https://orcid.org/0009-0005-5742-7915
SUMMARY
The response of well water temperature to earthquakes is crucial for understanding subsurface seismic fluid dynamics. However, recent studies have primarily focused on observations at a single depth and have employed single-aquifer models, which may lead to controversies when explaining fluid flow. In this study, we develop single- and double-aquifer models to estimate well-water temperature variations at different depths in response to changes in pore pressure, permeability and aquifer recharge temperature. The results indicate that variations in aquifer pore pressure and permeability result in significant differences in vertical flow velocity and temperature changes at various depths. When the borehole bottom is impermeable, for a single aquifer, temperature variation is maximal above the aquifer and variable at the aquifer depth, but nearly zero below the aquifer; for two aquifers, different pore pressure and permeability changes in each aquifer produce distinct temperature variation patterns, with minimal temperature change below the lower aquifer. If the borehole bottom is permeable, temperature variation becomes obvious below the lower aquifer. When cold or hot water from the aquifers flows into the borehole, significant temperature perturbations remain confined within a few metres of the aquifer within one day. Finally, a field case study investigates the co-seismic water temperature responses at three depths in the Chuan No. 03 well, triggered by the 2008 Mw 7.9 Wenchuan earthquake. The double-aquifer model effectively explains the complex co-seismic temperature fluctuations at different depths. Observation at a single depth risk missing crucial information, and multidepth temperature observation is a promising approach for interpreting and monitoring groundwater responses to earthquakes.
1 INTRODUCTION
Earthquakes can alter the aquifers’ permeability (Elkhoury et al. 2006; Xue et al. 2013) and pore pressure (Jónsson et al. 2003; Liu et al. 2020), affecting groundwater exchange between the aquifer and the well, ultimately leading to changes in well water temperature (Montgomery et al. 2003). Groundwater temperature is a critical indicator of fluid responses to earthquakes (Wang et al. 2021), manifested as significant transient or sustained anomalies, including increases or decreases, during and after earthquakes (Miyakoshi et al. 2020; Zhang et al. 2023). Between 1983–1984, four co-seismic groundwater temperature increases were recorded at the Yudani well in Japan (Kitagawa et al. 1996). Eleven co-seismic water temperature responses showed decreases in the Tangshan mine well in China in 2001–2007 (Shi et al. 2007). At the Mile well, China, temperature exhibited both increases and decreases in response to 13 earthquakes (Shi & Wang 2014a). Various post-earthquake recovery patterns have also been documented. At the Usami No.24 hot springs, Japan, water temperature remained lower than pre-earthquake levels from 1976 to 1987 (Mogi et al. 1989). Following the 1988 earthquake in Thessaloniki, Greece, temperatures in six wells recovered to levels that were either higher, lower or similar to pre-earthquake values (Asteriadis et al. 1989). These findings demonstrate the significance of studying earthquake-induced groundwater temperature changes. These diverse observations suggest that groundwater temperature responses to earthquakes are complex and may be influenced by multiple factors, such as the structure of the aquifer system. Understanding these complexities is crucial, as it not only deepens our insight into hydrological responses to earthquakes but also contributes to improving earthquake monitoring.
Well water temperature observations are typically conducted at a single depth (Asteriadis et al. 1989; Kitagawa et al. 1996; Shi & Wang 2014a; Zhang et al. 2023). However, due to the spatial variability of water temperature, groundwater flow can induce temperature differences at various depths within the well (Fulton et al. 2016; Liu et al. 2020; Liu et al. 2024). Recent research indicates that installing high-precision temperature sensors at different depths can provide more accurate insights into the mechanism of water temperature variation (Wang et al. 2021). Therefore, it is necessary to investigate the temperature variations at different depths under various mechanisms.
While these observations reveal the complexity of water temperature responses to earthquakes, most existing models rely on simplified assumptions that may not fully capture such variations. For instance, Fulton et al. (2016) investigated temperature variations at different depths caused by water inflow from the fault damage zone into the annular space surrounding the well. However, their model primarily considered a single aquifer and did not account for direct borehole inflow. Similarly, Yan et al. (2020) examined earthquake-induced temperature responses in hot springs through numerical simulations, demonstrating that co-seismic decreases in hot spring temperature could result from permeability changes in the hydrothermal system. However, their model assumed a single aquifer connected to the hot spring and did not explore the effects of multiple aquifers or temperature variations at different depths. Furthermore, well-single aquifer models fail to explain the simultaneous increases and decreases in water temperature at different depths, which implies that multi-aquifer models may improve the explanations (He et al. 2017). It is necessary to investigate the well water temperature changes induced by earthquakes using a multi-aquifer model. In particular, comparative analyses between single- and double-aquifer models will significantly enhance our understanding of the well water temperature responses to earthquakes.
In this study, we develop hydrothermal coupling well-aquifer models to examine groundwater temperature variations at different depths, considering cases where single or double aquifers are connected to the borehole. We examine the effects of earthquake-induced changes in pore pressure, permeability and recharge groundwater temperature on well water temperature. We also discuss the influence of the well bottom boundary conditions on the results. A field application of the model is conducted to account for multidepth groundwater temperature data from the Chuan No.03 well following the Wenchuan earthquake. Finally, we discuss the influence of pore pressure duration and offer suggestions for groundwater temperature monitoring in observation wells. This study provides a physical basis for interpreting earthquake-induced groundwater temperature responses at multiple depths.
2 METHOD
2.1 Governing equations
For water transport in aquifers, Darcy's law is used to describe fluid flow within porous media (Hubbert 1956):
where k is the hydraulic conductivity, Ss is the specific storage in the aquifer, h denotes the hydraulic head, which is defined as h = z + pm/ρg. pm is the pressure in the aquifer and z is the elevation head.
The flow of water in the borehole is described by the N–S equation (Doering et al. 1995; Temam 2001):
where uw is the fluid flow velocity, ρw is the fluid density, p is the pressure and μ is the coefficient of viscosity. There was no casing between the wellbore and the aquifer, allowing radial water flow at the connection.
Heat transport can be expressed as:
where ρ is the material density, Cp is the material heat capacity, T is temperature, ke is the thermal conductivity and u is the flow velocity of the material.
