Trace amounts of elements are useful as a cutting-edge tool that to understanding the evolution of many earth and planetary systems and are critical in this project. The first chapter focuses on development and precision of a new multi-element analytical method that combines XRF preparation methods and laser ablation analysis, to allow rapid sample throughput in a cost- efficient manner. The physical size of the samples is reduced to speed up the process and statistical analysis in this study shows that the reduced size ‘bits’ and ‘shards’ are statistically and chemically interchangeable. The second chapter focuses on the accuracy of the XRF-laser ablation method. Comparison of analyzed, well-characterized certified standards with their published values shows good agreement among most elements, with correlations of >0.95 for most elements. The XRF-laser ablation method is also applied to poorly constrained standards, which provides more comprehensive trace element data that is of use to the wider geochemical community. The third chapter focuses on electron microprobe-based methods applied to the rate of element mobility in olivine and element-based temperature and pressure calculations from two eruptions in the Snæfellsnes peninsula. Additionally, element-based temperature and pressure calculations on a database of glass and clinopyroxene data are used to assess any variations in where magma is stored under the peninsula. Results show that magma movement and storage in the non-spreading axis location (Snæfellsnes) is complex, with storage at multiple depths in the crust. The rates of movement of magma are similar under Snæfellsnes to those calculated at the main spreading axis in Iceland. Mineral pressure calculations showing where clinopyroxene rims are crystallizing, show a deepening trend from east to west along the peninsula (5 km to 15 km), and no deep clinopyroxene rim formation in the east of the peninsula, but deep rim formation moving west from the mid-peninsula (~22°W).