Statistical modeling of ground motion relations for seismic hazard analysis

We introduce a new approach for ground motion relations (GMR) in the probabilistic seismic hazard analysis (PSHA), being influenced by the extreme value theory of mathematical statistics. Therein, we understand a GMR as a random function. We derive mathematically the principle of area-equivalence; wherein two alternative GMRs have an equivalent influence on the hazard if these GMRs have equivalent area functions. This includes local biases. An interpretation of the difference between these GMRs (an actual and a modeled one) as a random component leads to a general overestimation of residual variance and hazard. Beside this, we discuss important aspects of classical approaches and discover discrepancies with the state of the art of stochastics and statistics (model selection and significance, test of distribution assumptions, extreme value statistics). We criticize especially the assumption of logarithmic normally distributed residuals of maxima like the peak ground acceleration (PGA). The natural distribution of its individual random component (equivalent to exp(epsilon_0) of Joyner and Boore 1993) is the generalized extreme value. We show by numerical researches that the actual distribution can be hidden and a wrong distribution assumption can influence the PSHA negatively as the negligence of area equivalence does. Finally, we suggest an estimation concept for GMRs of PSHA with a regression-free variance estimation of the individual random component. We demonstrate the advantages of event-specific GMRs by analyzing data sets from the PEER strong motion database and estimate event-specific GMRs. Therein, the majority of the best models base on an anisotropic point source approach. The residual variance of logarithmized PGA is significantly smaller than in previous models. We validate the estimations for the event with the largest sample by empirical area functions. etc

Characterizing the Adaptive Optics Off-Axis Point-Spread Function - I: A Semi-Empirical Method for Use in Natural-Guide-Star Observations

Even though the technology of adaptive optics (AO) is rapidly maturing, calibration of the resulting images remains a major challenge. The AO point-spread function (PSF) changes quickly both in time and position on the sky. In a typical observation the star used for guiding will be separated from the scientific target by 10" to 30". This is sufficient separation to render images of the guide star by themselves nearly useless in characterizing the PSF at the off-axis target position. A semi-empirical technique is described that improves the determination of the AO off-axis PSF. The method uses calibration images of dense star fields to determine the change in PSF with field position. It then uses this information to correct contemporaneous images of the guide star to produce a PSF that is more accurate for both the target position and the time of a scientific observation. We report on tests of the method using natural-guide-star AO systems on the Canada-France-Hawaii Telescope and Lick Observatory Shane Telescope, augmented by simple atmospheric computer simulations. At 25" off-axis, predicting the PSF full width at half maximum using only information about the guide star results in an error of 60%. Using an image of a dense star field lowers this error to 33%, and our method, which also folds in information about the on-axis PSF, further decreases the error to 19%.Comment: 29 pages, 9 figures, accepted for publication in the PAS

Highly site-specific H2 adsorption on vicinal Si(001) surfaces

Experimental and theoretical results for the dissociative adsorption of H_2 on vicinal Si(001) surfaces are presented. Using optical second-harmonic generation, sticking probabilities at the step sites are found to exceed those on the terraces by up to six orders of magnitude. Density functional theory calculations indicate the presence of direct adsorption pathways for monohydride formation but with a dramatically lowered barrier for step adsorption due to an efficient rehybridization of dangling orbitals.Comment: 5 pages, 4 figures, submitted to Phys. Rev. Lett. (1998). Other related publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm

Sensitivity of Localized Surface Plasmon Resonances to Bulk and Local Changes in the Optical Environment

This document is the Accepted Manuscript version of a Published Work that appeared in final form in Journal of Physical Chemistry C copyright © 2009 American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see http://dx.doi.org/10.1021/jp810322qSingle rod-shaped and disk-shaped gold nanoparticles with sizes ranging from 60 to 162 nm were analyzed using dark-field scattering spectroscopy. The sensitivity of the localized surface plasmon resonance (LSPR) of each nanoparticle to both a bulk and a local change in the refractive index of the environment was obtained by monitoring the change in the spectral position of the LSPR. It was found that the rods were more sensitive to changes in both the local environment and the bulk environment, in particular rods with a length > 110 nm. This behavior was confirmed by finite element modeling of the structures that clearly indicated a saturation of the relative wavelength shift for the disks as the diameter increased whereas the sensitivity of the rods continued to increase linearly with increasing length. This disparity in the behavior of the two types of nanoparticle may in part be attributed to two principal effects associated with the presence of the substrate: first, that the proportion of the surface area of the nanoparticle in contact with the substrate is larger for the disk than for the rod; second, that the LSPR electromagnetic field is more concentrated within the superstrate for the rod compared to the disk. Further analysis of data obtained from modeling a changing local environment indicates that, although the rods are more sensitive, both rods and disks exhibit a similar field confinement