arXiv subjects

J. Greenhough

Publications and source records attributed to J. Greenhough.

6 recordsLinked to original sources

arXiv2008

A Poisson model for earthquake frequency uncertainties in seismic hazard analysis

Frequency-magnitude distributions, and their associated uncertainties, are of key importance in statistical seismology. When fitting these distributions, the assumption of Gaussian residuals is invalid since event numbers are both discrete and of unequal variance. In general, the observed number in any given magnitude range is described by a binomial distribution which, given a large total number of events of all magnitudes, approximates to a Poisson distribution for a sufficiently small probability associated with that range. In this paper, we examine four earthquake catalogues: New Zealand (Institute of Geological and Nuclear Sciences), Southern California (Southern California Earthquake Center), the Preliminary Determination of Epicentres and the Harvard Centroid Moment Tensor (both held by the United States Geological Survey). Using independent Poisson distributions to model the observations, we demonstrate a simple way of estimating the uncertainty on the total number of events occurring in a fixed time period.

physics.geo-ph↗

arXiv2007

Synthesis of scaling exponents: a fractional Levy model

Mandelbrot introduced the concept of fractals to describe the non-Euclidean shape of many aspects of the natural world. In the time series context he proposed the use of fractional Brownian motion (fBm) to model non-negligible temporal persistence, the "Joseph Effect"; and Levy flights to quantify large discontinuities, the "Noah Effect". In space physics, both effects are manifested in the intermittency and long-range correlation which are by now well-established features of geomagnetic indices and their solar wind drivers. In order to capture and quantify the Noah and Joseph effects in one compact model we propose the application of the "bridging" fractional Levy motion (fLm) to space physics. We perform an initial evaluation of some previous scaling results in this paradigm, and show how fLm can model the previously observed exponents. We suggest some new directions for the future.

physics.space-ph↗

arXiv2003

Statistical characterisation of full-disk EUV/XUV solar irradiance and correlation with solar activity

We investigate the distribution of fluctuations in solar irradiance when integrated over the full disk, obtained using extreme ultraviolet/soft X-ray observations from the SOHO CELIAS/SEM instrument. This time series sums over both the contributions of single distinguishable flares, and of many other processes. By detrending we select events with timescales of less than a few hours such as waves, slow flows, and CMEs. The statistics generated by this range of phenomena can be characterised by power-law-tailed distributions. We show that (i) during the high-activity period 2000 Jan-June the tail exponent a(T)=1.5 +/- 0.1; (ii) during the low-activity period 1996 Jan-June a(T)=3.0 +/- 0.2; and (iii) in general a(T) decreases with increasing activity.

astro-ph↗

arXiv2002

Identification of a 12-17 day timescale in X-ray observations of GRS 1915+105

Measurement of the energy emitted from accreting astrophysical systems provides an observational constraint on the plasma processes that may be operating within the disk. Here we examine the continual time variation over the past six years of the total X-ray flux from the microquasar GRS 1915+105. The application of differencing and rescaling techniques to RXTE/ASM data shows that the small amplitude fluctuations scale up to 12-17 days. A 17-day timescale in the X-ray fluctuations corresponds to half the measured binary orbital period of this system (33.5 +/- 1.5 days). While this may be coincidental, it is possible that these two timescales may be linked by, for example, a turbulent cascade in the accretion disk driven by a tidally-induced two-armed spiral shock corotating with the binary system. Temporal scaling is found only in the ever-present small fluctuations, and not in the intermittent larger-amplitude fluctuations. This is consistent with the basic model for this source which consists of a steady, cold outer disk and an unstable inner disk.

astro-ph↗

arXiv2002

Football goal distributions and extremal statistics

We analyse the distributions of the number of goals scored by home teams, away teams, and the total scored in the match, in domestic football games from 169 countries between 1999 and 2001. The probability density functions (PDFs) of goals scored cannot be fitted over their entire ranges by Poisson or negative binomial distributions; here, we compare the PDFs with those arising from extremal statistics. In addition, we show that it is sufficient to model English top division and FA Cup matches in the seasons of 1970/71 to 2000/01 on Poisson or negative binomial distributions, as reported in analyses of earlier seasons, and that these are not consistent with extremal statistics.

cond-mat.stat-mech↗

arXiv2001

Characterising anomalous transport in accretion disks from X-ray observations

Whilst direct observations of internal transport in accretion disks are not yet possible, measurement of the energy emitted from accreting astrophysical systems can provide useful information on the physical mechanisms at work. Here we examine the unbroken multi-year time variation of the total X-ray flux from three sources: Cygnus X-1, the microquasar GRS1915+105, and for comparison the nonaccreting Crab nebula. To complement previous analyses, we demonstrate that the application of advanced statistical methods to these observational time-series reveals important contrasts in the nature and scaling properties of the transport processes operating within these sources. We find the Crab signal resembles Gaussian noise; the Cygnus X-1 signal is a leptokurtic random walk whose self-similar properties persist on timescales up to three years; and the GRS1915+105 signal is similar to that from Cygnus X-1, but with self-similarity extending possibly to only a few days. This evidence of self-similarity provides a robust quantitative characterisation of anomalous transport occuring within the systems.

astro-ph↗