Magnitude Uncertainties Impact Seismic Rate Estimates, Forecasts and Predictability Experiments

The Collaboratory for the Study of Earthquake Predictability (CSEP) aims to prospectively test time-dependent earthquake probability forecasts on their consistency with observations. To compete, time-dependent seismicity models are calibrated on earthquake catalog data. But catalogs contain much observational uncertainty. We study the impact of magnitude uncertainties on rate estimates in clustering models, on their forecasts and on their evaluation by CSEP's consistency tests. First, we quantify magnitude uncertainties. We find that magnitude uncertainty is more heavy-tailed than a Gaussian, such as a double-sided exponential distribution, with scale parameter nu_c=0.1 - 0.3. Second, we study the impact of such noise on the forecasts of a simple clustering model which captures the main ingredients of popular short term models. We prove that the deviations of noisy forecasts from an exact forecast are power law distributed in the tail with exponent alpha=1/(a*nu_c), where a is the exponent of the productivity law of aftershocks. We further prove that the typical scale of the fluctuations remains sensitively dependent on the specific catalog. Third, we study how noisy forecasts are evaluated in CSEP consistency tests. Noisy forecasts are rejected more frequently than expected for a given confidence limit. The Poisson assumption of the consistency tests is inadequate for short-term forecast evaluations. To capture the idiosyncrasies of each model together with any propagating uncertainties, the forecasts need to specify the entire likelihood distribution of seismic rates.Comment: 35 pages, including 15 figures, agu styl

Comment on "Analysis of the Spatial Distribution between Successive Earthquakes" by Davidsen and Paczuski

By analyzing a southern California earthquake catalog, Davidsen and Paczuski [Phys. Rev. Lett. 94, 048501 (2005)] claim to have found evidence contradicting the theory of aftershock zone scaling in favor of scale-free statistics. We present four elements showing that Davidsen and Paczuski's results may be insensitive to the existence of physical length scales associated with aftershock zones or mainshock rupture lengths, so that their claim is unsubstantiated. (i) Their exponent smaller than 1 for a pdf implies that the power law statistics they report is at best an intermediate asymptotic; (ii) their power law is not robust to the removal of 6 months of data around Landers earthquake within a period of 17 years; (iii) the same analysis for Japan and northern California shows no evidence of robust power laws; (iv) a statistical model of earthquake triggering that explicitely obeys aftershock zone scaling can reproduce the observed histogram of Davidsen and Paczuski, demonstrating that their statistic may not be sensitive to the presence of characteristic scales associated with earthquake triggering

Redshift and velocity dispersion of the cluster of galaxies around NGC 326

Redshifts of several galaxies thought to be associated with NGC 326 are determined. The results confirm the presence of a cluster and find a mean redshift of z = 0.0477 +/- 0.0007 and a line-of-sight velocity dispersion sigma_{z} = 599 (+230, -110) km/s. The velocity dispersion and previously measured X-ray gas temperature of kT ~ 1.9 keV are consistent with the cluster sigma_{z}/kT relation, and NGC 326 is seen to be a slowly-moving member of the cluster.Comment: 3 pages, to appear in MNRA

Element Abundance Determination in Hot Evolved Stars

The hydrogen-deficiency in extremely hot post-AGB stars of spectral class PG1159 is probably caused by a (very) late helium-shell flash or a AGB final thermal pulse that consumes the hydrogen envelope, exposing the usually-hidden intershell region. Thus, the photospheric element abundances of these stars allow us to draw conclusions about details of nuclear burning and mixing processes in the precursor AGB stars. We compare predicted element abundances to those determined by quantitative spectral analyses performed with advanced non-LTE model atmospheres. A good qualitative and quantitative agreement is found for many species (He, C, N, O, Ne, F, Si, Ar) but discrepancies for others (P, S, Fe) point at shortcomings in stellar evolution models for AGB stars. Almost all of the chemical trace elements in these hot stars can only be identified in the UV spectral range. The Far Ultraviolet Spectroscopic Explorer and the Hubble Space Telescope played a crucial role for this research.Comment: To appear in: Recent Advances in Spectroscopy: Theoretical, Astrophysical, and Experimental Perspectives, Proceedings, Jan 28 - 31, 2009, Kodaikanal, India (Springer