2.2 Modelling
The well-aquifer model was constructed using an axisymmetric simulation with a radius of 500.1 m and a depth of 200 m, while the borehole radius was 0.1 m. We separately considered cases where either single or double aquifers were connected to the borehole. The depth of 0 m was defined as the top of the borehole. For the well-single aquifer model, the centre of the aquifer was located at −100 m, with a thickness of 10 m (Fig. 1a). Vertical flow velocity and temperature variations were calculated at 15 locations within the borehole, ranging from −190 to −10 m, including locations within, above and below the aquifer. For the well-double aquifer model, the thickness of both the upper and lower aquifers was 10 m, and the two aquifers were separated by 100 m (Fig. 1b). We simulated vertical flow velocity and temperature variations at 23 locations in the borehole, ranging from −190 to −10 m, including locations above and within the upper aquifer, between the two aquifers, as well as within and below the lower aquifer.
Sketch of the numerical model. (a) A single-aquifer model. The aquifer was 10 m thick, with its centre located at a depth of −100 m. (b) A double-aquifer model which contained two 10 m thick aquifers, located at depths of −45 and −155 m, respectively. Both models were axisymmetric with a radius of 500.1 m and a depth of 200 m, and the borehole radius was 0.1 m.
The temperature at the upper boundary of the model was set to 23°C, with a vertical temperature gradient of 3°C hm−1. Both the lateral and bottom boundaries were defined as no-flow and thermally insulated. The top boundary of the well remained open. The bottom of the well was considered either permeable or impermeable, and we simulated both conditions. Given that in majority of cases, the bottom of the well is impermeable, we thus have invested more effort in this condition (Sections 3.1 and 3.2), and results for a permeable well bottom can be seen in Section 3.3 and the supplementary material. The initial velocity field and pressure variation compared to hydrostatic pressure were defined as zero. Based on previous studies (Fulton et al. 2016; Yan et al. 2020; Chen et al. 2022), the thermophysical parameters are listed in Table 1. Simulations were conducted to calculate water temperature changes over 1 d. The vertical flow velocity and temperature were calculated with an accuracy of 10−6 m s−1 and 0.1 mK, respectively. The maximum time step was set to 0.1 hr for the first 0.5 d and 1 hr for the remaining 0.5 d. More details were shown in the Supplementary material.
Thermophysical model parameters used for simulation.
| Parameter | Value |
|---|---|
| Dynamic viscosity of water | 0.001 Pa·s |
| Density of water | 1000 kg m−3 |
| Thermal conductivity of water | 0.6 W (m·K)−1 |
| Density of country rock and aquifer | 2000 kg m−3 |
| Initial permeability of country rock and aquifer | 1 × 10−15 m2 |
| Heat capacity of country rock and aquifer | 900 J (kg·K)−1 |
| Thermal conductivity of country rock and aquifer | 3 W (m·K)−1 |
| Parameter | Value |
|---|---|
| Dynamic viscosity of water | 0.001 Pa·s |
| Density of water | 1000 kg m−3 |
| Thermal conductivity of water | 0.6 W (m·K)−1 |
| Density of country rock and aquifer | 2000 kg m−3 |
| Initial permeability of country rock and aquifer | 1 × 10−15 m2 |
| Heat capacity of country rock and aquifer | 900 J (kg·K)−1 |
| Thermal conductivity of country rock and aquifer | 3 W (m·K)−1 |
Thermophysical model parameters used for simulation.
| Parameter | Value |
|---|---|
| Dynamic viscosity of water | 0.001 Pa·s |
| Density of water | 1000 kg m−3 |
| Thermal conductivity of water | 0.6 W (m·K)−1 |
| Density of country rock and aquifer | 2000 kg m−3 |
| Initial permeability of country rock and aquifer | 1 × 10−15 m2 |
| Heat capacity of country rock and aquifer | 900 J (kg·K)−1 |
| Thermal conductivity of country rock and aquifer | 3 W (m·K)−1 |
| Parameter | Value |
|---|---|
| Dynamic viscosity of water | 0.001 Pa·s |
| Density of water | 1000 kg m−3 |
| Thermal conductivity of water | 0.6 W (m·K)−1 |
| Density of country rock and aquifer | 2000 kg m−3 |
| Initial permeability of country rock and aquifer | 1 × 10−15 m2 |
| Heat capacity of country rock and aquifer | 900 J (kg·K)−1 |
| Thermal conductivity of country rock and aquifer | 3 W (m·K)−1 |
Previous studies have shown that earthquakes can change the pore pressure (Davis et al. 2001; Brodsky et al. 2005; Fulton et al. 2016) and permeability (Rojstaczer et al. 1995; Elkhoury et al. 2006; Xue et al. 2013; Shi et al. 2014b; Zhang et al. 2019) of aquifers and can also affect aquifer recharge temperature (He et al. 2017). All of these factors may lead to changes in water temperature in wells; therefore, our model simulated changes in water temperature caused by each of these three mechanisms. On the basis of previous observations of pore pressure changes induced by earthquakes (Davis et al. 2001; Fulton et al. 2016, 2023), we modelled the variations in aquifer pore pressure as a Gaussian distribution with a duration of approximately 0.2 d (Fig. S1 in the supplementary material). The peak pore pressure variations were set at 10, 50, 100, 200, 500 and 1000 kPa. According to studies of co-seismic and post-seismic permeability changes (Elkhoury et al. 2006; Xue et al. 2013; Shi et al. 2014b), permeability variations following an earthquake can persist in the short term. Thus, we represented earthquake-induced permeability variation as a step function (Fig. S2 in the supplementary material). The initial aquifer permeability was set at 1 × 10−15 m2, and four sets of models were simulated, assuming that the aquifer permeability varied to 0.2 × 10−15, 0.5 × 10−15, 2 × 10−15 and 5 × 10−15 m2, respectively. To simulate the inflow of cold or hot water from the aquifer into the borehole, the amplitude of the change in aquifer temperature relative to the normal temperature gradient was set to 0.2 °C. Recharge groundwater temperature of the aquifer that was higher than the well water temperature at the same depth was defined as ‘hot’ water; otherwise, it was defined as ‘cold’ water. For the single-aquifer model, we conducted 12 sets of simulations (Table 2) for both the impermeable and permeable well bottoms. For the double-aquifer model, we performed 20 sets of simulations for each bottom boundary conditions, considering similar and different parameter variations in the two aquifers (Table 3).
