Seismic moment‐frequency relation for shallow earthquakes: Regional comparison

Abstract

We test the hypothesis that no statistically significant variation in Mxg occurs in subduction and continent collision zones; the hypothesis cannot be rejected with available data. For the midocean ridges, the Mxg estimate cannot be unambiguously determined; it is quite possible that the estimate is significantly biased because only a small part of tectonic deformation at the ridges is released by earthquakes. These results have importance in evaluating seismic risk and may also lead to developing a physical theory for earthquake generation.

Characterization of the Frequency of Extreme Earthquake Events by the Generalized Pareto Distribution

“…In a recent analysis, Bird et al (2000) explain the difference of b-value found earlier (Okal and Romanovicz, 1994;Kagan, 1997Kagan, , 1999 and confirmed here, on the basis that an effective larger b-value will be found when mixing power law distribution with different "corner" magnitudes. Indeed, a similar effect has been shown to increase the b-value in a population of faults with a continuous power law distribution of lengths (Sornette et al, 1991;Lomnitz-Adler, 1992).…”

“…The statistical technique presented here is illustrated using the well-known seismological problem of earthquake energy distribution. A new evidence of spatial homogeneity of shallow earthquake distributions in subduction zones is demonstrated and confirm known results in this domain [Gutenberg and Richter, 1954;Main and Burton, 1984;Main, 1992Main, , 1996Cornell, 1994;Sornette and Sornette, 1999;Kagan, 1994Kagan, , 1997Kagan, , 1999Romanowicz and Rundle, 1993;Romanowicz, 1994;Okal and Romanowicz, 1994;Pacheco and Sykes, 1992;Scholz, 1994aScholz, , 1994b. We confirm that the b-value is very different (b=1.50±0.09) in mid-ocean ridges compared to other zones (b=1.00±0.05) with a very high statistical confidence and propose a physical mechanism contrasting "crack-type" rupture with "dislocation-type" behavior.…”

“…Below, we propose a new method for the statistical analysis of the tail behavior which is much more sensitive to possible deviations between the sample tails and the fitted distribution. Table 1 demonstrates a significant difference in the estimates of the shape parameter ξ between SZ and MORZ, which was noticed earlier [Okal and Romanowicz, 1994;Kagan, 1997Kagan, , 1999. The statistical significance of this difference is so large that there is no doubt on its reality.…”

Probabilistic Analysis of Tsunami Hazards*

“…where the exponent b is related to the b-value of the G-R distribution according to b=(3/2) b ( Kagan, 1997Kagan, , 1999). An example of a modified G-R distribution is plotted in Figure 3 for M t =7.0 and M c =9.0 (dashed line) along with a the cumulative distribution of 100 random samples taken from Equation (10) (medium solid line).…”

Statistical physics of earthquakes: Comparison of distribution exponents for source area and potential energy and the dynamic emergence of log‐periodic energy quanta

“…However, seismicity has only been recorded over a time period which is small compared to the typical average recurrence times of the largest earthquakes which dominate both the total seismic moment release and the damage. The earthquake frequency-magnitude distribution for such rare, damaging earthquakes can be constrained to some extent by the local seismic moment release rate, increasingly available at higher resolution from geodetic data from ground-based and satellite geodesy [Kagan, 1991[Kagan, , 1997Main, 1996]. However, the moment release rate itself does not specify the type of distribution, only the parameters for a given distribution.…”