Kriging with Inequality Constraints

A Gaussian random field with an unknown linear trend for the mean is considered. Methods for obtaining the distribution of the trend coefficients given exact data and inequality constraints are established. Moreover, the conditional distribution for the random field at any location is calculated so that predictions using e.g. the expectation, the mode, or the median can be evaluated and prediction error estimates using quantiles or variance can be obtained. Conditional simulation techniques are also provided.     

New England granites: Trace element evidence regarding their origin and differentiation

The abundances of Sc, rare earths, Zr, Hf, Ta and Th were determined in five New England granitic plutons. Similar data are reported for separated minerals from three of the units. The granites can be divided into the Massachusetts alkaline group (Cape Ann, Peabody, Quincy) and the Rhode Island subalkaline group (Narragansett Pier, Westerly).Analyses for three samples from each pluton indicate that the Westerly granite is heterogeneous in both major and trace elements. Th abundances vary considerably (factor of 2) in both Rhode Island granites. Zr and Hf are heterogeneously distributed in all the granites while the rare earths are more homogeneous (< ± 20% deviation from mean).Eu depletions in all the granites imply that feldspar was involved either as a cumulate during fractional crystallization or as a residual phase during anatexis. Because the Massachusetts granites are associated with syenites and show evidence for low water fugacity and denser rocks at depth, these granites probably developed from basic magmas as a result of extensive feldspar crystallization.Depletion of Tb, Dy, Yb, Lu, Zr, Hf and Ta in the Rhode Island granites suggest participation of zircon or garnet as residues of partial melting or as crystal cumulates. These granites crystallized under nearly water saturated conditions and are characterized by abundant pegmatites. The presence of a water rich phase may also have been important in the depletion of elements which form stable complexes in aqueous solutions.     

A Rubidium-Strontium study of the Twilight Gneiss,West Needle Mountains,Colorado

The Precambrian trondhjemitic Twilight Gneiss (Twilight Granite of Cross and Howe, 1905b) of the West Needle Mountains, southwestern Colorado, and its interlayered amphibolite and metarhyodacite yield a Rb-Sr isochron of 1,805±35 m.y. A low initial Sr⁸⁷/Sr⁸⁶ ratio of 0.7015 implies that metamorphism of these rocks to amphibolite facies took place soon after their emplacement. The mild metamorphism of Uncompahgran age, prior to 1,460 m.y. ago, and Laramide volcanism did not affect the Rb-Sr system in the Twilight. Rb contents of 26.5 to 108 ppm, Sr contents of 114 to 251 ppm, and K₂O percentages of 1.23 to 3.64 in the Twilight Gneiss, in conjunction with high K/Rb ratios and the low initial ratio of Sr⁸⁷/Sr⁸⁶, lend support to geologic data that suggest the Twilight originated as volcanic or hypabyssal igneous rocks in a basaltic volcanic pile.Publication authorized by the Director, U.S. Geological Survey.     

Urbanization and vulnerable urban groups in Gaborone/Botswana

This article examines two factors which are of major importance for urban poverty groups in Botswana: the costs the urban poor have to pay for housing, and the role assets like cattle and land play as safety elements in the urban livelihood system.     

Tidal triggering of reservoir-associated earthquakes

If the effect of a reservoir is to bring a fault zone gradually to failure and trigger an earthquake, then it is reasonable that rapidly fluctuating tidal stresses may influence the time of the induced earthquakes. An examination of earthquakes from eight reservoirs shows that earthquakes at six sites occur at preferred times in the semidiurnal tidal cycle. Tidal-stress orientations and the phase within the semidiurnal tidal cycle were calculated for only the largest earthquakes occurring at each site. This insures the elimination of aftershocks and selects earthquakes which are independent of each other. Sites of a significant earthquake/tide correlation with less than a 3% chance of occurring randomly include Hebgen Lake, Mont., U.S.A.; Kariba, Rhodesia; Kerr Dam, Mont., U.S.A.; Kremasta, Greece; Lake Mead, Nev., U.S.A.; and Monteynard, France. Each data set includes from about ten to twenty earthquakes. In most of the above cases earthquake triggering seems to occur when tidal stress enhances slip, i.e., when tidal stresses are oriented to enhance the tectonic stress.