{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,3]],"date-time":"2026-09-03T05:16:57Z","timestamp":1788412617535,"version":"build-2803163510"},"reference-count":32,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006256","name":"Universit\u00e0 degli Studi dell\u2019Aquila","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100006256","id-type":"DOI","asserted-by":"crossref"}]},{"id":[{"id":"https:\/\/ror.org\/01j9p1r26","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Earthquakes exhibit well-documented statistical regularities at the catalogue level, such as the Gutenberg\u2013Richter magnitude\u2013frequency relation and the Omori\u2013Utsu aftershock decay, often interpreted as signatures of seismicity as a driven, dissipative system far from thermodynamic equilibrium. However, whether comparable signatures, such as scale invariance and anomalous diffusion, can be detected directly within individual ground motion recordings remains an open question. This work investigates whether acceleration, velocity, and displacement signals recorded during the 2009 Mw 6.1 L\u2019Aquila earthquake display statistical properties consistent with non-equilibrium complex systems, and whether different seismic phases carry distinct, reproducible statistical signatures. P- and S-wave onset times are estimated using AR-AIC, with adaptive search windows centred on theoretical arrivals from the CRUST1.0 velocity model. Coda onset is determined using three complementary criteria combined into a median ensemble, enabling the segmentation of each recording into up to five temporal windows. Displacement moment scaling is analysed for each window and signal type, within the framework of strong anomalous diffusion, yielding the scaling exponents \u03b6(q). Robustness is systematically assessed against the choice of coda onset method, the empirical thresholds defining coda onset and end, the sub-interval of \u03c4 used in the moment scaling fit, and the filter band applied to the ground motion signals. Evidence for anomalous diffusion is nuanced: both its sign and magnitude depend on the seismic phase, with only a subset of configurations remaining stable across all segmentation schemes tested. These results indicate that anomalous scaling signatures, when present, are not universal, and that systematic robustness analyses are essential to distinguish genuine physical effects from segmentation artefacts.<\/jats:p>","DOI":"10.3390\/e28090972","type":"journal-article","created":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T15:08:43Z","timestamp":1788275323000},"page":"972","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Scaling Analysis of Seismic Ground Motion Signals"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-0296-8498","authenticated-orcid":false,"given":"Giuliana","family":"Paradiso","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"methodology","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1244-6942","authenticated-orcid":false,"given":"Federica","family":"Di Michele","sequence":"additional","affiliation":[{"name":"Istituto Nazionale di Geofisica e Vulcanologia, 20133 Milan, Italy"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7424-7888","authenticated-orcid":false,"given":"Matteo","family":"Colangeli","sequence":"additional","affiliation":[{"name":"Department of Information Engineering, Computer Science and Mathematics, University of L\u2019Aquila, Via Vetoio, 67100 L\u2019Aquila, Italy"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"},{"role":"funding-acquisition","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6546-8390","authenticated-orcid":false,"given":"Bruno","family":"Rubino","sequence":"additional","affiliation":[{"name":"Department of Information Engineering, Computer Science and Mathematics, University of L\u2019Aquila, Via Vetoio, 67100 L\u2019Aquila, Italy"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"},{"role":"funding-acquisition","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4223-6279","authenticated-orcid":false,"given":"Lamberto","family":"Rondoni","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy"},{"name":"INFN, Sezione di Torino, Via P. Giuria 1, 10125 Turin, Italy"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Scholz, C.H. (2018). The Mechanics of Earthquakes and Faulting, Cambridge University Press. [3rd ed.].","DOI":"10.1017\/9781316681473"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1785\/BSSA0340040185","article-title":"Frequency of earthquakes in California","volume":"34","author":"Gutenberg","year":"1944","journal-title":"Bull. Seismol. Soc. Am."},{"key":"ref_3","first-page":"111","article-title":"On aftershocks of earthquakes","volume":"7","author":"Omori","year":"1894","journal-title":"J. Coll. Sci. Imp. Univ. Tokyo"},{"key":"ref_4","first-page":"521","article-title":"A statistical study on the occurrence of aftershocks","volume":"30","author":"Utsu","year":"1961","journal-title":"Geophys. Mag."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"15635","DOI":"10.1029\/JB094iB11p15635","article-title":"Earthquakes as a Self-Organized Critical Phenomenon","volume":"94","author":"Bak","year":"1989","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1244","DOI":"10.1103\/PhysRevLett.68.1244","article-title":"Self-organized criticality in a continuous, nonconservative cellular automaton modeling earthquakes","volume":"68","author":"Olami","year":"1992","journal-title":"Phys. Rev. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Meyers, R.A. (2009). Statistical Physics Approaches to Seismicity. Encyclopedia of Complexity and Systems Science, Springer.","DOI":"10.1007\/978-0-387-30440-3"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1016\/j.physd.2011.12.005","article-title":"Equilibrium, fluctuation relations and transport for irreversible deterministic dynamics","volume":"241","author":"Colangeli","year":"2012","journal-title":"Phys. D. Nonlinear Phenom."},{"key":"ref_9","unstructured":"Vollmer, J., Giberti, C., Orchard, J., Reinhard, H., Mej\u00eda-Monasterio, C., and Rondoni, L. (2024). Universal hyper-scaling relations, power-law tails, and data analysis for strong anomalous diffusion. arXiv."