推导Boussinesq方程的一种新方法

潜水含水层中的饱和地下水流动可以用两种方式描述。一种是严格的自由潜水面模型,用线性的三维连续性方程作为控制方程,在潜水面处用非线性自由潜水面边界条件。第二种是基于Dupuit假设和非线性Boussinesq方程的垂向平均模型。其中,第一种模型中的潜水自由面边界条件可以用两种方式描述,第一种只含有水头的偏导数,第二种则同时含有水头和潜水面标高的偏导数。前人分别从不同出发点推导了这两种边界条件,但是并未说明他们的等价性。用严格的数学推导证明了这两种边界条件的等价性,进一步完善了前人的工作。另一方面,已有人从第一种边界条件出发,对三维连续性水流方程求积分推导出了Boussinesq方程,但这种方法比较抽象,物理意义不太明确。从第二种边界条件出发直接推导Boussinesq方程,所用方法简单、物理意义明确,易于理解。在自由潜水面边界条件下,Boussinesq方程可以直接通过对三维连续性方程在整个饱和含水层厚度上求积分而得到。此外,潜水含水层的隔水底板可以推广为一个曲面。阐明了两种边界条件、三维连续性水流方程、Dupuit假设、Boussinesq方程之间的内在关系。     

Recent developments in uranium exploration using the U.S. geological survey's mobile helium detector

A mobile mass spectrometer to measure He concentrations has been developed by the U.S. Geological Survey. This instrument has been tested in areas of known uranium deposits, and He anomalies have been found in both soil gas and water. A gas sample is collected in a hypodermic syringe, injected into the spectrometer, and analyzed for He. Over 100 analyses a day can be performed with a sensitivity of 10 parts per billion (ppb). One detailed study conducted in Weld County, Colorado, shows that values for He in soil gas can be contoured to outline an anomalous area and that the anomaly is displaced from the deposit in the direction of groundwater flow. Other studies include the Schwartzwalder uranium mine, Jefferson County, Colorado, where He anomalies may be related to geologic structure; near Ambrosia Lake, New Mexico, where the location of He anomalies are related to groundwater movement; and tests for diurnal effects showing only slight variations probably related to soil-moisture content.