Molodensky边值问题中解析延拓法g1项的小波算法

运用小波分析理论研究了Molodensky边值问题的计算方法，论证了该类问题的计算对于精化重力场模型的意义，即可以放弃考虑地球密度的各种重力改正．针对解析延拓法，证明g1项奇异积分在Chauchy主值意义下的存在性．计算结果表明，该算法具有快速、准确的特征，特别适用大范围计算g     

Roles of Melting and Metasomatism in the Formation of the Lithospheric Mantle beneath the Leizhou Peninsula, South China

This study characterizes the nature of fluid interaction andmelting processes in the lithospheric mantle beneath the Yingfenglingand Tianyang volcanoes, Leizhou Peninsula, South China, usingin situ trace-element analyses of clinopyroxene, amphibole andgarnet from a suite of mantle-derived xenoliths. Clinopyroxenesfrom discrete spinel lherzolites exhibit large compositionalvariations ranging from extremely light rare earth element (LREE)-depletedto LREE-enriched. Trace-element modelling for depleted samplesindicates that the Leizhou lherzolites are the residues of amantle peridotite source after extraction of 1–11% meltgenerated by incremental melting in the spinel lherzolite fieldwith the degree of melting increasing upwards from about 60km to 30 km. This process is consistent with gradational meltingat different depths in an upwelling asthenospheric column thatsubsequently cooled to form the current lithospheric mantlein this region. The calculated melt production rate of thiscolumn could generate mafic crust 5–6 km thick, whichwould account for most of the present-day lower crust. The formationof the lithospheric column is inferred to be related to Mesozoiclithosphere thinning. Al-augite pyroxenites occur in compositexenoliths; these are geochemically similar to HIMU-type oceanisland basalt. These pyroxenites postdate the lithospheric columnformation and belong to two episodes of magmatism. Early magmatism(forming metapyroxenites) is inferred to have occurred duringthe opening of the South China Sea Basin (32–15 Ma), whereasthe most recent magmatic episode (producing pyroxenites withigneous microstructures) occurred shortly before the eruptionof the host magmas (6–0·3 Ma). Trace-element traversesfrom the contacts of the Al-augite pyroxenite with the spinelperidotite wall-rock in composite xenoliths record gradientsin the strength and nature of metasomatic effects away fromthe contact, showing that equilibrium was not attained. Significantenrichment in highly incompatible elements close to the contacts,with only slight enrichment in Sr, LREE and Nb away from thecontact, is inferred to reflect the different diffusion ratesof specific trace elements. The observed geochemical gradientsin metasomatic zones show that Sr, La, Ce and Nb have the highestdiffusion rates, other REE are intermediate, and Zr, Hf andTi have the lowest diffusion rates. Lower diffusion rates observedfor Nb, Zr, Hf and Ti compared with REE may cause high fieldstrength element (HFSE) negative anomalies in metasomatizedperidotites. Therefore, metasomatized lherzolites with HFSEnegative anomalies do not necessarily require a carbonatiticmetasomatizing agent. KEY WORDS: China; lithosphere; mantle xenoliths; clinopyroxene trace elements; mantle partial melting; mantle metasomatism; trace-element diffusion rates