Seismic motion and response prediction alternatives

Statistical methods are available which predict the maximum response of simple oscillators given the peak acceleration (A_p), peak velocity (V_p) or peak displacement (D_p) of seismic ground motions. An alternative parameter, namely an ordinate (or ordinates) of the Fourier amplitude spectrum of ground motion acceleration, FS(f), may in fact be a preferred predictor of peak response, especially in a frequency range close to f. Other statistical methods (attenuation laws) use distance R and other parameters such as magnitude (M), Modified Mercalli epicentral Intensity (I_o) and Modified Mercalli site Intensity (MMI or I_s) to predict spectral velocity (S_v(f)), etc. In using such approaches, it is most desirable to know the total uncertainty in the predicted peak response of the system given the starting parameter values. An extensive strong motion data set is used to study these questions, The most direct prediction models are found to be preferable (have lower prediction dispersion) but data may not be available in all regions to permit their use.     

Model Simulations on the Variability of Particulate MSA to Non-Sea-Salt Sulfate Ratio in the Marine Environment

A box model was constructed to investigate connections between the particulate MSA to non-sea-salt sulfate ratio, R, and DMS chemistry in a clean marine boundary layer. The simulations demonstrated that R varies widely with particle size, which must be taken into account when interpreting field measurements or comparing them with each other. In addition to DMS gas-phase chemistry, R in the submicron size range was shown to be sensitive to the factors dictating sulfate production via cloud processing, to the removal of SO₂ from the boundary layer by dry deposition and sea-salt oxidation, to the entrainment of SO₂ from the free troposphere, to the relative concentration of sub- and supermicron particles, and to meteorology. Three potential explanations for the increase of R toward high-latitudes during the summer were found: larger MSA yields from DMS oxidation at high latitudes, larger DMSO yields from DMS oxidation followed by the conversion of DMSO to MSA at high latitudes, or lower ambient H₂O₂ concentrations at high latitudes leading to less efficient sulfate production in clouds. Possible reasons for the large seasonal amplitude of R at mid and high latitudes include seasonal changes in the partitioning of DMS oxidation to the OH and NO₃ initiated pathways, seasonal changes in the concentration of species participating the DMS-OH reaction pathway, or the existence of a SO₂ source other than DMS oxidation in the marine boundary layer. Even small anthropogenic perturbations were shown to have a potential to alter the MSA to non-sea-salt sulfate ratio.     

Second order elasticity theory: An improved formulation of the Grüneisen parameter at high pressure

The second order theory of elasticity, in which terms to second order in strain are retained in calculating atomic bond length changes and elastic moduli, is extended to describe thermal vibration of a face-centred cubic crystal. Coupled with equations relating the pressure dependences of elastic constants, this yields a new formulation of the thermal Grüneisen parameter γ in terms of pressure P, incompressibility K and rigidity, μ

$\text{λ}\text{1}\text{2}\text{d}\text{K}\text{d}\text{P}\text{?}\text{1}\text{2}\text{+}\text{1}\text{9}\text{P}\text{K}\text{?}\text{1}\text{3}\text{?}\text{1}\text{9}\text{P}\text{K}\text{f}\text{1?}\text{2}\text{3}\text{P}\text{K}\text{?}\text{2}\text{3}\text{P}\text{K}\text{f}$

where f = 24 (3 K ? 2 P)/(3 K + 115 μ + 90 P). The factor f arises from bond interactions and the case f = 1, representing independent bonds (no interactions), yields the free-volume γ- Since we have shown earlier that the second order elasticity theory provides a convincing explanation of the elasticity of the inner core, we believe that the new formula is appropriate for the inner core. It is, however, inadequate to describe the lower mantle γ, in which atomic bond angle rigidity, not considered here, may be appreciable.     

