Earthquake recurrence as a record breaking process

Extending the central concept of recurrence times for a point process to recurrent events in space-time allows us to characterize seismicity as a record breaking process using only spatiotemporal relations among events. Linking record breaking events with edges between nodes in a graph generates a complex dynamical network isolated from any length, time or magnitude scales set by the observer. For Southern California, the network of recurrences reveals new statistical features of seismicity with robust scaling laws. The rupture length and its scaling with magnitude emerges as a generic measure for distance between recurrent events. Further, the relative separations for subsequent records in space (or time) form a hierarchy with unexpected scaling properties

Spatiotemporal correlations of aftershock sequences

Aftershock sequences are of particular interest in seismic research since they may condition seismic activity in a given region over long time spans. While they are typically identified with periods of enhanced seismic activity after a large earthquake as characterized by the Omori law, our knowledge of the spatiotemporal correlations between events in an aftershock sequence is limited. Here, we study the spatiotemporal correlations of two aftershock sequences form California (Parkfield and Hector Mine) using the recently introduced concept of "recurrent" events. We find that both sequences have very similar properties and that most of them are captured by the space-time epidemic-type aftershock sequence (ETAS) model if one takes into account catalog incompleteness. However, the stochastic model does not capture the spatiotemporal correlations leading to the observed structure of seismicity on small spatial scales.Comment: 31 pages, 5 figure

Identification of the X-ray pulsar in Hercules: A new optical pulsar

A series of photographic, photoelectric, and spectroscopic observations beginning June 1, 1972 has led to the optical identification of Her X-1 (2U 1705 + 34), a pulsed X-ray source in an eclipsing binary system, with the thirteenth magnitude blue variable star HZ Herculis. The detection of optical pulses at the frequency of the X-ray pulsar on three nights makes the identification conclusive and establishes HZ Her as the second known optical pulsar. The strength of the optical pulses may be correlated with the orbital phase but is not obviously related to the high or low intensity states of the X-ray source

Network of recurrent events for the Olami-Feder-Christensen model

We numerically study the dynamics of a discrete spring-block model introduced by Olami, Feder and Christensen (OFC) to mimic earthquakes and investigate to which extent this simple model is able to reproduce the observed spatiotemporal clustering of seismicty. Following a recently proposed method to characterize such clustering by networks of recurrent events [Geophys. Res. Lett. {\bf 33}, L1304, 2006], we find that for synthetic catalogs generated by the OFC model these networks have many non-trivial statistical properties. This includes characteristic degree distributions -- very similar to what has been observed for real seismicity. There are, however, also significant differences between the OFC model and earthquake catalogs indicating that this simple model is insufficient to account for certain aspects of the spatiotemporal clustering of seismicity.Comment: 11 pages, 16 figure

Network of Earthquakes and Recurrences Therein

We quantify the correlation between earthquakes and use the same to distinguish between relevant causally connected earthquakes. Our correlation metric is a variation on the one introduced by Baiesi and Paczuski (2004). A network of earthquakes is constructed, which is time ordered and with links between the more correlated ones. Data pertaining to the California region has been used in the study. Recurrences to earthquakes are identified employing correlation thresholds to demarcate the most meaningful ones in each cluster. The distribution of recurrence lengths and recurrence times are analyzed subsequently to extract information about the complex dynamics. We find that the unimodal feature of recurrence lengths helps to associate typical rupture lengths with different magnitude earthquakes. The out-degree of the network shows a hub structure rooted on the large magnitude earthquakes. In-degree distribution is seen to be dependent on the density of events in the neighborhood. Power laws are also obtained with recurrence time distribution agreeing with the Omori law.Comment: 17 pages, 5 figure

1/f noise from correlations between avalanches in self-organized criticality

We show that large, slowly driven systems can evolve to a self-organized critical state where long range temporal correlations between bursts or avalanches produce low frequency $1/f^{\alpha}$ noise. The avalanches can occur instantaneously in the external time scale of the slow drive, and their event statistics are described by power law distributions. A specific example of this behavior is provided by numerical simulations of a deterministic ``sandpile'' model.Comment: Completely revised version: 4 pages (revtex), 3 eps figure

Networks of Recurrent Events, a Theory of Records, and an Application to Finding Causal Signatures in Seismicity

We propose a method to search for signs of causal structure in spatiotemporal data making minimal a priori assumptions about the underlying dynamics. To this end, we generalize the elementary concept of recurrence for a point process in time to recurrent events in space and time. An event is defined to be a recurrence of any previous event if it is closer to it in space than all the intervening events. As such, each sequence of recurrences for a given event is a record breaking process. This definition provides a strictly data driven technique to search for structure. Defining events to be nodes, and linking each event to its recurrences, generates a network of recurrent events. Significant deviations in properties of that network compared to networks arising from random processes allows one to infer attributes of the causal dynamics that generate observable correlations in the patterns. We derive analytically a number of properties for the network of recurrent events composed by a random process. We extend the theory of records to treat not only the variable where records happen, but also time as continuous. In this way, we construct a fully symmetric theory of records leading to a number of new results. Those analytic results are compared to the properties of a network synthesized from earthquakes in Southern California. Significant disparities from the ensemble of acausal networks that can be plausibly attributed to the causal structure of seismicity are: (1) Invariance of network statistics with the time span of the events considered, (2) Appearance of a fundamental length scale for recurrences, independent of the time span of the catalog, which is consistent with observations of the ``rupture length'', (3) Hierarchy in the distances and times of subsequent recurrences.Comment: 19 pages, 13 figure

HUT observations of carbon monoxide in the coma of Comet Levy (1990c)

Observations of comet Levy (1990c) were made with the Hopkins Ultraviolet Telescope during the Astro-1 Space Shuttle mission on 10 Dec. 1990. The spectrum, covering the wavelength range 415 to 1850 A at a spectral emission of 3 A (in first order), shows the presence of carbon monoxide and atomic hydrogen, carbon, and sulfur in the coma. Aside from H I Lyman-beta, no cometary features are detected below 1200 A, although cometary O I and O II would be masked by the same emissions present in the day airglow spectrum. The 9.4 x 116 arcsec aperture corresponds to 12,000 x 148,000 km at the comet. The derived production rate of CO relative to water, 0.13 + or - 0.02, compared with the same ratio derived from IUE observations (made in Sep. 1990) which sample a much smaller region of the coma, 0.04 + or - 0.01, suggests the presence of an extended source of CO, as was found in comet Halley. Upper limits on Ne and Ar abundance are within an order of magnitude or solar abundances