Teleseismic b values; Or, much ado about 1.0

Abstract

In this paper we investigate the value of b in the Gutenberg‐Richter relation for four teleseismic catalogs of earthquakes: Abe's historical catalog, the Harvard Centroid Moment Tensor (CMT) catalog, the catalog of the International Seismological Centre (ISC), and the Blacknest catalog. An unfortunate result is that b differs by 30% or more when determined in different magnitude ranges, in different catalogs, or using different methods. For global catalogs separated into shallow, intermediate, and deep earthquake groups, all values determined for b lie between 0.72 and 1.34. We can identify no systematic global variation of b with depth. For teleseismic catalogs it is difficult to believe measured geographic variations in b because systematic errors cause problems of earthquake detection, earthquake location, aftershock identification, and magnitude determination. However, some variations in b are so persistent and large that they must be real. For deep earthquakes in Tonga‐Fiji, for example, various measurements of b He between 1.06 and 1.57, comparable to b for shallow earthquakes, whereas measurements of b for deep earthquakes in the rest of the world are much lower, between 0.53 and 0.96. For shallow earthquakes in the Harvard CMT catalog, earthquakes with thrust and strike slip focal mechanisms have significantly lower b values (0.86 and 0.77) than earthquakes with normal faulting mechanisms (1.06). When we separate the ISC catalog into primary events (mainshocks and earthquakes with no aftershocks or foreshocks) and secondary events (aftershocks and foreshocks), we observe that b for secondary events is nearly always significantly higher than b for mainshocks. However, we show that the difference has no physical significance, as it arises simply from the act of choosing mainshocks as the largest earthquake in a foreshock‐mainshock‐aftershock sequence. When we correct for this systematic effect by comparing the real catalogs to identical catalogs with randomly reassigned magnitudes, we find that b for secondary events in the real catalog is actually lower than expected. Thus among aftershocks large earthquakes are relatively more common than expected, perhaps because the mainshock rupture loads asperities in adjacent regions.

Landslides, sandpiles, and self-organized criticality

“…Correspondence to: S. Hergarten (hergarten@geo.uni-bonn.de) and 1.2 (Frohlich and Davis, 1993). In contrast, the parameter a quantifies the regional seismic activity and thus varies strongly.…”

“…Therefore, the relative importance of large landslides is lower than it is in the example of earth- Power-law exponents of the cumulative size distributions of some natural hazards (upper part) and results of the most widespread self-organized critical models (lower part). The tickmarks refer to the studies on landslides mentioned in the text, the rockfall data analyzed and reviewed by Dussauge-Peisser et al (2002), the four forest-fire data sets analyzed by Malamud et al (1998), and 38 earthquake catalogs from various geographic regions (Frohlich and Davis, 1993, quakes and much lower than in the example of forest fires. Geology, climate, type of landslides, and triggering mechanisms seem to be good candidates to account for the observed variations in the power-law exponents.…”

Universality of the Seismic Moment-frequency Relation

“…Only these fluctuations are analyzed by the statistical tests shown in Tables 1-5. (b) It is possible that systematic errors bias the i-value estimate. Such errors strongly influence the b-value estimate, which may differ significantly and without an obvious correlation for various tectonic regions, depending on the magnitude scale used (KAGAN, 1991b;FROHLICH and DAVIS, 1993; see more in the next subsection). Several factors may introduce a systematic bias in the b-or i-values.…”

Global risk of big earthquakes has not recently increased

“…This property is inconsistent with the triggering behavior implied by aftershock sequences, which are observed to have Gutenberg-Richter magnitude-frequency relationships reflecting a preponderance of smaller events (e.g., ref. 16). …”