Please use this identifier to cite or link to this item:
http://hdl.handle.net/2122/7260| DC Field | Value | Language |
|---|---|---|
| dc.contributor.authorall | De Santis, A.; Istituto Nazionale di Geofisica e Vulcanologia, Sezione Roma2, Roma, Italia | en |
| dc.contributor.authorall | Cianchini, G.; Istituto Nazionale di Geofisica e Vulcanologia, Sezione Roma2, Roma, Italia | en |
| dc.contributor.authorall | Favali, P.; Istituto Nazionale di Geofisica e Vulcanologia, Sezione Roma2, Roma, Italia | en |
| dc.contributor.authorall | Beranzoli, L.; Istituto Nazionale di Geofisica e Vulcanologia, Sezione Roma2, Roma, Italia | en |
| dc.contributor.authorall | Boschi, E.; Istituto Nazionale di Geofisica e Vulcanologia, Sezione AC, Roma, Italia | en |
| dc.date.accessioned | 2011-12-21T10:46:04Z | en |
| dc.date.available | 2011-12-21T10:46:04Z | en |
| dc.date.issued | 2011-06 | en |
| dc.identifier.uri | http://hdl.handle.net/2122/7260 | en |
| dc.description.abstract | A cumulative frequency-magnitude relation, the Gutenberg–Richter law, dominates the statistics of the occurrence of earthquakes. Although it is an empirical law, some authors have tried to give some physical meaning to its a and b parameters. Here, we recall some theoretical expressions for the probability of occurrence of an earthquake with magnitude M in terms of a and b values. A direct consequence of the maximum likelihood estimation (MLE) and the maximum entropy principle (MEP) is that a and b values can be expressed as a function of the mean magnitude of a seismic sequence over a certain area. We then introduce the definition of the Shannon entropy of earthquakes and show how it is related to the b value. In this way, we also give a physical interpretation to the b value: the negative logarithm of b is the entropy of the magnitude frequency of earthquake occurrence. An application of these concepts to two case studies, in particular to the recent seismic sequence in Abruzzi (central Italy; mainshock Mw 6.3, 6 April 2009 in L’Aquila) and to an older 1997 sequence (Umbria-Marche, central Italy; mainshock Mw 6.0, 26 September 1997 in Colfiorito), confirms their potential to help in understanding the physics of earthquakes. In particular, from the comparison of the two cases, a simple scheme of different regimes in succession is proposed in order to describe the dynamics of both sequences. | en |
| dc.language.iso | English | en |
| dc.publisher.name | SSA | en |
| dc.relation.ispartof | Bulletin of the Seismological Society of America | en |
| dc.relation.ispartofseries | 3/101 (2011) | en |
| dc.subject | Entropy | en |
| dc.subject | Earthquakes | en |
| dc.subject | Gutenberg-Richter law | en |
| dc.title | The Gutenberg–Richter Law and Entropy of Earthquakes: Two Case Studies in Central Italy | en |
| dc.type | article | en |
| dc.description.status | Published | en |
| dc.type.QualityControl | Peer-reviewed | en |
| dc.description.pagenumber | 1386-1395 | en |
| dc.subject.INGV | 04. Solid Earth::04.06. Seismology::04.06.02. Earthquake interactions and probability | en |
| dc.subject.INGV | 05. General::05.05. Mathematical geophysics::05.05.99. General or miscellaneous | en |
| dc.identifier.doi | 10.1785/0120090390 | en |
