz, P., Igel, J., Smolinski, K., Fichtner, A., Rossi, Y., Izgi, G., Vollmer, D., … Brokesova, J. (2021). Rotation, strain, and translation sensors performance tests with active seismic sources. Sensors, 21(1), 1–23. https://doi.org/10.3390/s21010264
Bernauer, F., Wassermann, J., Guattari, F., Frenois, A., Bigueur, A., Gaillot, A., de Toldi, E., Ponceau, D., Schreiber, U., & Igel, H. (2018). BlueSeis3A: Full Characterization of a 3C Broadband Rotational Seismometer. Seismological Research Letters, 89(2A), 620–629. https://doi.org/10.1785/0220170143
Bernauer, F., Wassermann, J., & Igel, H. (2012). Rotational sensors-a comparison of different sensor types. Journal of Seismology, 16(4), 595–602. https://doi.org/10.1007/s10950-012-9286-7
Bernauer, F., Wassermann, J., & Igel, H. (2020). Dynamic Tilt Correction Using Direct Rotational Motion Measurements. Seismological Research Letters, 91(5), 2872–2880. https://doi.org/10.1785/0220200132
Brokesova, J., & Malek, J. (2013). Rotaphone, a Self-Calibrated Six-Degree-of-Freedom Seismic Sensor and Its Strong-Motion Records. Seismological Research Letters, 84(5), 737–744. https://doi.org/10.1785/0220120189
Brotzer, A., Igel, H., Bernauer, F., Wassermann, J., Mellors, R., & Vernon, F. (2025). On single-station, six degree-of-freedom observations of local to regional seismicity at the Piñon Flat Observatory in Southern California. Seismica, 4(1). https://doi.org/10.26443/seismica.v4i1.1416
Chen, C., Wang, Y., Sun, L., Lin, C. J., Wei, Y., Liao, C., Lin, B., & Qin, L. (2023). Six-Component Earthquake Synchronous Observations Across Taiwan Strait: Phase Velocity and Source Location. Earth and Space Science, 10(12). https://doi.org/10.1029/2023EA003040
Clinton, J. F., & Heaton, T. H. (2002). Potential Advantages of a Strong-motion Velocity Meter over a Strong-motion Accelerometer. Seismological Research Letters, 73(3), 332–342. https://doi.org/10.1785/gssrl.73.3.332
Crawford, W. C., & Webb, S. C. (2000). Identifying and removing tilt noise from low-frequency (<0.1 Hz) seafloor vertical seismic data. Bulletin of the Seismological Society of America, 90(4), 952–963. https://doi.org/10.1785/0119990121
De Ridder, S. A. L., & Curtis, A. (2017). Seismic gradiometry using ambient seismic noise in an anisotropic Earth. Geophysical Journal International, 209(2), 1168–1179. https://doi.org/10.1093/gji/ggx073
Diebel, J. (2006). Representing Attitude: Euler Angles, Unit Quaternions, and Rotation Vectors.
Draper, C. S. (1981). Origins of inertial navigation. Journal of Guidance and Control, 4(5), 449–463. https://doi.org/10.2514/3.19748
Euler, L. (1775). Nova methodus motum corporum rigidorum determinandi. Novi Commentari Academiae Scientiarum Imperalis Petropolitanae, 20, 208–238.
Geng, J., Wen, Q., Chen, Q., & Chang, H. (2019). Six‐Degree‐of‐Freedom Broadband Seismogeodesy by Combining Collocated High‐Rate GNSS, Accelerometers, and Gyroscopes. Geophysical Research Letters, 46(2), 708–716. https://doi.org/10.1029/2018GL081398
Graizer, V. (2006). Tilts in strong ground motion. Bulletin of the Seismological Society of America, 96(6), 2090–2102. https://doi.org/10.1785/0120060065
Graizer, V. (2009). Tutorial on measuring rotations using multipendulum systems. Bulletin of the Seismological Society of America, 99(2 B), 1064–1072. https://doi.org/10.1785/0120080145
Hasan, A., Samsudin, K., & Rahman bin Ramli, A. (2009). A Review of Navigation Systems (Integration and Algorithms). Australian Journal of Basic and Applied Sciences, 3(2), 943–959. https://www.researchgate.net/publication/269990234
Ichinose, G. A., Ford, S. R., & Mellors, R. J. (2021). Regional Moment Tensor Inversion Using Rotational Observations. Journal of Geophysical Research: Solid Earth, 126(2). https://doi.org/10.1029/2020JB020827
Kalman, R. E. (1960). A New Approach to Linear Filtering and Prediction Problems 1. Journal of Basic Engineering, 35–45. https://doi.org/10.1115/1.3662552
Kurzych, A., Kowalski, J. K., Sakowicz, B., Krajewski, Z., & Jaroszewicz, L. R. (2016). The laboratory investigation of the innovative sensor for torsional effects in engineering structures’ monitoring. Opto-Electronics Review, 3(24), 134–143. https://doi.org/10.1515/oere−2016−0017
Lin, Chin-Jen. (2024). 6C dataset for Mw 7.4 Hualien earthquake on 2024-04-02 at station locations MDSA0 and NA01. In Dataset. https://doi.org/10.5281/zenodo.13653585
