Correcting the Gutenberg–Richter b-value for effects of rounding and noise
V. H. Ma´rquez-Ram?´rez1, F. A. Nava2, F. R. Zu´n˜iga1
1 UNAM Campus Quere´taro, Me´xico, Centro de Geociencias, Blvd. Juriquilla No 3001, 76230 Me´xico, Quere´taro, Me´xico 2 Seismology Department, CICESE, Carretera Ensenada-Tijuana No 3918, Zona Playitas, 22860 Ensenada, BC, Me´xico
Correcting the Gutenberg–Richter b-value for effects of rounding and noise
V. H. Ma´rquez-Ram?´rez1, F. A. Nava2, F. R. Zu´n˜iga1
1 UNAM Campus Quere´taro, Me´xico, Centro de Geociencias, Blvd. Juriquilla No 3001, 76230 Me´xico, Quere´taro, Me´xico 2 Seismology Department, CICESE, Carretera Ensenada-Tijuana No 3918, Zona Playitas, 22860 Ensenada, BC, Me´xico
摘要The effects of magnitude rounding and of the presence of noise in the rounded magnitudes on the estimation of the Gutenberg–Richter b-value are explored, and the ways to correct for these effects are proposed. For typical values, b = 1 and rounding interval DM = 0.1, the rounding error is approximately -10-3 and it can be corrected to a negligible approximately -10-5. For the same typical values, the effect of noise can be larger, depending on the characteristics of the noise distribution; for normally distributed noise with standard deviation r = 0.1, the correct b-value may be underestimated by a factor *0.97.
Abstract：The effects of magnitude rounding and of the presence of noise in the rounded magnitudes on the estimation of the Gutenberg–Richter b-value are explored, and the ways to correct for these effects are proposed. For typical values, b = 1 and rounding interval DM = 0.1, the rounding error is approximately -10-3 and it can be corrected to a negligible approximately -10-5. For the same typical values, the effect of noise can be larger, depending on the characteristics of the noise distribution; for normally distributed noise with standard deviation r = 0.1, the correct b-value may be underestimated by a factor *0.97.
基金资助:UNAMDGAPA postdoctoral scholarship (VH Ma´rquez-Ram?´rez), by CONACYT grant 222795, and UNAM-DGAPA-PAPIIT grant IN108115.
引用本文:
V. H. Ma′rquez-Ram?′rez, F. A. Nava, F. R. Zu′n?iga. Correcting the Gutenberg–Richter b-value for effects of rounding and noise[J]. 《地震学报》英文版, 2015, 28(2): 129-134.
V. H. Ma′rquez-Ram?′rez, F. A. Nava, F. R. Zu′n?iga. Correcting the Gutenberg–Richter b-value for effects of rounding and noise. Earthquake Science, 2015, 28(2): 129-134.