Exchange of ejecta between Telesto and Calypso: Tadpoles, horseshoes, and passing orbits

We have numerically integrated the orbits of ejecta from Telesto and Calypso, the two small Trojan companions of Saturn’s major satellite Tethys. Ejecta were launched with speeds comparable to or exceeding their parent’s escape velocity, consistent with impacts into regolith surfaces. We find that the fates of ejecta fall into several distinct categories, depending on both the speed and direction of launch.The slowest ejecta follow suborbital trajectories and re-impact their source moon in less than one day. Slightly faster debris barely escape their parent’s Hill sphere and are confined to tadpole orbits, librating about Tethys’ triangular Lagrange points L₄ (leading, near Telesto) or L₅ (trailing, near Calypso) with nearly the same orbital semi-major axis as Tethys, Telesto, and Calypso. These ejecta too eventually re-impact their source moon, but with a median lifetime of a few dozen years. Those which re-impact within the first 10 years or so have lifetimes near integer multiples of 348.6 days (half the tadpole period).Still faster debris with azimuthal velocity components ?10 m/s enter horseshoe orbits which enclose both L₄ and L₅ as well as L₃, but which avoid Tethys and its Hill sphere. These ejecta impact either Telesto or Calypso at comparable rates, with median lifetimes of several thousand years. However, they cannot reach Tethys itself; only the fastest ejecta, with azimuthal velocities ?40 m/s, achieve “passing orbits” which are able to encounter Tethys. Tethys accretes most of these ejecta within several years, but some 1% of them are scattered either inward to hit Enceladus or outward to strike Dione, over timescales on the order of a few hundred years.     

Assessment of the resonant perturbation errors in Galilean satellite ephemerides using precisely measured eclipse times

Astrometric satellite positions are derived from timings of their eclipses in the shadow of Jupiter. The 548 data points span 20 years and are accurate to about 0.006 arcsec for Io and Europa and about 0.015 arcsec or better for Ganymede and Callisto. The precision of the data set and its nearly continuous distribution in time allows measurement of regular oscillations with an accuracy of 0.001 arcsec. This level of sensitivity permits detailed evaluation of modern ephemerides and reveals anomalies at the 1.3 year period of the resonant perturbations between Io, Europa and Ganymede. The E5 ephemeris shows large errors at that period for all three satellites as well as other significant anomalies. The L1 ephemeris fits the observations much more closely than E5 but discrepancies for the resonant satellites are still apparent and the measured positions of Io are drifting away from the predictions. The JUP230 ephemeris fits the observations more accurately than L1 although there is still a measurable discordance between the predictions and observations for Europa at the resonance period.     

A hybrid artificial neural network-numerical model for ground water problems

Numerical models constitute the most advanced physical-based methods for modeling complex ground water systems. Spatial and/or temporal variability of aquifer parameters, boundary conditions, and initial conditions (for transient simulations) can be assigned across the numerical model domain. While this constitutes a powerful modeling advantage, it also presents the formidable challenge of overcoming parameter uncertainty, which, to date, has not been satisfactorily resolved, inevitably producing model prediction errors. In previous research, artificial neural networks (ANNs), developed with more accessible field data, have achieved excellent predictive accuracy over discrete stress periods at site-specific field locations in complex ground water systems. In an effort to combine the relative advantages of numerical models and ANNs, a new modeling paradigm is presented. The ANN models generate accurate predictions for a limited number of field locations. Appending them to a numerical model produces an overdetermined system of equations, which can be solved using a variety of mathematical techniques, potentially yielding more accurate numerical predictions. Mathematical theory and a simple two-dimensional example are presented to overview relevant mathematical and modeling issues. Two of the three methods for solving the overdetermined system achieved an overall improvement in numerical model accuracy for various levels of synthetic ANN errors using relatively few constrained head values (i.e., cells), which, while demonstrating promise, requires further research. This hybrid approach is not limited to ANN technology; it can be used with other approaches for improving numerical model predictions, such as regression or support vector machines (SVMs).