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"013067","DOI":"10.1103\/PhysRevResearch.3.013067","article-title":"Displacement autocorrelation functions for strong anomalous diffusion: A scaling form, universal behavior, and corrections to scaling","volume":"3","author":"Vollmer","year":"2021","journal-title":"Phys. Rev. Res."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"907","DOI":"10.1007\/BF00668821","article-title":"Toward a quantitative theory of self-generated complexity","volume":"25","author":"Grassberger","year":"1986","journal-title":"Int. J. Theor. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1016\/S0370-1573(01)00025-4","article-title":"Predictability: A way to characterize complexity","volume":"356","author":"Boffetta","year":"2002","journal-title":"Phys. Rep."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1016\/j.physrep.2012.02.001","article-title":"Statistical mechanics of two-dimensional and geophysical flows","volume":"515","author":"Bouchet","year":"2012","journal-title":"Phys. Rep."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2013.10.001","article-title":"Nonequilibrium statistical mechanics of systems with long-range interactions","volume":"535","author":"Levin","year":"2014","journal-title":"Phys. Rep."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"103033","DOI":"10.1088\/1367-2630\/ac95b7","article-title":"Nonequilibrium statistical mechanics and optimal prediction of partially-observed complex systems","volume":"24","author":"Rupe","year":"2022","journal-title":"New J. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1117","DOI":"10.1038\/s41467-024-45172-8","article-title":"Learning nonequilibrium statistical mechanics and dynamical phase transitions","volume":"15","author":"Tang","year":"2024","journal-title":"Nat. Commun."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"083132","DOI":"10.1063\/1.5110262","article-title":"On the fluctuation-dissipation relation in non-equilibrium and non-Hamiltonian systems","volume":"29","author":"Sarracino","year":"2019","journal-title":"Chaos Interdiscip. J. Nonlinear Sci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"014123","DOI":"10.1103\/ddjx-d1dv","article-title":"Multiscale energy spreading in hard-particle chains","volume":"112","author":"Pikovsky","year":"2025","journal-title":"Phys. Rev. E"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"178501","DOI":"10.1103\/PhysRevLett.88.178501","article-title":"Unified Scaling Law for Earthquakes","volume":"88","author":"Bak","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Michas, G. (2024). Complexity and Statistical Physics Approaches to Earthquakes. Entropy, 26.","DOI":"10.3390\/books978-3-7258-0206-7"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Dimri, V. (2016). The Multi-fractal Scaling Behavior of Seismograms Based on the Detrended Fluctuation Analysis. Fractal Solutions for Understanding Complex Systems in Earth Sciences, Springer International Publishing.","DOI":"10.1007\/978-3-319-24675-8"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"106328","DOI":"10.1016\/j.soildyn.2020.106328","article-title":"Multifractal analysis and wavelet leaders for structural damage detection of structures subjected to earthquake excitation","volume":"139","author":"Pnevmatikos","year":"2020","journal-title":"Soil Dyn. Earthq. Eng."},{"key":"ref_23","unstructured":"Felicetta, C., Russo, E., D\u2019Amico, M., Sgobba, S., Lanzano, G., Mascandola, C., Pacor, F., and Luzi, L. (2023). Italian Accelerometric Archive (ITACA), Version 4.0."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"530","DOI":"10.1785\/gssrl.81.3.530","article-title":"ObsPy: A Python Toolbox for Seismology","volume":"81","author":"Beyreuther","year":"2010","journal-title":"Seismol. Res. Lett."},{"key":"ref_25","unstructured":"Laske, G., Masters, G., Ma, Z., and Pasyanos, M. (2013, January 7\u201312). Update on CRUST1.0 - A 1-degree global model of Earth\u2019s crust. Proceedings of the Geophysical Research Abstracts. EGU General Assembly, Vienna, Austria."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"923","DOI":"10.1785\/BSSA0680040923","article-title":"The Use of the Coda for Determination of the Earthquake Source Spectrum","volume":"68","author":"Rautian","year":"1978","journal-title":"Bull. Seismol. Soc. Am."},{"key":"ref_27","unstructured":"Arias, A. (1970). A measure of earthquake intensity. Seismic Design for Nuclear Power Plants, MIT Press."},{"key":"ref_28","first-page":"581","article-title":"A study on the duration of strong earthquake ground motion","volume":"65","author":"Trifunac","year":"1975","journal-title":"Bull. Seismol. Soc. Am."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Filippucci, M., Lucente, S., de Lorenzo, S., Del Pezzo, E., Prosser, G., and Tallarico, A. (2021). Seismic Envelopes of Coda Decay for Q-coda Attenuation Studies of the Gargano Promontory (Southern Italy) and Surrounding Regions. Data, 6.","DOI":"10.3390\/data6090098"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"19635","DOI":"10.1029\/93JB03138","article-title":"Initial reference models in local earthquake tomography","volume":"99","author":"Kissling","year":"1994","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Colangeli, M., Rondoni, L., and Vozza, P. (2025). Dissipation Functions and Brownian Oscillators. Symmetry, 17.","DOI":"10.3390\/sym17081297"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1007\/s10955-025-03404-1","article-title":"A Hybrid Approach to Model Reduction of Generalized Langevin Dynamics","volume":"192","author":"Colangeli","year":"2025","journal-title":"J. Stat. Phys."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/9\/972\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,3]],"date-time":"2026-09-03T04:41:28Z","timestamp":1788410488000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/9\/972"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,1]]},"references-count":32,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2026,9]]}},"alternative-id":["e28090972"],"URL":"https:\/\/doi.org\/10.3390\/e28090972","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,1]]}}}