Universality of the Seismic Moment-frequency Relation

Abstract

Abstract-We analyze the seismic moment-frequency relation in various depth ranges and for different seismic regions, using Flinn-Engdahl's regionalization of global seismicity. Three earthquake lists of centroid-moment tensor data have been used: the Harvard catalog, the USGS catalog, and the HUANG et al. (1997) catalog of deep earthquakes. The results confirm the universality of the i-values and the maximum moment for shallow earthquakes in continental regions, as well as at and near continental boundaries. Moreover, we show that although fluctuations in earthquake size distribution increase with depth, the i-values for earthquakes in the depth range of 0 -500 km exhibit no statistically significant regional variations. The regional variations are significant only for deep events near the 660 km boundary. For declustered shallow earthquake catalogs and deeper events, we show that the worldwide i-values have the same value of 0.609 0.02. This finding suggests that the i-value is a universal constant. We investigate the statistical correlations between the numbers of seismic events in different depth ranges and the correlation of the tectonic deformation rate and seismic activity (the number of earthquakes above a certain threshold level per year). The high level of these correlations suggests that seismic activity indicates tectonic deformation rate in subduction zones. Combined with the universality of the i-value, this finding implies little if any variation in maximum earthquake seismic moment among various subduction zones. If we assume that earthquakes of maximum size are similar in different depth ranges and the seismic efficiency coefficient, , is close to 100% for shallow seismicity, then we can estimate for deeper earthquakes: for intermediate earthquakes :5%, and : 1% for deep events. These results may lead to new theoretical understanding of the earthquake process and better estimates of seismic hazard.

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

“…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.…”

Probabilistic Analysis of Tsunami Hazards*

“…For example, the maximum earthquake magnitude that any given fault can generate may be subject to different interpretations of, for example, fault length, seismogenic depth, and slip rate. More generally, different frequency-magnitude curves can be envisioned to conform to either a modified G-R relationship in which the b-value is greater for larger earthquakes (Pacheco et al, 1992;Sornette and Virieux, 1992;Romanowicz and Rundle, 1993;Kagan, 1999;Pisarenko and Sornette, 2004) or a characteristic model for the largest earthquake (Wesnousky, 1994;Kagan, 2002b). If hazard analysis is based on the seismic moment (M 0 =l LWD) of potential earthquakes, then values and associated uncertainties for first-order parameters such as rupture length (L), width (W), shear modulus (l), and average slip (D) must be provided.…”

“…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).…”

“…In comparison to local tsunamis, far-field tsunamis have a simpler parameterization according to the earthquake's mechanism, scalar seismic moment, and radiation pattern (BenMenahem andRosenman, 1972, Comer, 1980;Ward, 1980Ward, , 1982Pelayo and Wiens, 1992;Abe, 1995;Polet and Kanamori, 2000). Other than the general cumulative frequency-magnitude relationship for earthquakes known as the Gutenberg-Richter relationship (Rundle, 1989;Kagan, 1999), assigning specific probabilities to circum-Pacific, subduction-zone earthquakes has proven to be a difficult topic (Kagan and Jackson, 1995;Schwartz, 1999;Rong et al, 2003). In contrast, for local tsunamis where offshore faults may have established historic and paleoseismologic recurrence rates, the larger problem is constraining the many other seismic parameters that affect local tsunami generation (Kajiura, 1981;Geist, 1999;Geist and Bilek, 2001;Geist, 2002).…”

A systematic test of the hypothesis that the b value varies with depth in California

“…Every seismicity map shows clearly that the activity rate varies spatially and temporally; however, there is no consensus on the questions of whether or not significant spatial or temporal variations also exist in the relative size distribution of events. Some seismologists [Kagan, 1999;Frohlich and Davis, 1993] In this paper we address one aspect of this discussion by testing the following hypothesis: The b value for the shallowest part of the crust is significantly higher than for the bottom part of the crust. This hypothesis was originally proposed by Wyss [1973], and further studied by Wyss and For our study the presence of explosions adds a source of potential systematic error.…”