Please use this identifier to cite or link to this item:
http://hdl.handle.net/2122/3671
DC Field | Value | Language |
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dc.contributor.authorall | Sandri, L.; Istituto Nazionale di Geofisica e Vulcanologia, Sezione Bologna, Bologna, Italia | en |
dc.contributor.authorall | Marzocchi, W.; Istituto Nazionale di Geofisica e Vulcanologia, Sezione Bologna, Bologna, Italia | en |
dc.date.accessioned | 2008-02-26T13:03:31Z | en |
dc.date.available | 2008-02-26T13:03:31Z | en |
dc.date.issued | 2007-06 | en |
dc.identifier.uri | http://hdl.handle.net/2122/3671 | en |
dc.description.abstract | We investigate conceptually, analytically, and numerically the biases in the estimation of the b-value of the Gutenberg-Richter Law and of its uncertainty made through the least squares technique. The biases are introduced by the cumulation operation for the cumulative form of the Gutenberg-Richter Law, by the logarithmic transformation, and by the measurement errors on the magnitude. We find that the least squares technique, applied to the cumulative and binned form of the Gutenberg-Richter Law, produces strong bias in the b-value and its uncertainty, whose amplitudes depend on the size of the sample. Furthermore, the logarithmic transformation produces two different endemic bends in the Log(N) versus M curve. This means that this plot might produce fake significant departures from the Gutenberg-Richter Law. The effect of the measurement errors is negligible compared to those of cumulation operation and logarithmic transformation. The results obtained show that the least squares technique should never be used to determine the slope of the Gutenberg-Richter Law and its uncertainty. | en |
dc.language.iso | English | en |
dc.publisher.name | Editrice Compositori | en |
dc.relation.ispartof | Annals of Geophysics | en |
dc.relation.ispartofseries | 3/50 (2007) | en |
dc.subject | b-value | en |
dc.subject | seismology | en |
dc.subject | least squares technique | en |
dc.subject | syntheticearthquake catalogs | en |
dc.title | A technical note on the bias in the estimation of the b-value and its uncertainty through the Least Squares technique | en |
dc.type | article | en |
dc.description.status | Published | en |
dc.type.QualityControl | Peer-reviewed | en |
dc.description.pagenumber | 329-339 | en |
dc.subject.INGV | 04. Solid Earth::04.06. Seismology::04.06.99. General or miscellaneous | en |
dc.relation.references | BENDER, B. (1983): Maximum likelihood estimation of bvalues for magnitude grouped data, Bull. Seismol. Soc. Am., 73, 831-851. DEL PEZZO, E., F. BIANCO, S. PETROSINO and G. SACCOROTTI (2004): Changes in the coda decay rate and shear-wave splitting parameters associated with seismic swarms at Mt. Vesuvius, Italy, Bull. Seismol. Soc. Am., 94 (2), 439- 452. DRAPER, N.R. and H. SMITH (1981): Applied Regression Analysis (John Wiley & Sons Ltd., New York), 2nd edition, pp. 305. GROUP ON CALIFORNIA EARTHQUAKE PROBABILITIES (2003): Earthquake probabilities in the San Francisco Bay region: 2002-2031, U.S. Geol. Surv. Open File Rep. 03-214. GRUPPO DI LAVORO (2004): Redazione della mappa di pericolositá sismica prevista dall’Ordinanza PCM 3274 del 20 marzo 2003, Rapporto Conclusivo per il Dipartimento della Protezione Civile (INGV, Milano-Roma, aprile 2004), pp. 65. GUTENBERG, B. and C. RICHTER (1954): Seismicity of the Earth and Associated Phenomena (Princeton University Press, Princeton, New Jersey), 2nd edition, pp. 310. KALBFLEISCH, J.D. (1985): Probability and Statistical Inference (Springer-Verlag, New York), 2nd edition, pp. 364. KARNIK, V. and K. KLIMA (1993): Magnitude-frequency distribution in the European-Mediterranean earthquake regions, Tectonophysics, 220, 309-323. LEGRAND, D., D. VILLAGOMEZ, H. YEPES and A. CALAHORRANO (2004): Multifractal dimension and b-value analysis of the 1998-1999 Quito swarm related to Guagua Pichincha Volcano activity, Ecuador J. Geophys. Res., 109 (B1), B01307, doi: 