| dc.relation.references | Aki, K. (1965). Maximum likelihood estimate of b in the formula log N a bM and its confidence limits, Bull. Earthq. Res. Inst. Tokyo Univ. 43, 237–239. Amato, A., R. Azzara, C. Chiarabba, G. B. Cimini, M. Cocco, M. Di Bona, L. Margheriti, S. Mazza, F. Mele, G. Selvaggi, A. Basili, and E. Boschi (1998). The 1997 Umbria-Marche, Italy, earthquake sequence: a first look at the main shocks and aftershocks, Geophys. Res. Lett. 25, 2861–2864. Baranger, M., V. Latora, and A. Rapisarda (2002). Time evolution of thermodynamic entropy for conservative and dissipative chaotic maps, Chaos Solitons & Fractals 13, 471–478. Bender, B. (1983). Maximum likelihood estimation of b-values for magnitude grouped data, Bull. Seismol. Soc. Am. 73, 831–851. Ben-Naim, A. (2008). A Farewell of Entropy: Statistical Thermodynamics Based on Information, World Scientific, New Jersey. Berrill, J. B., and R. O. Davis (1980). Maximum entropy and the magnitude distribution, Bull. Seismol. Soc. Am. 70, 1823–1831. Boltzmann, L. (1871). Sitzunsber, K. Akad. Wiss. Wien, 63, 679–732. Bunde, A., J. Kropp, and H. J. Schellnhuber (Editors) (2002). The Science of Disasters. Climate Disruptions, Heart Attacks, and Market Crashes. Springer Berlin. Chen, C.-C., and C.-L. Chang (2004). Comment on ‘Entropy, energy, and proximity to criticality in global earthquake populations’ by Main and Al-Kindy, Geophys. Res. Lett. 31, L06608, doi 10.1029/ 2003GL019008. Cirella, A., A. Piatanesi, M. Cocco, E. Tinti, L. Scognamiglio, A. Michelini, A. Lomax, and E. Boschi (2009). Rupture history of the 2009 L’Aquila earthquake from non-linear joint inversion of strong motion and GPS data, Geophys. Res. Lett. 36, L19304, doi 10.1029/ 2009GL039795. Clausius, R. (1850). On the motive power of heat, and on the laws which can be deduced from it for theory of heat, Ann. Physik, LXXIX, 368, 500. De Santis, A. (2009). Geosystemics, Proc. Third IASME/WSEAS Int. Conf. Geol. Seismol. (GES’09), Feb. 2009 Cambridge, 36–40. De Santis, A., G. Cianchini, E. Qamili, and A. Frepoli (2010). The 2009 L’Aquila (central Italy) seismic sequence as a chaotic process, Tectonophysics, 496, 44–52. Dong, W. M., A. B. Bao, and H. C. Shah (1984). Use of maximum entropy principle in earthquake recurrence relationships, Bull. Seismol. Soc. Am. 74, 2, 725–737. Feng, L.-H., and G.-Y. Luo (2009). The relationship between seismic frequency and magnitude as based on the maximum entropy principle, Soft. Comp. 13, 979–983. Frohlich, C., and S. D. Davis (1993). Teleseismic b values; Or, much ado about 1.0, J. Geophys. Res. 98, 631–644. Grandy, W. T., Jr. (2008) Entropy and the Time Evolution of Macroscopic Systems, Oxford University Press, Oxford. Gutenberg, B., and C. F. Richter (1944). Frequency of earthquakes in California, Bull. Seismol. Soc. Am. 34, 185–188. Gutenberg, B., and C. F. Richter (1954). Seismicity of the Earth and Associated Phenomena, Second ed., Princeton University Press, Princeton. Hirata, T. (1989). A correlation between the b-value and the fractal dimension of earthquakes, J. Geophys. Res. 94, no. B6, 7507–7514. Jimenez, A., K. F. Tiampo, S. Levin, and A. M. Posadas (2006). Testing the persistence in earthquake catalogs: The Iberian Peninsula, Europhys. Lett. 73, 171–177, doi 10.1209/epl/i2005-10383-8. Kagan, Y. Y. (2006). Earthquake spatial distribution: The correlation dimension, Geophys. J. Int. 168, 1175–1194. Lolli, B., and P. Gasperini (2003). Aftershock hazard in Italy Part I: Estimation of time-magnitude distribution model parameters and computation of probabilities of occurrence, J. Seismol. 7, 235–257. Main, I., and F. Al-Kindy (2002). Entropy, energy, and proximity to criticality in global earthquake populations, Geophys. Res. Lett. 29, no. 7, doi 10.1029/2001GL014078. Main, I., and F. Al-Kindy (2004). Reply to “ Comment on ‘Entropy, energy, and proximity to criticality in global earthquake populations’” by Chen and Chang, Geophys. Res. Lett. 31, L06609, doi 10.1029/ 2004GL019497. Main, I., and P.W. Burton (1984). Information theory and the earthquake frequency- magnitude distribution, Bull. Seismol. Soc. Am. 74, 1409–1426. Marzocchi, W., and L. Sandri (2003). A review and new insights on the estimation of the b-value and its uncertainty, Ann. Geophys. 