Self-affine Asperity Model for earthquakes

A model for fault dynamics consisting of two rough and rigid brownian profiles that slide one over the other is introduced. An earthquake occurs when there is an intersection between the two profiles. The energy release is proportional to the overlap interval. Our model exhibits some specific features which follow from the fractal geometry of the fault: (1) non-universality of the exponent of the Gutenberg-Richter law for the magnitude distribution; (2) presence of local stress accumulation before a large seismic event; (3) non-trivial space-time clustering of the epicenters. These properties are in good agreement with various observations and lead to specific predictions that can be experimentally tested.Comment: TeX file, 14 pages, 3 figures available from [email protected]

Earthquake statistics and fractal faults

We introduce a Self-affine Asperity Model (SAM) for the seismicity that mimics the fault friction by means of two fractional Brownian profiles (fBm) that slide one over the other. An earthquake occurs when there is an overlap of the two profiles representing the two fault faces and its energy is assumed proportional to the overlap surface. The SAM exhibits the Gutenberg-Richter law with an exponent $\beta$ related to the roughness index of the profiles. Apart from being analytically treatable, the model exhibits a non-trivial clustering in the spatio-temporal distribution of epicenters that strongly resembles the experimentally observed one. A generalized and more realistic version of the model exhibits the Omori scaling for the distribution of the aftershocks. The SAM lies in a different perspective with respect to usual models for seismicity. In this case, in fact, the critical behaviour is not Self-Organized but stems from the fractal geometry of the faults, which, on its turn, is supposed to arise as a consequence of geological processes on very long time scales with respect to the seismic dynamics. The explicit introduction of the fault geometry, as an active element of this complex phenomenology, represents the real novelty of our approach.Comment: 40 pages (Tex file plus 8 postscript figures), LaTeX, submitted to Phys. Rev.

Integer and Fractional Order Entropy Analysis of Earthquake Data-series

This paper studies the statistical distributions of worldwide earthquakes from year 1963 up to year 2012. A Cartesian grid, dividing Earth into geographic regions, is considered. Entropy and the Jensen–Shannon divergence are used to analyze and compare real-world data. Hierarchical clustering and multi-dimensional scaling techniques are adopted for data visualization. Entropy-based indices have the advantage of leading to a single parameter expressing the relationships between the seismic data. Classical and generalized (fractional) entropy and Jensen–Shannon divergence are tested. The generalized measures lead to a clear identification of patterns embedded in the data and contribute to better understand earthquake distributions

A renormalization procedure for directed sandpile models

Directed models of self-organized criticality are studied in the framework of a real-space renormalization group of a different type. The identification of a suitable phase space in which to define the renormalization transformation and the coupling with the stationarity condition enables us to clarify the nature of the critical state. The renormalization equations are found to have an attractive fixed point, as expected from the self-critical nature of the model. The values of the critical exponents obtained by this procedure are in excellent agreement with exact results

Earthquakes statistics and fractal faults

We introduce a Self-affine Asperity Model (SAM) for the seismicity that mimics the fault friction by means of two fractional Brownian profiles (fBm) that slide one over the other. An earthquake occurs when there is an overlap of the two profiles representing the two fault faces and its energy is assumed proportional to the overlap surface. The SAM exhibits the Gutenberg-Richter law with an exponent $\beta$ related to the roughness index of the profiles. Apart from being analytically treatable, the model exhibits a non-trivial clustering in the spatio-temporal distribution of epicenters that strongly resembles the experimentally observed one. A generalized and more realistic version of the model exhibits the Omori scaling for the distribution of the aftershocks. The SAM lies in a different perspective with respect to usual models for seismicity. In this case, in fact, the critical behaviour is not Self-Organized but stems from the fractal geometry of the faults, which, on its turn, is supposed to arise as a consequence of geological processes on very long time scales with respect to the seismic dynamics. The explicit introduction of the fault geometry, as an active element of this complex phenomenology, represents the real novelty of our approach

Exploration of phylogeography of Monacha cantiana s.l. continues: the populations of the Apuan Alps (NW Tuscany, Italy) (Eupulmonata, Stylommatophora, Hygromiidae)

