Efficient analysis and representation of geophysical processes using localized spherical basis functions

While many geological and geophysical processes such as the melting of icecaps, the magnetic expression of bodies emplaced in the Earth's crust, or the surface displacement remaining after large earthquakes are spatially localized, many of these naturally admit spectral representations, or they may need to be extracted from data collected globally, e.g. by satellites that circumnavigate the Earth. Wavelets are often used to study such nonstationary processes. On the sphere, however, many of the known constructions are somewhat limited. And in particular, the notion of `dilation' is hard to reconcile with the concept of a geological region with fixed boundaries being responsible for generating the signals to be analyzed. Here, we build on our previous work on localized spherical analysis using an approach that is firmly rooted in spherical harmonics. We construct, by quadratic optimization, a set of bandlimited functions that have the majority of their energy concentrated in an arbitrary subdomain of the unit sphere. The `spherical Slepian basis' that results provides a convenient way for the analysis and representation of geophysical signals, as we show by example. We highlight the connections to sparsity by showing that many geophysical processes are sparse in the Slepian basis.Comment: To appear in the Proceedings of the SPIE, as part of the Wavelets XIII conference in San Diego, August 200

Carboxyhaemoglobin concentration, smoking habit, and mortality in 25 years in the Renfrew/Paisley prospective cohort study

Objective: To investigate how carboxyhaemoglobin concentration is related to smoking habit and to assess whether carboxyhaemoglobin concentration is related to mortality. Design: Prospective cohort study. Setting: Residents of the towns of Renfrew and Paisley in Scotland. Participants: The whole Renfrew/Paisley study, conducted between 1972 and 1976, consisted of 7048 men and 8354 women aged 45–64 years. This study was based on 3372 men and 4192 women who were screened after the measurement of carboxyhaemoglobin concentration was introduced about halfway through the study. Main outcome measures: Deaths from coronary heart disease (CHD), stroke, chronic obstructive pulmonary disease (COPD), lung cancer, and all causes in 25 years after screening. Results: Carboxyhaemoglobin concentration was related to self reported smoking and for each smoking category was higher in participants who reported inhaling than in those who reported not inhaling. Carboxyhaemoglobin concentration was positively related to all causes of mortality analysed (relative rates associated with a 1 SD (2.93) increase in carboxyhaemoglobin for all causes, CHD, stroke, COPD, and lung cancer were 1.26 (95% confidence interval (CI) 1.19 to 1.34), 1.19 (95% CI 1.13 to 1.26), 1.19 (95% CI 1.13 to 1.26), 1.64 (95% CI 1.47 to 1.84), and 1.69 (95% CI 1.60 to 1.79), respectively). Adjustment for self reported cigarette smoking attenuated the associations but they remained relatively strong. Conclusions: Self reported smoking data were validated by the objective measure of carboxyhaemoglobin concentration. Since carboxyhaemoglobin concentration remained associated with mortality after adjustment for smoking, carboxyhaemoglobin seems to capture more of the risk associated with smoking tobacco than does self reported tobacco consumption alone. Analysing mortality by self reported cigarette smoking underestimates the strength of association between smoking and mortality

Wood-Nymph

Photograph of woman standing in woods; Illustration of vines and leaves surrounding photographhttps://scholarsjunction.msstate.edu/cht-sheet-music/6840/thumbnail.jp