Alternative Statistical Methods for Analyzing Geological Phenomena: Bridging the Gap Between Scientific Disciplines

• Main Author: Van Gaalen, Joseph Frank
• Format: Others
• Published: Scholar Commons 2011
• Subjects: beach cusps; multi-scale; ratio map; s-transform; surficial aquifer system; terrestrial laser scanner; American Studies; Arts and Humanities; Geology; Geomorphology; Statistics and Probability
• Online Access: http://scholarcommons.usf.edu/etd/3424; http://scholarcommons.usf.edu/cgi/viewcontent.cgi?article=4619&context=etd

When we consider the nature of the scientific community in conjunction with a sense of typical economic circumstances we find that there are two distinct paths for development. One path involves hypothesis testing and evolution of strategies that are linked with iterations in equipment advances. A second, more complicated scenario, can involve external influences whether economic, political, or otherwise, such as the government closure of NASA's space program in 2011 which will no doubt influence research in associated fields. The following chapters are an account of examples of two statistical techniques and the importance of both on the two relatively unrelated geological fields of coastal geomorphology and ground water hydrology. The first technique applies a multi-dimensional approach to defining groundwater water table response based on precipitation in areas where it can reasonably be assumed to be the only recharge. The second technique applies a high resolution multi-scalar approach to a geologic setting most often restricted to either high resolution locally, or low resolution regionally. This technique uses time-frequency analysis to characterize cuspate patterns in LIDAR data are introduced using examples from the Atlantic coast of Florida, United States. These techniques permit the efficient study of beachface landforms over many kilometers of coastline at multiple spatial scales. From a LIDAR image, a beach-parallel spatial series is generated. Here, this series is the shore-normal position of a specific elevation (contour line). Well-established time-frequency analysis techniques, wavelet transforms, and S-Transforms, are then applied to the spatial series. These methods yield results compatible with traditional methods and show that it is useful for capturing transitions in cuspate shapes. To apply this new method, a land-based LIDAR study allowing for rapid high-resolution surveying is conducted on Melbourne Beach, Florida and Tairua Beach, New Zealand. Comparisons and testing of two different terrestrial scanning stations are evaluated during the course of the field investigation. Significant cusp activity is observed at Melbourne Beach. Morphological observations and sediment analysis are used to study beach cusp morphodynamics at the site. Surveys at Melbourne were run ~500 m alongshore and sediment samples were collected intertidally over a five-day period. Beach cusp location within larger scale beach morphology is shown to directly influence cusp growth as either predominantly erosional or accretional. Sediment characteristics within the beach cusp morphology are reported coincident with cusp evolution. Variations in pthesis size distribution kurtosis are exhibited as the cusps evolve; however, no significant correlation is seen between grain size and position between horn and embayment. During the end of the study, a storm resulted in beach cusp destruction and increased sediment sorting. In the former technique using multi-dimensional studies, a test of a new method for improving forecasting of surficial aquifer system water level changes with rainfall is conducted. The results provide a more rigorous analysis of common predictive techniques and compare them with the results of the tested model. These results show that linear interpretations of response-to-rainfall data require a clarification of how large events distort prediction and how the binning of data can change the interpretation. Analyses show that the binning ground water recharge data as is typically done in daily format may be useful for quick interpretation but only describes how fast the system responds to an event, not the frequency of return of such a response. Without a secure grasp on the nonlinear nature of water table and rainfall data alike, any binning or isolation of specific data carries the potential for aliasing that must be accounted for in an interpretation. The new model is proven capable of supplanting any current linear regression analysis as a more accurate means of prediction through the application of a multivariate technique. Furthermore, results show that in the Florida surficial aquifer system response-to-rainfall ratios exhibit a maxima most often linked with modal stage.