Theoretical spectral response for water-level and strain measurements in a sealed borehole.
Tools to calculate the theoretical spectral response of fluid-pressure in an open, or sealed, water well to harmonic straining.
The theoretical model for the sealed well is from Kitagawa et al (2011). This package is named after the author, Y. Kitagawa.
Frequency characteristics of the response of water pressure in a closed well to volumetric strain in the high-frequency domain Yuichi Kitagawa, Satoshi Itaba, Norio Matsumoto, and Naoji Koizumi Oscillations of water pressures and crustal strains due to the seismic waves of the 2010 Chile earthquake were observed in Japan. The oscillations of water pressures observed over the frequency range of 0.002 to 0.1 Hz were negative proportional to the oscillations of volumetric strains. The responses of water pressures in closed wells are frequency-dependent. The expression for the response of water pressure in a closed well to crustal strain is developed based on the poroelastic theory. The expression developed in the present paper describes the frequency characteristics of the responses. The response is useful for the estimation of rock properties. In addition, the responses of water pressure due to tidal volumetric strain are estimated and compared with the responses due to the seismic waves. J. Geophys. Res., 116, B08301, doi:10.1029/2010JB007794, 2011.
The theoretical model for the sealed well is from Cooper et al (1965).
The response of well-aquifer systems to seismic waves Hilton H. Cooper Jr., John D. Bredehoeft, Istavros S. Papadopulos, and Robert R. Bennett The degree to which the water level in an open well fluctuates in response to a seismic wave is determined by the dimensions of the well, the transmissibility, storage coefficient, and porosity of the aquifer, and the type, period, and amplitude of the wave. The water level responds to pressure-head fluctuations due to dilatation of the aquifer and to vertical motion of the well-aquifer system; hence a wave that produces either of these can cause the water level to fluctuate. However, the response to dilatation is much larger than the response to vertical motion. A solution is derived for the nonsteady drawdown in the aquifer due to a harmonic motion of the water level. This solution is then used in the equation of motion of the water column to derive expressions for the amplification, which is defined as the ratio X0/h0 (for oscillation due to dilatation) or the ratio X0/a (for oscillation due to vertical motion of the well-aquifer system), where X0 is the amplitude of water-level fluctuation, h0 is the amplitude of pressure-head fluctuation, and a is the amplitude of vertical motion of well-aquifer system. Amplification curves are given for differing well dimensions and aquifer constants. J. Geophys. Res., 70(16), 3915–3926, doi:10.1029/JZ070i016p03915, 1965.