This dissertation analyzes the spatial distribution and kinematics of the Late Cenozoic Basin and Range (BR) and cross normal fault (CF) systems and their related graben basins around the Snake River Plain (SRP), and investigates the spatio-temporal patterns of lavas that were erupted by the migrating Yellowstone hotspot along the SRP, applying a diverse set of GIS-based spatial statistical techniques. The spatial distribution patterns of the normal fault systems, revealed by the Ripley's K-function, display clustered patterns that correlate with a high linear density, maximum azimuthal variation, and high box-counting fractal dimensions of the fault traces. The extension direction for normal faulting is determined along the major axis of the fractal dimension anisotropy ellipse measured by the modified Cantor dust method and the minor axis of the autocorrelation anisotropy ellipse measured by Ordinary Kriging, and across the linear directional mean (LDM) of the fault traces. Trajectories of the LDMs for the cross faults around each caldera define asymmetric sub-parabolic patterns similar to the reported parabolic distribution of the epicenters, and indicate sub-elliptical extension about each caldera that may mark the shape of hotspot’s thermal doming that formed each generation of cross faults. The decrease in the spatial density of the CFs as a function of distance from the axis of the track of the hotspot (SRP) also suggests the role of the hotspot for the formation of the cross faults. The parallelism of the trend of the exposures of the graben filling Sixmile Creek Formation with the LDM of their bounding cross faults indicates that the grabens were filled during or after the CF event. The global and local Moran’s I analyses of Neogene lava in each caldera along the SRP reveal a higher spatial autocorrelation and clustering of rhyolitic lava than the coeval basaltic lava in the same caldera. The alignment of the major axis of the standard deviational ellipses of lavas with the trend of the eastern SRP, and the successive spatial overlap of older lavas by progressively younger mafic lava, indicate the migration of the centers of eruption as the hotspot moved to the northeast.

The intended contribution of this work is to systematically discuss a selection of methodological topics and some of the empirical and technical issues that have been driving the measurement of inequality in Mexico so far. This discussion has two strands: firstly, the general case, and second, the particular case of Mexico. The general case include some philosophical concerns, along with a review of the traditional inequality measurement, the most common operational decisions in empirical calculations, and the recent methodological contribution of development literature that is mostly centered around the capability approach of Sen (1985b). The philosophical part contrasted with other approaches and rejected the Marxist view of economic inequality, which is mostly viewed as an outcome of exploitation. The distributional judgments are compared with more ancient schools of thought in regards to justice. Another methodological issue is such that social inequality, approximated by income inequality, might be considered as an additional functioning that measures the degree of social cohesion in the country, this finding is an implication that comes from the definition of functionings within the capability approach; then, social inequality is a functioning that is different in nature from other measures of destitution, and it is also different from the destitution that is captured by absolute poverty measurement. Our general case includes a review of the most popular ways to measure inequality, such as normative and pragmatic inequality measures that are mentioned with their properties, with their rankings of the distributions provided by the use of stochastic dominance and quantile comparisons, and the construction of statistical models and some graphic representations of income economic inequality; the approach of inequality concerns included in the measurement of relative poverty is rejected for the sake of clarity. Then this general view would guide us to a better understanding of the Mexican literature for the consideration of income distribution. The measurement of destitution provided by governmental offices is necessary to discuss, because there might be some lack of coherence between the design of the measurement and the complex legal system in Mexico. We also consider a set of regulatory concerns that might not be unique to the Mexican law, but may be generalized for developing countries as a whole. Some of the methodological discussions that show how the Mexican research has been influenced by the international literature about human destitution will be good to clarify, looking at the value judgments that have been automatically accepted by the researchers. A sensitivity analysis was performed to the empirical calculation of inequality in Mexico, so the measurement showed to be different in regards to a variety of operational concerns: the recipient unit, the different data from income and consumption-expenditure surveys, various non-responses and underreported biases, the inclusion of a regional price index, among other things. In this work was also covered the reasons why it might be the case that destitution and poverty assessment was studied more deeply than inequality itself, so the possible ambiguity of inequality with poverty measurement is challenged in this work with a variety of theoretical remarks and empirical arguments. The final topic for the particular case of Mexico is to shed light in regards to the context of the capability approach and the use of equivalence scales, because these methodological approaches consider respectively directly and indirectly the assessment of distributional judgments. This discussion is followed by an empirical assessment of inequality measures that is related with a set of functionings and services, where a direct relationship of measures of inequality with other measures of destitution is made clear.