Oscillatory pumping wells in phreatic, compressible, and homogeneous aquifers

Oscillatory well pumping was proposed recently as a tool for hydraulic tomography. Periodic pumping at a few frequencies is carried out through vertical intervals along the pumping well and the periodic head is measured along a few piezometers. The paper presents an analytical solution for the head field in an unconfined aquifer of finite depth under the common assumptions of a linearized water table condition, different horizontal and vertical constant permeabilities, constant specific storativity and water table drainable porosity, and small well radius to length ratio. The solution provides the expressions of the amplitude and phase of the head as a function of coordinates, frequency, and the problem parameters. The solution simplifies to one pertaining to an upper constant head condition and a rigid aquifer for a wide range of the dimensionless frequency values.