On Certain Divisibility Property of Polynomials

We review the definition of D-rings introduced by H. Gunji & D. L. MacQuillan. We provide an alternative characterization for such rings that allows us to give an elementary proof of that a ring of algebraic integers is a D-ring. Moreover, we give a characterization for D-rings that are also unique factorization domains to determine divisibility of polynomials using polynomial evaluations

Development of a Seismic Snow Streamer and Use of Multi-Offset Reflection for Determining Glacier Ice Properties

Glaciers and ice sheets are important to climate research due to their role in controlling worldwide weather and temperature patterns as well as their potential impact in sea level rise. Because of this, scientists are attempting to model large ice sheets and important fast flowing glaciers. These models are limited in large part to the lack of data which govern the nonlinear behavior of ice flow. Seismic data acquisition can provide high resolution data which can be used to extract information of variables like bed topography, ice temperature and preferred ice crystal orientation. But seismic data acquisition in polar environments is challenging. This is mainly due to the labor intensive process of manually hand planting geophones. In order to improve the efficiency of active source seismic reflection data acquisition in polar environments, two prototype seismic snow-streamers were constructed for this investigation and optimized for deployment in remote locations. The first snow-streamer (experimental snow-streamer) was field tested in the Jakobshavn Glacier located in central western Greenland. The experimental snow-streamer was equipped with multiple geophone configurations and two plate materials. Twenty-two variable angle records were collected using the stationary snow streamer in the center of the survey. The source consisted of 0.5 kg of explosives buried 10 m below the snow surface at 160 m intervals. The resultant data set consisted of offsets ranging from -1760 to +1600 m and the ice-bed interface as well as two internal ice layers were imaged at approximately 1.85, 1.5 and 1.7 km depth respectively. The snow-streamer data was simultaneously collected with a mirror arrangement of hand planted buried geophones in order to test for the effects of plate weight, wind noise, geophone burial and plate to snow coupling in the seismic signal. The signal analysis and the comparison of streamer vs. buried geophones showed that geophone burial can degrade the seismic signal while the wind and signal analysis revealed that the best snow-streamer configuration was a combination of aluminum plates with vertical geophones. Using these results a second 480m full scale snow-streamer was tested in the Thwaites Glacier Antarctica. The snow-streamer data was simultaneously collected with a mirrored arrangement of surface planted and buried geophones. The trace by trace comparison revealed higher signal to noise in the data collected using the snow-streamer when compared to the surface planted and buried geophones. The full scale snow-streamer was easy to maneuver, very light and could be pulled in speeds up to 15 km/h. The use of the snow-streamer proved to be an efficient data acquisition tool, yielding high quality data. Therefore the use of snow-streamers can represent a significant improvement in the efficiency of seismic data acquisition in polar environments opening the possibility of determining important ice column properties for areas of interest. An important parameter affecting glacier flow is preferred ice crystal orientation. Seismic waves in ice travel up to 5% faster along the c-axis than when travelling perpendicular to it. Therefore, reflected seismic wave slowness (inverse of the velocity) variability as a function of angle of incidence can be used to detect anisotropy in ice crystal orientation. By combining the multi-offset seismic reflection data set acquired with the experimental snow-streamer and a 2D seismic reflection profile simultaneously collected for the same location, we investigated the presence of preferred ice crystal orientation for the area of study on the Jakobshavn Glacier. The combination of both data sets allowed the approximation of the average ray velocity as a function of angle of incidence. Given that the seismic velocity varies as a function of ice crystal orientation, we can use an existing model to relate the variation of seismic velocity as a function of offset to estimate the mean ice crystal orientation for the bed and imaged internal layers in terms of a conical c-axes distribution. Based on the anisotropy analysis we concluded that the upper 1640 m of the ice column consists mostly of isotropic. The lower 300 m of the ice column is characterized by ice with preferred ice crystal orientation. These observations are consistent with laterally extensive complex ice fabric development reported over the same region of Jakobshavn Glacier