The fractal description of seismicity

Abstract

S U M M A R YThe stable estimation of multifractal characteristics of seismicity is considered. The data are world and accessible regional catalogues of m ≥ 2-4 events. Our attention is focused on the range of scales in which the Renyi functionals admit of scale-invariant behaviour. We find that the stable fractal analysis of hypocentres is generally difficult. As to epicentres, we have carried out a stable analysis for seven regions worldwide in the range of scales 1-1.7 decades. The estimates of generalized dimensions admit of tectonic interpretation.

Earthquake clusters in southern California I: Identification and stability

“…The algorithm is completely parameterized by the triplet ( b , d f , η 0 ) whose values are estimated from the observations, so it does not involves any ad‐hoc choices or tuning parameters. Nevertheless, there exist statistical variability in the estimation of each parameter— Marzocchi and Sandri [2003] give a review of b ‐value estimation with numerous references; the results on estimating fractal distribution of epicenters are reviewed by Harte [], Kagan [], and Molchan and Kronrod []; the estimation of the threshold η 0 is discussed by Hicks []. The results of the cluster detection might be also affected by the catalog completeness magnitude and earthquake location errors.…”

Temporal and spatial variations of seismicity scaling behavior in Southern México

“…The multifractal structure of the interevent periods between successive earthquakes has been also explored, showing a gradual increment of multifractality prior to the major seismic activity (Dimitriu et al, 2000) and a loss of multifractality during aftershocks (Telesca and Lapenna, 2006;Zamani and AghAtabai, 2009). Remarkably, the estimates of generalized dimensions from multifractal features of interevent periods allow a tectonic interpretation (Molchan and Kronrod, 2009). It was also suggested that the combined characterization of the fractal properties of earthquake sequences and faults provides a better view of the seismic risk in a given geographic region (Henares-Romero et al, 2010).…”

Fractal Seismicity and Seismic Risk

“…is typical of discussions on nontriviality of similarity in physics literature [Malkai et al, 1997]. Under conditions (11) The above requirements, in particular, the stability and the condition (14), have proved rather stringent on the world and regional catalogs available at the time of [Molchan and Kronrod, 2009] work. We analyzed world seismicity to identify only six regions (southern California, M>2; Kamchatka, M>3.5; New Zealand, M>2.5; Central American arc, M>4; Costa Rica, M>3.2; Greece, M>3 ;…”

“…Unfortunately, rigorous analyses of fractality in seismicity [see e.g. Goltz, 1997;Harte, 2001;Molchan and Kronrod, 2009] are still few. Summary.…”