List of aquifer parameter variations for well single-aquifer system simulation. ∆P and ∆k are pore pressure and permeability changes in the aquifer, and ∆T is change in recharge groundwater temperature of the aquifer. Negative indicates a decrease.
| No. | ∆P (kPa) | ∆k (×10−15 m2) | ∆T (°C) |
|---|---|---|---|
| 1 | 10 | 0 | 0 |
| 2 | 50 | 0 | 0 |
| 3 | 100 | 0 | 0 |
| 4 | 200 | 0 | 0 |
| 5 | 500 | 0 | 0 |
| 6 | 1 000 | 0 | 0 |
| 7 | 1 000 | −0.8 | 0 |
| 8 | 1 000 | −0.5 | 0 |
| 9 | 1 000 | 1 | 0 |
| 10 | 1 000 | 4 | 0 |
| 11 | 1 000 | 1 | 0.2 |
| 12 | 1 000 | 1 | −0.2 |
| No. | ∆P (kPa) | ∆k (×10−15 m2) | ∆T (°C) |
|---|---|---|---|
| 1 | 10 | 0 | 0 |
| 2 | 50 | 0 | 0 |
| 3 | 100 | 0 | 0 |
| 4 | 200 | 0 | 0 |
| 5 | 500 | 0 | 0 |
| 6 | 1 000 | 0 | 0 |
| 7 | 1 000 | −0.8 | 0 |
| 8 | 1 000 | −0.5 | 0 |
| 9 | 1 000 | 1 | 0 |
| 10 | 1 000 | 4 | 0 |
| 11 | 1 000 | 1 | 0.2 |
| 12 | 1 000 | 1 | −0.2 |
List of aquifer parameter variations for well single-aquifer system simulation. ∆P and ∆k are pore pressure and permeability changes in the aquifer, and ∆T is change in recharge groundwater temperature of the aquifer. Negative indicates a decrease.
| No. | ∆P (kPa) | ∆k (×10−15 m2) | ∆T (°C) |
|---|---|---|---|
| 1 | 10 | 0 | 0 |
| 2 | 50 | 0 | 0 |
| 3 | 100 | 0 | 0 |
| 4 | 200 | 0 | 0 |
| 5 | 500 | 0 | 0 |
| 6 | 1 000 | 0 | 0 |
| 7 | 1 000 | −0.8 | 0 |
| 8 | 1 000 | −0.5 | 0 |
| 9 | 1 000 | 1 | 0 |
| 10 | 1 000 | 4 | 0 |
| 11 | 1 000 | 1 | 0.2 |
| 12 | 1 000 | 1 | −0.2 |
| No. | ∆P (kPa) | ∆k (×10−15 m2) | ∆T (°C) |
|---|---|---|---|
| 1 | 10 | 0 | 0 |
| 2 | 50 | 0 | 0 |
| 3 | 100 | 0 | 0 |
| 4 | 200 | 0 | 0 |
| 5 | 500 | 0 | 0 |
| 6 | 1 000 | 0 | 0 |
| 7 | 1 000 | −0.8 | 0 |
| 8 | 1 000 | −0.5 | 0 |
| 9 | 1 000 | 1 | 0 |
| 10 | 1 000 | 4 | 0 |
| 11 | 1 000 | 1 | 0.2 |
| 12 | 1 000 | 1 | −0.2 |
List of aquifer parameter variations for well double-aquifer system simulation. ∆P1 and ∆P2 are pore pressure change in the upper and lower aquifers, respectively. ∆k1 and ∆k2 are permeability changes in the upper and lower aquifers. ∆T1 and ∆T2 are changes in recharge groundwater temperature of the upper and lower aquifer. Negative indicates a decrease.
| No. | ∆P1 (kPa) | ∆P2 (kPa) | ∆k1 (×10−15 m2) | ∆k2 (×10−15 m2) | ∆T1 (°C) | ∆T2 (°C) |
|---|---|---|---|---|---|---|
| 1 | 10 | 10 | 0 | 0 | 0 | 0 |
| 2 | 50 | 50 | 0 | 0 | 0 | 0 |
| 3 | 100 | 100 | 0 | 0 | 0 | 0 |
| 4 | 200 | 200 | 0 | 0 | 0 | 0 |
| 5 | 500 | 500 | 0 | 0 | 0 | 0 |
| 6 | 1 000 | 1 000 | 0 | 0 | 0 | 0 |
| 7 | 1 000 | 1 000 | −0.8 | −0.8 | 0 | 0 |
| 8 | 1 000 | 1 000 | −0.5 | −0.5 | 0 | 0 |
| 9 | 1 000 | 1 000 | 1 | 1 | 0 | 0 |
| 10 | 1 000 | 1 000 | 4 | 4 | 0 | 0 |
| 11 | 1 000 | 1 000 | 1 | 1 | 0.2 | 0.2 |
| 12 | 1 000 | 1 000 | 1 | 1 | −0.2 | −0.2 |
| 13 | 1 000 | 500 | 1 | 1 | 0 | 0 |
| 14 | 500 | 1 000 | 1 | 1 | 0 | 0 |
| 15 | 1 000 | −1 000 | 0 | 0 | 0 | 0 |
| 16 | −1 000 | 1 000 | 0 | 0 | 0 | 0 |
| 17 | 1 000 | 1 000 | 1 | −0.5 | 0 | 0 |
| 18 | 1 000 | 1 000 | −0.5 | 1 | 0 | 0 |
| 19 | 1 000 | 1 000 | 1 | 1 | 0.2 | −0.2 |
| 20 | 1 000 | 1 000 | 1 | 1 | −0.2 | 0.2 |
| No. | ∆P1 (kPa) | ∆P2 (kPa) | ∆k1 (×10−15 m2) | ∆k2 (×10−15 m2) | ∆T1 (°C) | ∆T2 (°C) |
|---|---|---|---|---|---|---|
| 1 | 10 | 10 | 0 | 0 | 0 | 0 |
