2009 Class Abstracts

Measuring a Galaxy's Spiral Arm Pattern Speed

Jason Speights

The angular rotation rate of a galaxy's spiral pattern, also known as the pattern speed, is a fundamental parameter in the structure, dynamics, and evolution of a spiral galaxy. The current paradigm in galactic structure assumes spiral patterns are density waves and the pattern speed is usually measured from this assumption. This method for measuring the pattern speed involves matching photometric features of a spiral pattern with the kinematics that would result from spiral density waves thus limiting what is known about spiral patterns to the interpretation of spiral galaxy observations. More direct methods are needed to test the accuracy of measuring pattern speeds from photometric features and to determine whether spiral patterns are indeed spiral density waves. One such method involves integrating the continuity equation applied to a class of spiral tracer. The resulting integral equation relates the pattern speed to observable density and kinematic properties. This paper includes a summary of the derivation of the integral equation for the pattern speed followed by a summary of the different procedures used to date to solve this equation.

Modeling Ambiguous Forces Generated by Endogenic Voclanic Processes

Richard Sanderson

Physical processes occurring in active volcanoes are numerate and complex, ranging from slow magma ascent to rapid volatile expansion and consequent explosion. Details of these processes are often interpreted from seismic waves that result from the interplaying forces within volcanic conduits. Ultra-long period (ULP) seismic-waves with periods on the order of several minutes have been observed at several volcanoes globally with varying interpretations. Modeling of the recently detected ULPs at Santiaguito volcano, Guatemala, that occur contemporaneously with explosions would help illuminate some of the underlying reasons for the characteristic and long-lived activity there. To find source-time histories, a moment tensor inversion of the recorded (filtered) data will be carried out in the frequency domain. Stationary non-destructive sources are often found for ULPs, permitting Green’s functions to be determined by deconvolving signals recorded at a station from each other. Detailed study of determined combinations of moment tensor components and/or single forces will elucidate dimensions and orientations of possible cracks, conduits or chambers whose magma inflation/deflation is likely the source of the seismic signals. Depths will be ascertained though a combination of 3D particle motions and a grid search. The potential for direct ground motion (tilt) rather than propagating seismic waves will also be investigated.

Comparison and Analysis of Group Velocity Models for Seismic Coda Calibration

Pamela Moyer

Seismic coda (the scattered energy following the direct wave arrivals of an earthquake) may be analyzed to arrive at source spectra estimations for apparent stress calculations. During the calibration stage of seismic coda analysis, estimates for processes that affect the seismic energy as it travels through the Earth from the source to the receiver are made. One parameter that must be determined at the beginning of calibration is that of coda group velocity. Here, a nonlinear, overdetermined system consisting of epicentral distance and coda peak velocity values from nearly 500 local earthquakes is presented. MATLAB is used for graphical presentation and data analysis while several models for coda group velocity are examined and compared. Models that are examined include an exponential model and the accepted hyperbolic model using one or more minimization techniques. A comparative analysis that includes the evaluation of the goodness-of-fit, condition number, distribution of residuals, and other methods as applicable between the models is made. From this analysis, a better understanding of the coda group velocity model and subsequent models used in the calibration stage of seismic coda analysis may be gained..

Cash’s C Statistic and S Statistic in X-ray Astronomy

Guohui Wu

As an observational branch of astronomy, X-ray astronomy deals with the study of X-ray emission from celestial objects. Its main objective is to detect a weak source against a fairly strong background, which is done on a photon-by-photon basis. Speaking generally, the issue of collecting X-ray data is reduced to tallying individual photons, which are sampled from Poisson distribution. As far as the fitting of a parameterized model to Poisson-distributed data is concerned, there are two statistics that can be used as goodness-of-fit indicators.In this project, we will introduce S statistic and Cash’s C-statistics and demonstrate their advantages and disadvantages along with the differences between them. First, we will introduce the S statistics based on Gaussian distribution and develop the confidence intervals for the parameter value. Second, we will introduce Cash’s C statistic, which is not subject to some inadequacies of the Gaussianity, followed by the generation of confidence intervals for true parameter. Finally, comparison between these two statistics and their asymptotic relation will be addressed.

Decoding the Interference from Sea-surface Reflections Using Nonlinear Regression

Sonja Behnke

Two LMA antennas recorded VHF lightning sources during the eruption of Mt. Augustine on January 28th, 2006. The two station data provides only azimuthal position of the sources. Fortunately, one of the antennas was situated on a bluff overlooking the sea and received multiple beam interference due to sea-surface reflections. Methods have been developed using nonlinear regression to model the interference pattern and hence determine the source altitudes. Knowledge of the LMA source altitudes is critical to interpreting charge layers in the volcanic plume. The interference model is parametrized by the initial altitude and velocity of the sources and the reflection coefficient. In this paper the methods of nonlinear regression, particularly the Levenberg-Marquardt method, will be presented and applied to the interference model.

