Theoretical spectral response for water-level and strain measurements in a sealed borehole.

View the Project on GitHub abarbour/kitagawa


Tools to calculate the theoretical spectral response of fluid-pressure in an open, or sealed, water well to harmonic straining.

Sealed Well

The theoretical model for the sealed well is from Kitagawa et al (2011). This package is named after the author, Y. Kitagawa.

Abstract of Original Article


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.

Open Well

The theoretical model for the sealed well is from Cooper et al (1965).

Abstract of Original Article


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

J. Geophys. Res., 70(16), 3915–3926, doi:10.1029/JZ070i016p03915, 1965.