| 2 | 50 | 50 | 0 | 0 | 0 | 0 |
| 3 | 100 | 100 | 0 | 0 | 0 | 0 |
| 4 | 200 | 200 | 0 | 0 | 0 | 0 |
| 5 | 500 | 500 | 0 | 0 | 0 | 0 |
| 6 | 1 000 | 1 000 | 0 | 0 | 0 | 0 |
| 7 | 1 000 | 1 000 | −0.8 | −0.8 | 0 | 0 |
| 8 | 1 000 | 1 000 | −0.5 | −0.5 | 0 | 0 |
| 9 | 1 000 | 1 000 | 1 | 1 | 0 | 0 |
| 10 | 1 000 | 1 000 | 4 | 4 | 0 | 0 |
| 11 | 1 000 | 1 000 | 1 | 1 | 0.2 | 0.2 |
| 12 | 1 000 | 1 000 | 1 | 1 | −0.2 | −0.2 |
| 13 | 1 000 | 500 | 1 | 1 | 0 | 0 |
| 14 | 500 | 1 000 | 1 | 1 | 0 | 0 |
| 15 | 1 000 | −1 000 | 0 | 0 | 0 | 0 |
| 16 | −1 000 | 1 000 | 0 | 0 | 0 | 0 |
| 17 | 1 000 | 1 000 | 1 | −0.5 | 0 | 0 |
| 18 | 1 000 | 1 000 | −0.5 | 1 | 0 | 0 |
| 19 | 1 000 | 1 000 | 1 | 1 | 0.2 | −0.2 |
| 20 | 1 000 | 1 000 | 1 | 1 | −0.2 | 0.2 |
List of aquifer parameter variations for well double-aquifer system simulation. ∆P1 and ∆P2 are pore pressure change in the upper and lower aquifers, respectively. ∆k1 and ∆k2 are permeability changes in the upper and lower aquifers. ∆T1 and ∆T2 are changes in recharge groundwater temperature of the upper and lower aquifer. Negative indicates a decrease.
| No. | ∆P1 (kPa) | ∆P2 (kPa) | ∆k1 (×10−15 m2) | ∆k2 (×10−15 m2) | ∆T1 (°C) | ∆T2 (°C) |
|---|---|---|---|---|---|---|
| 1 | 10 | 10 | 0 | 0 | 0 | 0 |
| 2 | 50 | 50 | 0 | 0 | 0 | 0 |
| 3 | 100 | 100 | 0 | 0 | 0 | 0 |
| 4 | 200 | 200 | 0 | 0 | 0 | 0 |
| 5 | 500 | 500 | 0 | 0 | 0 | 0 |
| 6 | 1 000 | 1 000 | 0 | 0 | 0 | 0 |
| 7 | 1 000 | 1 000 | −0.8 | −0.8 | 0 | 0 |
| 8 | 1 000 | 1 000 | −0.5 | −0.5 | 0 | 0 |
| 9 | 1 000 | 1 000 | 1 | 1 | 0 | 0 |
| 10 | 1 000 | 1 000 | 4 | 4 | 0 | 0 |
| 11 | 1 000 | 1 000 | 1 | 1 | 0.2 | 0.2 |
| 12 | 1 000 | 1 000 | 1 | 1 | −0.2 | −0.2 |
| 13 | 1 000 | 500 | 1 | 1 | 0 | 0 |
| 14 | 500 | 1 000 | 1 | 1 | 0 | 0 |
| 15 | 1 000 | −1 000 | 0 | 0 | 0 | 0 |
| 16 | −1 000 | 1 000 | 0 | 0 | 0 | 0 |
| 17 | 1 000 | 1 000 | 1 | −0.5 | 0 | 0 |
| 18 | 1 000 | 1 000 | −0.5 | 1 | 0 | 0 |
| 19 | 1 000 | 1 000 | 1 | 1 | 0.2 | −0.2 |
| 20 | 1 000 | 1 000 | 1 | 1 | −0.2 | 0.2 |
| No. | ∆P1 (kPa) | ∆P2 (kPa) | ∆k1 (×10−15 m2) | ∆k2 (×10−15 m2) | ∆T1 (°C) | ∆T2 (°C) |
|---|---|---|---|---|---|---|
| 1 | 10 | 10 | 0 | 0 | 0 | 0 |
| 2 | 50 | 50 | 0 | 0 | 0 | 0 |
| 3 | 100 | 100 | 0 | 0 | 0 | 0 |
| 4 | 200 | 200 | 0 | 0 | 0 | 0 |
| 5 | 500 | 500 | 0 | 0 | 0 | 0 |
| 6 | 1 000 | 1 000 | 0 | 0 | 0 | 0 |
| 7 | 1 000 | 1 000 | −0.8 | −0.8 | 0 | 0 |
| 8 | 1 000 | 1 000 | −0.5 | −0.5 | 0 | 0 |
| 9 | 1 000 | 1 000 | 1 | 1 | 0 | 0 |
| 10 | 1 000 | 1 000 | 4 | 4 | 0 | 0 |
| 11 | 1 000 | 1 000 | 1 | 1 | 0.2 | 0.2 |
| 12 | 1 000 | 1 000 | 1 | 1 | −0.2 | −0.2 |
| 13 | 1 000 | 500 | 1 | 1 | 0 | 0 |
| 14 | 500 | 1 000 | 1 | 1 | 0 | 0 |
| 15 | 1 000 | −1 000 | 0 | 0 | 0 | 0 |
| 16 | −1 000 | 1 000 | 0 | 0 | 0 | 0 |
| 17 | 1 000 | 1 000 | 1 | −0.5 | 0 | 0 |
| 18 | 1 000 | 1 000 | −0.5 | 1 | 0 | 0 |
| 19 | 1 000 | 1 000 | 1 | 1 | 0.2 | −0.2 |
| 20 | 1 000 | 1 000 | 1 | 1 | −0.2 | 0.2 |
3 SIMULATION RESULTS
Sections 3.1 and 3.2 present the modelling results for an impermeable bottom boundary, based on the aquifer parameter variations shown in Tables 2 and 3, respectively. Section 3.3 explores the results under the assumption of a fully permeable bottom boundary for comparative analysis.