46, no. 6, 1271–1282. Mega, M. S., P. Allegrini, P. Grigolini, V. Latora, L. Palatella, A. Rapisarda, and S. Vinciguerra (2003). Power-law time distribution of large earthquakes, Phys. Rev. Lett. 90, no. 18, 188,501.1–188,501.4. Mogi, K. (1969). Some features of the recent seismic activity in and near Japan, Bull. Earthq. Res. Inst. Univ. Tokyo 47, 395–417. Mogi, K. (1985). Earthquake Prediction, Academic Press, Tokyo. Nicholson, T., M. Sambridge, and O. Gudmundsson (2000). On entropy and clustering in earthquake hypocentre distributions, Geophys. J. Int. 142, 37–51. Padhy, S. (2004). Intermittent criticality on a regional scale in Bhuj, Geophys. J. Int. 158, 676–680. Page, R. (1968). Aftershocks and microaftershocks of the Great Alaska earthquake of 1964, Bull. Seismol. Soc. Am. 58, 1131–1168. Pickering, G., J. M. Bull, and D. J. Sanderson (1995). Sampling power–law distributions, Tectonophysics 248, 1–20. Pondrelli, S., S. Salimbeni, A. Morelli, G. Ekström, M. Olivieri, and E. Boschi (2010). Seismic moment tensors of the April 2009, L’Aquila (central Italy), earthquake sequence, Geophys. J. Inter. 180, no. 1, 238–242. Scafetta, N., V. Latora, and P. Grigolini (2002). Lévy scaling: the diffusion entropy analysis applied to DNA sequences, Phys. Rev. E 66, 031906. Schorlemmer, D., F. Mele, and W. Marzocchi (2010). A completeness analysis of the national seismic network of Italy, J. Geophys. Res. 115, B04308, doi 10.1029/2008JB006097. Schorlemmer, D., S.Wiemer, and M.Wyss (2005). Variations in earthquakesize distribution across different stress regimes, Nature 437, 539–542. Shannon, C. E. (1948). A mathematical theory of communication, Bell Syst. Tech. J. 27, 379, 623. Shen, P. Y., and L. Mansinha (1983). On the principle of maximum entropy and the earthquake frequency-magnitude relation, Geophys. J. R. Astr. Soc. 74, 777–785. Shi, Y., and B. A. Bolt (1982). The standard error of the magnitudefrequency b-value, Bull. Seismol. Soc. Am. 87, 1074–1077. Singh, C., P. M. Bhattacharya, and R. K. Chadha (2008). Seismicity in the Konya-Warna reservoir site in Western India: Fractal and b-value mapping, Bull. Seismol. Soc. Am. 98, no. 1, 476–482. Singh, C., A. Singh, and R. K. Chadha (2009). Fractal and b-value in Eastern Himalaya and Southern Tibet, Bull. Seismol. Soc. Am. 99, no. 6, 3529–3533. Smith, W. D. (1981). The b-value as an earthquake precursor, Nature 289, 136–139. Sornette, D. (2006). Critical Phenomena in Natural Sciences. Second ed., Springer, Berlin Heidelberg, New York. Telesca, L., V. Lapenna, and M. Lovallo (2004). Information entropy analysis of Umbria-Marche region (central Italy), Nat. Hazards Earth Syst. Sci. 4, 691–695. Tinti, S., and F. Mulargia (1987). Confidence intervals of b-values for grouped magnitudes, Bull. Seismol. Soc. Am. 77, 2125–2134. Turcotte, R. (1997). Fractals and Chaos in Geology and Geophysics, Cambridge University Press, Cambridge. Utsu, T. (1965). A method for determining the value of b in a formula log n q bM showing the magnitude-frequency relation for earthquakes, Proc. Microzonation Conf., Seattle, Washington, 897–909. Utsu, T. (1966). A statistical significance test of the difference in b-value between two earthquakes groups, J. Phys. Earth 14, 37–40. Utsu, T. (1978). Estimation of parameter values in the formula for the magnitude-frequency relation of earthquake occurrence, Zisin 31, 367–382. Utsu, T. (1999). Representation and analysis of the earthquakes size distribution: a historical review and some new approaches, Pure Appl. Geophys. 