Lin, C.-J., Huang, H.-P., Liu, C.-C., & Chiu, H.-C. (2010). Application of Rotational Sensors to Correcting Rotation-Induced Effects on Accelerometers. Bulletin of the Seismological Society of America, 100(2), 585–597. https://doi.org/10.1785/0120090123
Lindner, F., Wassermann, J., Schmidt‐Aursch, M. C., Schreiber, K. U., & Igel, H. (2017). Seafloor Ground Rotation Observations: Potential for Improving Signal‐to‐Noise Ratio on Horizontal OBS Components. Seismological Research Letters, 88(1), 32–38. https://doi.org/10.1785/0220160051
Ma, K.-F., von Specht, S., Kuo, L.-W., Huang, H.-H., Lin, C.-R., Lin, C.-J., Ku, C.-S., Wu, E.-S., Wang, C.-Y., Chang, W.-Y., & Jousset, P. (2024). Broad-band strain amplification in an asymmetric fault zone observed from borehole optical fiber and core. Communications Earth & Environment, 5(1), 402. https://doi.org/10.1038/s43247-024-01558-6
Pancha, A., Webb, T. H., Stedman, G. E., McLeod, D. P., & Schreiber, K. U. (2000). Ring laser detection of rotations from teleseismic waves. Geophysical Research Letters, 27(21), 3553–3556. https://doi.org/10.1029/2000GL011734
Rossi, Y. (2023). Next Generation Monitoring of Strong Ground Motions and Structural Vibrations - Combining Accelerometer, GNSS and Rotation Sensors [Phdthesis, ETH Zürich]. https://doi.org/10.3929/ethz-b-000645882
Rossi, Y. (2025). YaraRossi/QuantifyRotationErrors: Code for: Quantifying Rotation-Induced Errors in Near-Field Seismic Recordings: Assessing Impact on Rotation and Acceleration Measurements. (v1.0.2). Zenodo. https://doi.org/10.5281/zenodo.15387179
Rossi, Y., Tatsis, K., Awadaljeed, M., Arbogast, K., Chatzi, E., Rothacher, M., & Clinton, J. (2021). Kalman Filter-Based Fusion of Collocated Acceleration, GNSS and Rotation Data for 6C Motion Tracking. Sensors, 21(4), 1543. https://doi.org/10.3390/s21041543
Rossi, Y., Tatsis, K., Hohensinn, R., Clinton, J., Chatzi, E., & Rothacher, M. (2024). Unscented Kalman Filter–Based Fusion of GNSS, Accelerometer, and Rotation Sensors for Motion Tracking. Journal of Structural Engineering, 150(7). https://doi.org/10.1061/JSENDH.STENG-12872
Rossi, Y., Tatsis, K., Hohensinn, R., Clinton, J., Rothacher, M., & Chatzi, E. (2023). Unscented Kalman filter-based fusion of GNSS, Accelerometer and Rotation Sensors for Motion Tracking. Journal of Structural Engineering (Submitted).
Savage, P. G. . (2000). Strapdown analytics. Strapdown Associates.
Sollberger, D., Greenhalgh, S. A., Schmelzbach, C., Van Renterghem, C., & Robertsson, J. O. A. (2018). 6-C polarization analysis using point measurements of translational and rotational ground-motion: theory and applications. Geophysical Journal International, 213(1), 77–97. https://doi.org/10.1093/gji/ggx542
U.S. Geological Survey. (2024). M7.4 - 15 km S of Hualien City, Taiwan, Finite Fault. https://earthquake.usgs.gov/earthquakes/eventpage/us7000m9g4/finite-fault?source=us&code=us7000m9g4_1
USGS Hawaiian Volcano Observatory (HVO). (1956a). Hawaiian Volcano Observatory Network. International Federation of Digital Seismograph Networks. https://doi.org/10.7914/SN/HV
USGS Hawaiian Volcano Observatory (HVO), U. S. of A. (1956b). Hawaiian Volcano Observatory Network (HVO).
Venkateswara, K., Paros, J., Bodin, P., Wilcock, W., & Tobin, H. J. (2021). Rotational Seismology with a Quartz Rotation Sensor. Seismological Research Letters, 93(1), 173–180. https://doi.org/10.1785/0220210171
Wassermann, J., Bernauer, F., Shiro, B., Johanson, I., Guattari, F., & Igel, H. (2020). Six‐Axis Ground Motion Measurements of Caldera Collapse at Kīlauea Volcano, Hawai’i—More Data, More Puzzles? Geophysical Research Letters, 47(5), 1–7. https://doi.org/10.1029/2019GL085999
Yuan, S., Gessele, K., Gabriel, A. A., May, D. A., Wassermann, J., & Igel, H. (2021). Seismic Source Tracking With Six Degree-of-Freedom Ground Motion Observations. Journal of Geophysical Research: Solid Earth, 126(3). https://doi.org/10.1029/2020JB021112
Downloads
Additional Files
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Yara Rossi, Felix Bernauer, Chin-Jen Lin, Frédéric Guattari, Baptiste Pinot

This work is licensed under a Creative Commons Attribution 4.0 International License.
Funding data
-
Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung
Grant numbers P500PN_217932