3.1 The well-single aquifer system simulation
Simulations of pore pressure variations within a single aquifer revealed significant differences in vertical velocity variations at different depths in the well (Fig. S3 in the supplementary material). The vertical velocity variations below the aquifer were nearly zero, while those above the aquifer remained nearly uniform. Changes in flow velocity led to changes in water temperature. As shown in Figs 2(a)–(c), temperature variations below the aquifer were minimal. The magnitude of water temperature change increased with distance from the centre of the aquifer. The peak temperature variation lagged approximately 1.6 hr behind the peak flow velocity change. To study the effect of varying pore pressures on temperature variations, we plotted the maximum temperature variations at seven depths: −30, −92, −96, −100, −104, −108 and −170 m. As shown in Fig. 2(i), the temperature variation exhibited a linear relationship with the pore pressure change.
Results of the well single-aquifer system simulation. (a)–(c) Water temperature variations in the well when the peak pore pressure change was 200, 500 and 1000 kPa. (d)–(f) Water temperature variations when permeability changes were −0.5 × 10−15, 1 × 10−15 and 4 × 10−15 m2 relative to the initial values. (g) Change in well water temperature when ‘hot’ water (higher by 0.2 °C at the same depth) flows into the borehole. (h) Change in water temperature when ‘cold’ water (lower by 0.2 °C at the same depth) flows into the borehole. (i) Maximum water temperature variations versus pore pressure variations at different depths. (j) Maximum water temperature variations versus permeability variations at different depths. In (a)–(h), the dotted and solid lines indicate temperatures inside and outside the aquifer. In (i) and (j), the shaded area is the depth range where the aquifer is located. The black dashed line shows the trend of maximum temperature variation.
The effects of aquifer permeability changes were similar to those of pore pressure changes. As expected, when the permeability of the aquifer decreased, the vertical flow velocity reduced; conversely, it increased when permeability rose (Fig. S4 in the supplementary material). Vertical velocity variations at depths below the aquifer were nearly zero, while those above the aquifer were nearly uniform. As shown in Figs 2(d)–(f), unlike the results for pore pressure variations, differences in the amplitude of the temperature changes at various depths above the aquifer were observed. For example, when the permeability increased to twice its initial value, the temperature curves at −94, −92, −30 and −10 m above the aquifer were no longer identical, with a difference of approximately 2 mK. When the permeability increased to five times its initial value, the temperature changes at −94 and −92 m were significantly different from those at −90 and −30 m, with the difference increasing to 5 to 15 mK. The temperature variation exhibited a linear relationship with the permeability change (Fig. 2j).
Changes in the groundwater recharge temperature did not affect the vertical flow velocity of water (Fig. S5 in the supplementary material) but did cause significant temperature variations at the aquifer depth (Figs 2g and h). The amplitude of temperature variations within the aquifer increased significantly with the inflow of ‘hot’ water. The temperature change was more pronounced near the top of the aquifer. When ‘cool’ water flowed in, the temperature variation near the top of the aquifer was less significant. Temperature above and below the aquifer remained nearly identical to those observed without the inflow of ‘cold’ or ‘hot’ water over the one-day period.
3.2 The well-double aquifer system simulation
Simulations of pore pressure variations in the well-double aquifer system showed that the vertical flow velocity (Fig. S6 in the supplementary material) and temperature changes (Figs 3a–c) at depths between the two aquifers fell between those observed at the individual aquifers. Vertical flow velocity and temperature above the upper aquifer exhibited the most significant variations. The greater the peak pore pressure, the larger the variations in temperature and vertical flow velocity. Below the lower aquifer, variations in vertical flow velocity and temperature were minimal. A statistical analysis was conducted using temperature variation data from 23 depths (Fig. 3i). The results indicated that water temperature variation followed a linear relationship with pore pressure, consistent with findings from the single-aquifer well model.
Results of the well-double aquifer system simulation. (a)–(c) Water temperature variations in the well when peak pore pressure changes were 200, 500 and 1000 kPa. (d)–(f) Water temperature variations for permeability changes of −0.5 × 10−15, 1 × 10−15 and 4 × 10−15 m2 compared to initial values. (g) Change in temperature when ‘hot’ water flowed into the borehole from both aquifers. (h) Change in temperature when ‘cold’ water flowed into the borehole from both aquifers. (i) Maximum water temperature variations versus pore pressure variations at different depths. (j) Maximum water temperature variations versus permeability variations at different depths. In (a)–(h), the dotted and solid lines indicate temperatures inside and outside the aquifer. In (i) and (j), the orange area represents the depth range where the upper aquifer is located, the purple area represents the depth range where the lower aquifer is located and the dashed line represents the trend of maximum temperature variations.
For the well-double aquifer system, more complex cases involve parameters of the two aquifers varying in different ways. Due to length limitations, we discuss only four cases, considering different pore pressure variations in the two aquifers (Models 13–16 in Table 3). For additional results, see Table S1. When the pore pressure variations in the upper and lower aquifers increase by 500 and 1000 kPa (Fig. 4a), and 1000 and 500 kPa (Fig. 4b), respectively, the increase in water temperature above the upper aquifer remains the same. The water temperature variations within and between the two aquifers ranged between the results corresponding to pore pressure variations of 500 kPa (Fig. 3b) and 1000 kPa (Fig. 3c), remaining zero at depths below the lower aquifer. When the pore pressure decreased by 1000 kPa in the lower aquifer and increased by 1000 kPa in the upper aquifer (Fig. 4c), water temperatures decreased at depths in and between the two aquifers but remained nearly unchanged above the upper aquifer and below the lower aquifer. When the pore pressure increased by 1000 kPa in the lower aquifer and decreased by 1000 kPa in the upper aquifer (Fig. 4d), temperature variation between the two aquifers was maximized, while temperatures remained stable above the upper aquifer and below the lower aquifer.
The water temperature variations when the peak pore pressure variations in the upper and lower aquifers were (a) 500 and 1000 kPa, (b) 1000 and 500 kPa, (c) 1000 and −1000 kPa and (d) −1000 and 1000 kPa.
