Spatial representation of economic and financial measures used in agriculture via wavelet analysis

A foundation is set forth for use of the wavelet transform as a spatial analysis tool for modelling the geographical representation of economic and financial measures used in agriculture. This provides a framework from which to estimate a smooth nonparametric function which describes complex, multivariate relationships embedded in spatial data, with the resulting maps conveying large amounts of information in a familiar format. We illustrate this approach for tasks which include the graphical presentation of information, density estimation and wavelet-based nonparametric regression. A redundant wavelet transform is used, and we detail the properties which make it particularly appropriate for these objectives.     

Reversal of Fe-Mg Partitioning Between Garnet and Staurolite in Eclogite-facies Metapelites from the Champtoceaux Nappe (Brittany, France)

This paper concentrates on the petrology of eclogite-faciesmetapelites and, particularly, the significance of staurolitein these rocks. A natural example of staurolite-bearing eclogitic micaschistsfrom the Champtoceaux nappe (Brittany, France) is first described.The Champtoceaux metapelites present, in addition to quartz,phengite, and rutile, two successive parageneses: (1) chloritoid+staurolite+garnetcores, and (2) garnet rims+kyanite?chloritoid. Detailed microprobe analyses show that garnet and chloritoidevolve towards more magnesian compositions and that stauroliteis more Fe-rich than coexisting garnet. A comparison of thestudied rocks with other known occurrences of eclogitic metapelitesshows that whereas staurolite is always more Fe-rich than garnetin high-pressure eclogites, the reverse is true in low- to medium-pressuremicaschists. Phase relations between garnet, staurolite, chloritoid, biotite,and chlorite are analysed in the KFMASH system (with excessquartz, phengite, rutile, and H₂O). The topology of univariantreactions is depicted for a normal and a reverse Fe-Mg partitioningbetween garnet and staurolite. Mineral compositional changesare also predicted for varying bulk-rock chemistries. In the studied micaschists, the zonal arrangement of garnetinclusions and the progressive compositional changes of ferromagnesianphases record part of the prograde P–T path, before theattainment of ‘peak’ metamorphic conditions (atabout 65O–7OO?C, 18–20 kb). The retrograde path,which records the uplift of the Champtoceaux nappe, occurs underdecreasing temperatures.