10.1029/2003JB002572. LOPEZ PINEDA, L. and C.J. REBOLLAR (2005): Source characteristics of the Mw 6.2 Loreto earthquake of 12 March 2003 that occurred in a transform fault in the middle of the Gulf of California, Mexico, Bull. Seismol. Soc. Am., 95 (2), 419-430. MAIN, I. (2000): Apparent breaks in scaling in the earthquake cumulative frequency-magnitude distribution: fact or artifact?, Bull. Seismol. Soc. Am., 90, 86-97. MANDAL, P., B.K. RASTOGI, H.V.S. SATYANARAYANA and M. KOUSALYA (2004): Results from local earthquake velocity tomography; implications toward the source process involved in generating the 2001 earthquake in the lower crust beneath Kachchh (India), Bull. Seismol. Soc. Am., 94 (2), 633-649. MARZOCCHI, W. and L. SANDRI (2003): A review and new insights on the estimation of the b-value and its uncertainty, Ann. Geophysics, 46 (6), 1271-1282. MURRU, M., C. MONTUORI, R. CONSOLE and A. LISI (2005): Mapping of the b-value anomalies beneath Mt. Etna, Italy, during JulyAugust 2001 lateral eruption, Geophys. Res. Lett., 32 (5), L05309, doi: 10.1029/ 2004GL021545. OKAL, E.A. and S.H. KIRBY (1995): Frequency-moment distribution of deep earthquake; implications for the seismogenic zone at the bottom of Slabs, Phys. Earth Planet. Inter., 92, 169-187. PACHECO, J.F. and L.R. SYKES (1992): Seismic moment catalog of large shallow earthquakes, 1900 to 1989, Bull. Seismol. Soc. Am., 82, 1306-1349. PACHECO, J.F., C.H. SCHOLZ and L.R. SYKES (1992):Changes in frequencysize relationship from small to large earthquakes, Nature, 355, 71-73. PAGE, R. (1968): Aftershocks and microaftershocks of the Great Alaska earthquake of 1964, Bull. Seismol. Soc. Am., 58, 1131-1168. RATCHKOVSKI, N.A., S. WIEMER and R.A. HANSEN (2004): Seismotectonics of the Central Denali Fault, Alaska, and the 2002 Denali Fault earthquake sequence, Bull. Seismol. Soc. Am., 94 (6), Part B, 156-174. RIEDEL, C., T. PETERSEN, F. THEILEN and S. NEBEN (2003): High b-values in the leaky segment of the Tjornes fracture zone north of Iceland; are they evidence for shallow magmatic heat sources?, J. Volcanol. Geotherm. Res., 128 (1-3), 15-29. SCHOLZ, C.H. (1997): Size distributions for large and small earthquakes, Bull. Seismol. Soc. Am., 87, 1074-1077. SCHORLEMMER, D., S. WIEMER and M. WYSS (2005): Variations in earthquake-size distribution across different stress regimes, Nature, 437, doi: 10.1038/nature04094. TRIEP, E.G. and L.R. SYKES (1997): Frequency of occurrence of moderate to great earthquakes in intracontinetal regions: implications for changes in stress, earthquake prediction, and hazard assessment, J. Geophys. Res., 102, 9923-9948. WYSS, M., C.G. SAMMIS, R.M. NAUDEAU and S. WIEMER (2004): Fractal dimension and b-value on creeping and locked patches of the San Andreas Fault near Parkfield, California, Bull. Seismol. Soc. Am., 94 (2), 410-421. | en |
dc.description.journalType | JCR Journal | en |
dc.description.fulltext | open | en |
dc.contributor.author | Sandri, L. | en |
dc.contributor.author | Marzocchi, W. | en |
dc.contributor.department | Istituto Nazionale di Geofisica e Vulcanologia, Sezione Bologna, Bologna, Italia | en |
dc.contributor.department | Istituto Nazionale di Geofisica e Vulcanologia, Sezione Bologna, Bologna, Italia | en |
item.openairetype | article | - |
item.cerifentitytype | Publications | - |
item.languageiso639-1 | en | - |
item.grantfulltext | open | - |
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 Bologna, Bologna, Italia | - |
crisitem.author.orcid | 0000-0002-3254-2336 | - |
crisitem.author.orcid | 0000-0002-9114-1516 | - |
crisitem.author.parentorg | Istituto Nazionale di Geofisica e Vulcanologia | - |
crisitem.classification.parent | 04. Solid Earth | - |
crisitem.department.parentorg | Istituto Nazionale di Geofisica e Vulcanologia | - |
crisitem.department.parentorg | Istituto Nazionale di Geofisica e Vulcanologia | - |
Appears in Collections: | Annals of Geophysics Article published / in press |
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