Results for permeability variations in the well-double aquifer system mirrored those in the well-single aquifer system. A decrease in aquifer permeability reduced the vertical flow velocity (Fig. S7 in the supplementary material). When the aquifer permeability variation was doubled (Fig. 3e), the peak temperature variation was approximately 99 mK above −36 m, around 95 mK at −38 m, roughly 79 mK at the depth of the upper aquifer and about 24 mK at the depth of the lower aquifer. When permeability was increased to five times the initial value (Fig. 3f), the peak temperature variation was around 202 mK at −38 m and about 220 mK at −36 m. At depths of −30 and −10 m, the peak temperature variation reached 245 mK. Within the upper aquifer, peak temperature variations ranged from 123 to 164 mK. The maximum temperature variations at 23 depths were plotted against varying permeability (Fig. 3j). The results demonstrate that the temperature variation exhibits a linear relationship with the permeability change.
We analysed two cases with different permeability variations in the two aquifers: one case in which permeability variations were set to 1 × 10−15 m2 in the upper aquifer and −0.5 × 10−15 m2 in the lower aquifer, and another case in which the permeability variation was set to −0.5 × 10−15 and 1 × 10−15 m2 in the upper and lower aquifers. Peak pore pressure variations in both aquifers were 1000 kPa. The results showed that only the temperature variation at depths between and within the aquifers changed with permeability variation. The temperature variations observed above the upper aquifer were almost the same in the two cases (Figs 5a and b, Table S2), influenced by the total permeability change in aquifers, making it difficult to determine which aquifer the changes came from. Temperature variations within the lower aquifer were insensitive to permeability variation in the upper aquifer (Table S2). Consequently, it was not possible to assess permeability variations in the upper aquifer based on temperature variations within the lower aquifer.
The water temperature variations when the permeability of two aquifers varied in different ways: (a) permeability increased by 1 × 10−15 m2 in the upper aquifer and decreased by 0.5 × 10−15 m2 in the lower aquifer, and (b) permeability decreased by 0.5 × 10−15 m2 in the upper aquifer and increased by 1 × 10−15 m2 in the lower aquifer.
We also calculated water temperature variations when the recharge groundwater temperature changed in the two aquifers. Although changes in recharge temperature did not influence the vertical flow velocity in the well (Fig. S8 in the supplementary material), they did affect water temperatures variations at aquifer depths (Figs 3g and h). When ‘hot’ water flowed in, the maximum temperature changes at depths of −30, −45, −155 and −170 m were 99, 200, 200 and 0 mK, respectively. When ‘cold’ water flowed in, the maximum temperature changes were 99, −200, −200 and 0 mK at depths of −30, −45, −155 and −170 m. The temperature variations above the upper aquifer and below lower aquifer were consistent with those observed when the recharge water temperature did not change. Therefore, the inflow of hot or cold water did not cause significant temperature changes at greater distances from the aquifer over short periods.
We conducted additional numerical simulations to examine opposite recharge groundwater temperature variations in the upper and lower aquifers (Figs 6a and b). In one case, ‘hot’ water from the upper aquifer and ‘cold’ water from the lower aquifer flowed into the borehole. In the other case, ‘cold’ water from the upper aquifer and ‘hot’ water from the lower aquifer flowed into the borehole. The findings indicated that, even if the recharge water temperatures of the two aquifers differed, significant temperature variations in the well were only observed within a few metres of the two aquifers. The maximum temperature variation remained around 99 mK at depths of −30 and −10 m above the upper aquifer and closed to 0 mK below the lower aquifer. These results were consistent with those observed when the recharge water temperature of the aquifer remained unchanged or the recharge water temperature of both aquifers was identical.
The water temperature variations when the change in temperature of two aquifers varied in different ways: (a) water temperature increased by 0.2 °C in the upper aquifer and decreased by 0.2 °C in the lower aquifer, and (b) water temperature increased by 0.2 °C in the upper aquifer and decreased by 0.2 °C in the lower aquifer.
3.3 Influence of well bottom boundary conditions
Fully permeable and fully impermeable well bottoms represent two extreme scenarios. Given that many well bottoms are located in impervious beds, the bottom was set as impermeable in the previous simulations (Sections 3.1 and 3.2). However, since the bottom boundary condition may influence both water flow and temperature, simulations were also conducted with a fully permeable well bottom. Due to space limitations, only typical cases are presented here, with additional results available in supplementary material S9 and S10.
As the results show, when the peak pore pressure variation was 1000 kPa with permeability maintained at 1 × 10−15 m2, the maximum temperature variation was 16 and 27 mK (Figs 7a and 8a) in the single and double aquifers model, respectively. The temperature variation was half of the value obtained under an impermeable bottom boundary. When the permeability increased by 1 × 10−15 m2, the maximum temperature variation was 28 and 50 mK (Figs 7b and 8b) in single and double aquifers model, respectively. The temperature variation was also half of the value obtained under an impermeable bottom boundary. If the recharge water temperature in aquifers increased by 0.2 °C, the temperature variation increased by 200 mK at the depth of aquifer in both single and double aquifer model (Figs 7c and 8c); however, the maximum temperature variation was 28 and 50 mK more than 5 m away from the aquifer in the two models, which was consistent with the previous results (Figs 7b and 8b). The maximum temperature variation was −27 and −50 mK below the aquifer in the single aquifer and double aquifer models, which was quite different from zero temperature variation when the bottom was impermeable (Figs 2g and 3g). Additionally, the temperature variations between the two aquifers were zero when the changes in permeability and pore pressure were identical (Figs 8a–c); but not zero when these changes in the two aquifers differed (Figs 8d and e).
The water temperature variations in well single-aquifer model when the bottom boundary was fully permeable, with the peak pore pressure variation reaching 1000 kPa. (a) Permeability maintained at 1 × 10−15 m2, (b) permeability increased by 1 × 10−15 m2, (c) permeability increased by 1 × 10−15 m2 and the recharge water temperature in aquifer increased by 0.2 °C.
