THE DISTRIBUTION OF SERVICE ESTABLISHMENTS*

ABSTRACT All previous theory and research have led to the expectation that the density of service establishments will be proportional to the 2/3 power of the density of the population served by them. Study of the distribution of over 400 nongovernmental establishments refutes this expectation for such cases. A previous derivation from time minimization theory is reformulated to encompass these new findings.     

Hydrothermal monitoring in a quiescent volcanic arc: Cascade Range,northwestern United States

Ongoing (1996–present) volcanic unrest near South Sister, Oregon, is accompanied by a striking set of hydrothermal anomalies, including elevated temperatures, elevated major ion concentrations, and ³He/⁴He ratios as large as 8.6 R_A in slightly thermal springs. These observations prompted the US Geological Survey to begin a systematic hydrothermal‐monitoring effort encompassing 25 sites and 10 of the highest‐risk volcanoes in the Cascade volcanic arc, from Mount Baker near the Canadian border to Lassen Peak in northern California. A concerted effort was made to develop hourly, multiyear records of temperature and/or hydrothermal solute flux, suitable for retrospective comparison with other continuous geophysical monitoring data. Targets included summit fumarole groups and springs/streams that show clear evidence of magmatic influence in the form of high ³He/⁴He ratios and/or anomalous fluxes of magmatic CO₂ or heat. As of 2009–2012, summit fumarole temperatures in the Cascade Range were generally near or below the local pure water boiling point; the maximum observed superheat was <2.5°C at Mount Baker. Variability in ground temperature records from the summit fumarole sites is temperature‐dependent, with the hottest sites tending to show less variability. Seasonal variability in the hydrothermal solute flux from magmatically influenced springs varied from essentially undetectable to a factor of 5–10. This range of observed behavior owes mainly to the local climate regime, with strongly snowmelt‐influenced springs and streams exhibiting more variability. As of the end of the 2012 field season, there had been 87 occurrences of local seismic energy densities approximately ≥ 0.001 J/m³ during periods of hourly record. Hydrothermal responses to these small seismic stimuli were generally undetectable or ambiguous. Evaluation of multiyear to multidecadal trends indicates that whereas the hydrothermal system at Mount St. Helens is still fast‐evolving in response to the 1980–present eruptive cycle, there is no clear evidence of ongoing long‐term trends in hydrothermal activity at other Cascade Range volcanoes that have been active or restless during the past century (Baker, South Sister, and Lassen). Experience gained during the Cascade Range hydrothermal‐monitoring experiment informs ongoing efforts to capture entire unrest cycles at more active but generally less accessible volcanoes such as those in the Aleutian arc.