## 1 Introduction

[2] The water level in a well is a highly sensitive strainmeter, which can respond to external load, such as the Earth tide [*Bredehoeft*, 1967; *Bodvarsson*, 1970; *Hsieh et al*., 1987; 1988], atmospheric loading [*Weeks*, 1979; *Van Der Kamp and Gale*, 1983; *Rojstaczer and Riley*, 1990), fault activities [*Wakita*, 1975; *Quilty and Roeloffs*, 1997; *Zhang and Huang*, 2011], and seismic wave propagation [*Cooper et al*., 1965; *Liu et al*., 1989; *Brodsky et al*., 2003; *Kano and Yanagidani*, 2006; *Wang et al*., 2009; *Kitagawa et al*., 2011]. When there is no imposed dynamic stress, the well-aquifer system can be regarded as a stable linear system [*Bendat and Piersol*, 1986]. It is important to study the transfer functions of the linear system so as to determine the well-aquifer properties, which are significant for further study on its response to seismic wave propagation and the extraction of some reliable underground media and stress variations [*Carr and Van Der Kamp*, 1969; *Johnson et al*., 1973; 1974; *Rhoads and Robinson*, 1979; *Hsieh et al*., 1987; *Doan et al*., 2006; *Burbey et al*., 2011].

[3] The Earth tide and barometric pressure are two major continuous loadings on the well-aquifer system. When the aquifer is perfectly confined and has high lateral permeability and the well diameter is sufficiently small, the water level fluctuations related to Earth tide and barometric pressure changes can be expressed by a simple constant, known as the tidal sensitivity and barometric efficiency, respectively. These parameters can be obtained by the least square fit method and used for the estimation of the formation material properties [*Jacob*, 1940; *Roeloffs*, 1988; *Rojstaczer and Agnew*, 1989; *Igarashi and Wakita*, 1991]. However, most of the well-aquifers are not perfectly confined, and the permeability can be very low, so the simple constant is not enough to describe the frequency-dependent response of the water level in a well to Earth tide and barometric pressure [*Rojstaczer*, 1988a; 1988b; *Rojstaczer and Riley*, 1990].

[4] With both the Earth tide and barometric pressure as input signals, the water level as output signal, the transfer functions of the well-aquifer system carry lots of information about the properties of the well and the aquifer, and can be used to determine the well-aquifer properties and their variations over time. *Rojstaczer* [1988a] used the cross-spectra estimation to obtain the transfer functions of the water level response to atmospheric loading in the frequency band of 0.02–2 cycles per day (hereafter referred as cpd) in three wells and compared the results with the theoretical curves to get the fluid flow properties of the well-aquifer systems. *Rojstaczer and Riley* [1990] adopted a similar approach to study the response of a well tapping an unconfined aquifer to Earth tide and atmospheric loading. *Quilty and Roeloffs* [1991] used the average transfer function of the water level response to barometric pressure at frequencies lower than 1 cpd, to eliminate the frequency-dependent barometric effects from water level data. *Doan et al*. [2006] estimated the barometric response up to 8 cpd. Because the signals at high frequencies are quite noisy due to the lack of any large barometric pressure changes, the study on barometric response at frequencies higher than 8 cpd is almost blank. However, at high frequencies, the water level still responds to barometric pressure, and the response can be used to evaluate whether the wellbore storage effect can be ignored [*Rojstaczer*, 1988a], to determine the properties of the aquifer, and to extract some stress-related variations.

[5] In China, the digital transformation has been implemented to the Groundwater Monitoring Network, including hundreds of water level monitoring well stations, and the sampling interval of the observation data is one minute [*The Monitoring and Forecasting Department of China Earthquake Administration*, 2007]. Currently, a large number of waveform records are accumulated at these stations, which provide a basic database for studying the transfer functions of multiple well-aquifer systems. In this paper, we will extend the transfer functions to the high-frequency band and obtain the amplitude- and phase-frequency responses of the water level to barometric pressure from low to high-frequency band; we will also use this method to study the tidal responses in the intermediate frequency band and apply the obtained barometric and tidal response to the estimation of the well-aquifer properties.