Gravitational attraction due to solids of revolution and its application to hydraulic testing of groundwater aquifers

A general technique is presented for calculating the gravitational attraction of any solid of revolution with radial variation of density. The technique is based on the attraction of semi-infinite, vertical, circular, cylindrical shells. For constant density, further generalization to arbitrary orientation is made by considering both vertical and radial components and as an extension, corresponding magnetic formulas are given. The technique is demonstrated through a proposed new application for the gravimetric method that involves monitoring drawdown during hydraulic testing of groundwater aquifers.; The theory for determining the gravitational response due to hydraulic testing is established based on the attraction of solids of revolution associated with the drawdown cone. Expressions are derived for both confined and unconfined aquifers. These expressions can accommodate any radially symmetric drawdown solution. Two commonly used solutions—Theis' and Neuman's for confined and unconfined cases, respectively—are specifically considered.; Simulations indicate that hydraulic testing of shallow groundwater aquifers (<50-m depth) with typical properties produces gravitational responses of a few to several tens of microGals (10−8m/s 2) at the pumping well. The response at the 1-μGal level can extend hundreds of meters away from the pumping well. For the unconfined case, survey resolutions between 10−3 to 10−2 and 10−2 to 0.1 μGal are required to delineate incremental drawdown at the 2- and 15-cm levels, respectively. Concerning vertical differential response (sensors separated by <1 m), resolutions that are better by one order-of-magnitude are needed to detect these same levels.; The use of the gravimetric method to augment hydraulic testing is assessed with due consideration of current and prototype technologies. For the unconfined case, simulated responses are within survey resolutions achievable with present-day gravimeters. High-resolution surveying could provide a relatively convenient and cost-effective means to spatially map drawdown that otherwise would require an extensive network of monitoring wells. A methodology for surveying is presented based on pseudo steady-state drawdown. The full potential of using the gravimetric method, however, will not be realized until the expectant near-future development of arrays of sensors capable of real-time measurements at the sub-microGal level.