155, 509–535. Walters, R. J., J. R. Elliott, N. D’Agostino, P. C. England, I. Hunstad, J. A. Jackson, B. Parsons, R. J. Phillips, and G. Roberts (2009). The 2009 L’Aquila earthquake (central Italy): A source mechanism and implications for seismic hazard, Geophys. Res. Lett. 36, L17312, doi 10.1029/ 2009GL039337. Weichert, D. H. (1980). Estimation of the earthquake recurrence parameters for unequal observation periods for different magnitudes, Bull. Seismol. Soc. Am. 70, no. 4, 1338–1346. Wesnousky, S. G. (1999). Crustal deformation processes and the stability of the Gutenberg-Richter relationship, Bull. Seismol. Soc. Am. 89, no. 4, 1131–1137. Wiemer, S., and S. McNutt (1997). Variations in the frequency-magnitude distribution with depth in two volcanic areas: Mount St. Helens, Washington, and Mt. Spurr, Alaska, Geophys. Res. Lett. 24, no. 2, 189–192. Wiener, N. (1948). Cybernetics, MIT Press, Cambridge, Massachussets. Wyss, M., C. G. Sammis, R. M. Nadeau, and S. Wiemer (2004). Fractal dimension and b-value on creeping and locked patches of the San Andrea fault near Parkfield, California, Bull. Seismol. Soc. Am. 94, no. 2, 410–421. | en |
| dc.description.obiettivoSpecifico | 3.1. Fisica dei terremoti | en |
| dc.description.journalType | JCR Journal | en |
| dc.description.fulltext | reserved | en |
| dc.contributor.author | De Santis, A. | en |
| dc.contributor.author | Cianchini, G. | en |
| dc.contributor.author | Favali, P. | en |
| dc.contributor.author | Beranzoli, L. | en |
| dc.contributor.author | Boschi, E. | en |
| dc.contributor.department | Istituto Nazionale di Geofisica e Vulcanologia, Sezione Roma2, Roma, Italia | en |
| dc.contributor.department | Istituto Nazionale di Geofisica e Vulcanologia, Sezione Roma2, Roma, Italia | en |
| dc.contributor.department | Istituto Nazionale di Geofisica e Vulcanologia, Sezione Roma2, Roma, Italia | en |
| dc.contributor.department | Istituto Nazionale di Geofisica e Vulcanologia, Sezione Roma2, Roma, Italia | en |
| dc.contributor.department | Istituto Nazionale di Geofisica e Vulcanologia, Sezione AC, Roma, Italia | en |
| item.openairetype | article | - |
| item.cerifentitytype | Publications | - |
| item.languageiso639-1 | en | - |
| item.grantfulltext | restricted | - |
| item.openairecristype | http://purl.org/coar/resource_type/c_18cf | - |
| item.fulltext | With Fulltext | - |
| crisitem.author.dept | Istituto Nazionale di Geofisica e Vulcanologia (INGV), Sezione Roma2, Roma, Italia | - |
| crisitem.author.dept | Istituto Nazionale di Geofisica e Vulcanologia (INGV), Sezione Roma2, Roma, Italia | - |
| crisitem.author.dept | Istituto Nazionale di Geofisica e Vulcanologia (INGV), Sezione Roma2, Roma, Italia | - |
| crisitem.author.dept | Istituto Nazionale di Geofisica e Vulcanologia (INGV), Sezione Roma2, Roma, Italia | - |
| crisitem.author.orcid | 0000-0002-3941-656X | - |
| crisitem.author.orcid | 0000-0003-2832-0068 | - |
| crisitem.author.orcid | 0000-0002-0810-0263 | - |
| crisitem.author.orcid | 0000-0002-2273-3593 | - |
| crisitem.author.parentorg | Istituto Nazionale di Geofisica e Vulcanologia | - |
| crisitem.author.parentorg | Istituto Nazionale di Geofisica e Vulcanologia | - |
| crisitem.author.parentorg | Istituto Nazionale di Geofisica e Vulcanologia | - |
| crisitem.author.parentorg | Istituto Nazionale di Geofisica e Vulcanologia | - |
| crisitem.classification.parent | 04. Solid Earth | - |
| crisitem.classification.parent | 05. General | - |
| crisitem.department.parentorg | Istituto Nazionale di Geofisica e Vulcanologia | - |
| crisitem.department.parentorg | Istituto Nazionale di Geofisica e Vulcanologia | - |
| crisitem.department.parentorg | Istituto Nazionale di Geofisica e Vulcanologia | - |
| crisitem.department.parentorg | Istituto Nazionale di Geofisica e Vulcanologia | - |
| crisitem.department.parentorg | Istituto Nazionale di Geofisica e Vulcanologia | - |
| Appears in Collections: | Article published / in press | |
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