Inverse Application of Transit Time Distributions

Jesus Gomez

It is common practice in hydrology to use transfer functions that describe the lumped behavior of complex systems. Imagine for instance a basin (or control volume) in which the input of solutes comes from precipitation (P) and have concentration c_P(t). Also, the solutes leaving the subsurface are transported by the baseflow (ground water contribution to the stream) and have concentration c_B(t). If the catchment is assumed to be a transient, linear system (a strong assumption in general, but common given the complexities involved and the lack of information) the baseflow concentration of a conservative solute can be expressed as:

(1)

where is the transit time, t0 is the time of the first solute mass input, and g is the transit time distribution (TTD) (or transfer function) of the system. Furthermore, if the system is assumed steady-state, Eq. (1) reduces to:

(2)

Eq. (2) is largely used in practical applications and will be the focus of this project; however, the transient case is a major concern in the scientific community.

This work uses inverse theory to explore the following applications: (i) for c_P(t) and c_B(t) known from field measurements, g(τ) and its uncertainty are estimated, also, some of the most common models used in practice (Gemma distribution, Exponential distribution, Dispersion model) are fitted, and (ii) equation (2) is used as a predictive tool for estimating c_P(t) and its uncertainty assuming that c_B(t) is known from field observations and g(τ) follows one of the distributions mentioned before. Data from Valles Caldera Natural Preserve in NM and synthetic time series with known uncertainties are used to explore the error propagation when estimating these parameters.

Fitting Specific Heat Relaxation in Simple Glass Forming Systems

Jon Brown

Specific heat spectroscopy has been seen as useful in the investigation of relaxation in glassy systems. In this work, two different models of glass formers are studied by simulation. A polymer glass is modeled with molecular dynamics simulations of bead spring chains with differing temperatures, densities, and bond angle restrictionn Another simple glassy system considered is the east Ising spin model. The complex-valued, frequency-dependent specific heat is computed from simulations with low-amplitude, sinusoidally-varying temperature. The specific heat of both systems show non-Debye relaxation behavior, and it is shown by Cole-Cole plots that these can be fit to the Cole-Davidson (CD) function. A method for tting the full complex data to the CD function is developed and implemented.

Inverting Filtered Infrasonic Waves for Characterizing Diffraction Coefficients Due to Topographic Edges

Omar Marcillo

Data from a three-station infrasound network deployed on June 2008 at the summit of Kilahuea volcano will be used to determine the influence of diffraction on the propagation of infrasonic waves near topographic edges. Certain features in the topography can selectively attenuate the amplitude of infrasonic waves. Several approximations based on diffraction effects can be used to model this attenuation. One of these models is the Harden and Pierce solution for the diffraction of spherical waves around a semi-infinite wedge. Using this approach, frequency-dependent coefficients can be calculated to estimate the attenuation of waves. This project aims to calculate diffraction coefficients for topography by the inversion of the measured attenuation in the propagation of infrasonic waves. The results will help us to determine the influence of the topographic effects in our measurements.

Receiver Function Studies at the South Pole

Julien Chaput

Gathering accurate information on the subsurface using very limited means has always been the prerogative of the seismologist, and as such a wide variety of methods designed to use all available data have been developed. One particularly useful methodology consists of the deconvolution of radial-by-vertical components of a seismic trace with a teleseismic event as a source, so as to generate a result particularly sensitive to P-SV wavepath conversions. These aptly named receiver functions are particularly useful in the imaging of large velocity discontinuities such as the Moho, the 440 and the 660 km discontinuities, though the deconvolution problem is typically ill-posed, necessitating regularization. As a prequel to the POLENET project which will include a large number of receiver function images of West Antarctica, I will attempt recover receiver functions from South Pole station while solving the regularization problem. This effort will serve as a test of viability for later POLENET trials.

P_f₀ Estimation by Orthogonal Distance Regression

Robert Aumer

Currently geoscientists are developing dating techniques that involve measuring higher than background concentrations of a suite of radioactive nuclides, which are produced by cosmic radiation. For each of the nuclides there are a handful of production pathways that must be estimated. The major contributor to production rate uctuation is linked to the temporal changes in Earth's magnetic field strength. Additionally, both the measured concentrations of cosmogenic nuclides and the independent ages from the calibration data set contain errors. For these reason, we will implement the method of nonlinear orthogonal distance regression to estimate the parameter for thermal neutron capture, (P_f₀), for ³⁶Cl.