Two new lineages CAN-5 and CAN-6 were recognised in four populations of Monacha cantiana (Montagu, 1803) s.l. from the Italian Apuan Alps by joint molecular and morphological analysis. They are different from other M. cantiana lineages known from English, Italian, Austrian and French populations, i.e. CAN-1, CAN-2, CAN-3 and CAN-4, as well as from the other Italian Monacha species used for comparisons (M. parumcincta and M. cartusiana). Although a definite taxonomic and nomenclatural setting seems to be premature, we suggest that the name or names for these new lineages as one or two species should be found among 19th century names (Helix sobara Mabille, 1881, H. ardesa Mabille, 1881, H. apuanica Mabille, 1881, H. carfaniensis De Stefani, 1883 and H. spallanzanii De Stefani, 1884)

Exploring Monacha cantiana (Montagu, 1803) phylogeography: cryptic lineages and new insights into the origin of the English populations (Eupulmonata, Stylommatophora, Hygromiidae).

Molecular analysis of nucleotide sequences of mitochondria] cytochromc oxidase subunit 1 (COI) and 16S ribosomal DNA (16SrDNA) as well as nuclear histone 3 (H3) and internal transcribed spacer 2 of rDNA (ITS2) gene fragments together with morphological analysis of shell and genitalia features showed that English, French and Italian populations usually assigned to Monacha cantiana consist of four distinct lineages (CAN-1, CAN-2, CAN-3, CAN-4). One of these lineages (CAN-1) included most of the UK (five sites) and Italian (five sites) populations examined. Three other lineages represented populations from two sites in northern Italy (CAN-2), three sites in northern Italy and Austria (CAN-3), and two sites in south-eastern France (CAN-4). The taxonomic and nomenclatural setting is only currently available for lineages CAN-1 and CAN-4; a definitive frame for the other two requires much more research. The lineage CAN-1 corresponds to the true M. cantiana (Montagu, 1803) because it is the only one that includes topotypical English populations. The relationships and genetic distances support the hypothesis of the Italian origin of this lineage which was probably introduced to England by the Romans. The lineage CAN-4 is attributed to M. cemenelea (Risso, 1826), for which a neotype has been designated and deposited. Its diagnostic sequences of COI, 16SrDNA, H3 and ITS2 genes have also been deposited in GenBank. Molecular and morphological (shell and genitalia) features showed that M. parumcincia (Rossmassler, 1834) is a distinct taxon from the M. cantiana lineages

Redescription of Monacha pantanelii (De Stefani, 1879), a species endemic to the central Apennines, Italy (Gastropoda, Eupulmonata, Hygromiidae) by an integrative molecular and morphological approach

Specimens obtained from ten populations of a Monacha species from the central Apennines were compared with six molecular lineages of Monacha cantiana s. l. (CAN-1, CAN-2, CAN-3, CAN-4, CAN-5, CAN-6) and two other Monacha species (M. cartusiana and M. parumcincta), treated as outgroup, by molecular (nucleotide sequences of two mitochondrial COI and 16S rDNA as well as two nuclear ITS2 and H3 gene fragments) and morphological (shell and genital anatomy) analysis. The results strongly suggest that these populations represent a separate species for which two names are available: the older Helix pantanellii De Stefani, 1879 and the junior M. ruffoi Giusti, 1973. The nucleotide sequences created well separated clades on each phylogenetic tree. Genital anatomy included several distinctive features concerning vaginal appendix, penis, penial papilla and flagellum; instead, shell characters only enabled them to be distinguished from M. cartusiana and M. parumcincta. Remarkably, populations of M. pantanellii show high morphological variability. Shell variability mainly concerns size, some populations having very small dimensions. Genital variability shows a more intricate pattern of all anatomical parts, being higher as regards the vagina and vaginal appendix. Despite this morphological variability, the K2P distance range of COI sequences between populations is narrow (0.2-4.5%), if we consider all but three of the 53 sequences obtained. This research confirmed that the species of Monacha and their molecularly distinguished line-ages can only occasionally be recognised morphologically and that they have significant interand intrapopulation variability. The possibility of using an overall approach, including shell, genital and molecular evidence, was taken in order to establish a reliable taxonomic setting