The water temperature variations in well double-aquifer model when the bottom boundary was fully permeable, with the peak pore pressure variation reaching 1000 kPa. (a) Permeability maintained at 1 × 10−15 m2, (b) permeability increased by 1 × 10−15 m2, (c) permeability increased by 1 × 10−15 m2, with water temperature in both aquifers increased 0.2 °C, (d) permeability maintained 1 × 10−15 m2, and peak pore pressure variations were 1000 kPa in the upper aquifer and −1000 kPa in the lower aquifer, (e) permeability decreased by 0.5 × 10−15 m2 in the upper aquifer and increased by 1 × 10−15 m2 in the lower aquifer, (f) permeability maintained at 1 × 10−15 m2, and water temperature increased by 0.2 °C in the upper aquifer and decreased by 0.2 °C in the lower aquifer.
Overall, when the bottom was permeable, the temperature variation was smaller than that observed in the impermeable case. Significant temperature variations were observed beneath the lower aquifer in both the single- and double- aquifer models, whereas no temperature variation was detected at the corresponding depths when the bottom was impermeable.
4 A FIELD EXAMPLE: TEMPERATURE RESPONSE TO THE WENCHUAN EARTHQUAKE IN THE CHUAN NO. 03 WELL
4.1 Background and data
Chuan No. 03 well (27° 54′ 18.11″ N, 102° 08′ 34.40″ E, elevation 1571 m) is located in Taihe, Xichang, Sichuan Province, China, in the Anning River Fault Zone (Fig. 9a). The well is approximately 362 km from the epicentre of the Ms8.0 Wenchuan earthquake (31.1° N, 103.7° E). It has a total depth of 756.6 m, with a casing diameter of 108 mm up to 100 m; below this depth, the diameter is approximately 91 mm in the open hole (uncased). The main exposed strata consist of Palaeozoic gabbro iron and vanadium-titanium magnetite rocks. The well penetrates confined fractures in gabbroic rock. The primary aquifer is located at approximately 202.9 m, with a thickness of 46 m and permeability ranging from 1 × 10−14 to 3 × 10−13 m2. A secondary aquifer, about 8.9 m thick, is situated at a depth of 490 m (Fig. 9b). The temperature gradient with depth is shown in Fig. 9(c), approximately 2–3°C hm−1 (He et al. 2017). Since 2007, digital recorders have been used to monitor both water levels and temperatures. A quartz crystal temperature sensor, with a resolution of 0.0001°C and a sampling rate of 1 min−1, has been utilized for temperature monitoring (Shimamura 1980; Shimamura et al. 1984) at depths of 395, 595 and 765 m. The temperature sensor at 395 m is situated between the two aquifers, while those at 595 and 765 m are beneath the lower aquifer. Both co-seismic and post-seismic temperature responses to the Wenchuan earthquake were recorded at all three depths (Fig. 10). At 395 m, the temperature decreased simultaneously with the earthquake and eventually dropped by approximately 11 mK post-earthquake. In contrast, temperatures at 595 and 765 m increased stepwise during the earthquake, with the increase at 765 m being less than 7 mK and at 595 m rising by about 17 mK. The water level data revealed a marked and continuous decline post-earthquake.
(a) Location of the epicentre of the Wenchuan earthquake and the Chuan No. 03 well. This well was about 362 km from the epicentre of the Wenchuan earthquake. (b) Temperature gradient of the Chuan No. 03 well. The blue and red lines were measured in 2007 and 2011. (c) Well, lithology and aquifers of the Chuan No. 03 well. The dots indicated the depths at which sensors were installed in the well.
Water temperature and water level data from the Chuan No. 03 well before and after the Wenchuan earthquake. To display the water temperature variations at different depths at a convenient scale, 5.05 °C and 8.15 °C were subtracted from the temperature data at 595 and 765 m, respectively.
4.2 Numerical simulation
Given the presence of two main aquifers connected to the Chuan No. 03 well, a double-aquifer model was implemented to calculate the temperature distribution. The axisymmetric model was configured with a radius of 500.1 m and a depth of 765.6 m, with the rock formation extending 500 m from the well. The shallow aquifer was 46 m thick and the deeper aquifer was 8.9 m thick. The temperature at the upper boundary of the model was set at 23 °C, and the vertical temperature gradient was 3 °C hm−1. Both the lateral and bottom boundaries of the rock were configured as no-flow and thermally insulated. The top boundary of the well was open. All other parameters, except for initial permeability, were consistent with those listed in Table 1. Temperature variations were calculated at the three depths where the temperature sensors were installed (Fig. 11).
Well-aquifer model for the Chuan No. 03 well. The model was axisymmetric with a radius of 500.1 m and a depth of 765.6 m, and the borehole radius was 0.1 m. The centres of the two aquifers were at depths of 225 and 471.45 m, respectively. The dots are the depths where temperature sensors were installed.
The co-seismic temperature response in Chuan No. 03 well showed significant temperature variation beneath the lower aquifer. Our previous simulations, based on the assumption of an impermeable bottom boundary, demonstrated that the temperature beneath the lower aquifer remained nearly unchangeable (Figs 3–6), which were inconsistent with the observed data. In contrast, a permeable well bottom boundary may result in significant temperature variations beneath the lower aquifer (Fig. 8). The co-seismic temperature response in the well showed a decrease between the two aquifers. The modelling result (Fig. 8d), in which the pore pressure increases in the upper aquifer and decreases in the lower aquifer, was the most consistent with the observed data. Thus, the following modelling referred to this mode of parameters changes in the aquifers.
The documented permeability of the primary aquifer ranged from 1 × 10−14 to 3 × 10−13 m2, and the observed water level decreased by about 1 cm within 6 hr of the Wenchuan earthquake in Chuan No. 03 well (He et al. 2017). Based on these observations, we set the initial permeability to 1 × 10−14 m2 for our simulations. With the initial permeability, the pore pressure reduction in the lower aquifer may exceed 50 kPa, calculated using the flow rate determined from water level variations in the well and the Darcy's Law, under the conditions of inflow from the upper aquifer and outflow into the lower aquifer. The pore pressure reduction decreases reduced to 25 kPa when the permeability was increased by 1 × 10−14 m2.
If the pore pressure was increased by 1 kPa in upper aquifer and decreased by 100 kPa in the lower aquifer (Gaussian distribution), the temperature variations were −18, 30 and 15 mK at 395, 595 and 765 m (Fig. 12a), which exceeded the observed values. Therefore, the pore pressure in lower aquifer needed to be reduced.
Simulated changes in water temperature at different depths of the Chuan No. 03 well, with permeability increased by 1 × 10−14 m2, (a) pore pressure were increased by 1 kPa in the upper aquifer and decreased by 100 kPa in the lower aquifer, following a Gaussian distribution, (b) pore pressure were increased by 10 kPa in the upper aquifer and decreased by 50 kPa in the lower aquifer, following a Gaussian distribution, (c) pore pressure were increased by 2 kPa in the upper aquifer and decreased by 30 kPa in the lower aquifer, following a Gaussian distribution, (d) pore pressure were increased by 2 kPa in the upper aquifers and decreased by 30 kPa in the lower aquifer, following a combination of the Gaussian distribution and step form. The dots indicated observed values, and solid lines indicated calculated values.
With a pore pressure increase of 10 kPa in the upper aquifer and a decrease of 50 kPa in the lower aquifer (Gaussian distribution), the temperature variations observed at depths of 395, 595 and 765 m were −16, 8 and 8 mK (Fig. 12b), respectively. The temperature variation at 395 m was larger than the observed values, indicating that the pore pressure of the aquifers needed to be reduced.
By adjusting the pore pressure parameters, the optimal parameter was that the pore pressure was increased by 2 kPa in the upper aquifer and decreased by 30 kPa in the lower aquifer (Gaussian distribution). This resulted in temperature variations of −7, 8 and 8 mK at 395, 595 and 765 m, respectively (Fig. 12c). Despite this, the simulated values still deviated from the observed data. Moreover, the observation data revealed that the temperature at the three depths did not return to its initial values within one day. Therefore, we suppose that there may be a combination of permanent and recoverable changes in the aquifer hydraulic parameters.
Finally, we applied a 2 kPa pore pressure increase in the upper aquifer and a 30 kPa decrease in the lower aquifer, using a combination of Gaussian distribution and step form. Under these conditions, temperature variations of −12, 15 and 9 mK were observed at 395, 595 and 765 m (Figs. 12d), with the change stabilizing after 0.5 d. The trends and magnitudes matched with observed data, although some differences in detail remained. As previously discussed, the well bottom boundary condition was likely between fully permeable and fully impermeable. This setting strongly affected the simulated water temperature near the well bottom at 765 m, potentially biasing the calculated temperature changes. We proposed that the temperature variations observed in the Chuan No. 03 well might involve transient inflow of water from the upper aquifer, accompanied by the drainage of water to the lower aquifer.
4.3 Uncertainty analyses
To investigate the effect of uncertainty in the values of pore pressure and permeability variations on the simulation results, we performed an uncertainty analysis on these two parameters. We investigated the effect of a 20 per cent uncertainty in pore pressure and permeability on the calculated temperature changes at three depths. Since the permeability of the bed rock broadly ranges from 1 × 10−23 to 1 × 10−12 m2 (Screaton 2010), we also conducted simulations with permeability values ranging from 1 × 10−12 to 1 × 10−18 m2 (Fig. S11).
As shown in Fig. 13, uncertainties in pore pressure and permeability primarily influence the magnitude of the temperature variation in the simulation results, without significantly altering the overall trend of temperature variation at the three depths. Specifically, when the pore pressure in the upper and lower aquifers varied by 20 per cent, the resulting temperature variations at the three depths ranged from 1 to 6 mK. Similarly, a 20 per cent variation in the permeability of the upper and lower aquifers led to temperature variations within the same range of 1 to 6 mK. Consequently, the uncertainties in these two parameters do not affect the validity of the simulation conclusions.
Uncertainty analysis of simulation results to aquifer pore pressure and permeability, (a) pore pressure varied by ± 0.4 kPa (20 per cent) in the upper aquifer and ±6 kPa (20 per cent) in the lower aquifer, (b) permeability varied by ± 0.2 × 10−14 m2 (20 per cent) in both aquifers. The shading area was the temperature variation range resulting from parameters changed, the dashed line indicated the calculation of the parameters used in Fig. 12(d).
5 DISCUSSIONS
5.1 Influence of pore pressure duration
To investigate the effect of pore pressure duration on vertical flow velocity and temperature variation in the well, we set the duration of pore pressure variation to 0.2, 0.1 and 0.01 d, respectively (Fig. S12 in the Supplementary Material). A double aquifer system model was used, with peak pore pressure variations in the upper and lower aquifers reaching 1000 kPa, and the permeability was kept constant at 1 × 10−15 m2. The temperature of the recharge groundwater in the aquifer remained constant.
The amplitude of water temperature variation increased with the duration of pore pressure variation, while the amplitude of vertical flow velocity variations remained constant (Fig. S13 in the Supplementary Material). Water temperature responses varied with depth (Fig. 14). Specifically, when the pore pressure durations were 0.2, 0.1 and 0.01 d, the peak temperature variations were approximately 120, 39 and 5 mK, respectively. In addition, the patterns of temperature changes differed. Longer pore pressure durations resulted in relatively slow temperature changes (Fig. 13a), whereas shorter durations led to a rapid increase in temperature, followed by a gradual recovery (Fig. 13c).
Water temperature variation at various depths with pore pressure durations of 0.2 d (a), 0.1 d (b) and 0.01 d (c), respectively.
5.2 Implications for temperature observation in monitoring wells
Progress in understanding of temperature changes in response to earthquakes has been slow, largely because systematic measurements are relatively scarce compared to water level observations (Wang et al. 2021). Ambiguities arise when interpreting data and observations from a single depth (Shi et al. 2007; Wang et al. 2021). Our modelling results, which account for groundwater temperature changes throughout the well and consider both single and double aquifers, provide insights to help interpret temperature anomalies and guide the scientific deployment of temperature sensors in monitoring wells. Reasonable deployment of temperature sensors at multiple depths can provide valuable information about the subsurface hydrogeological processes.
Both the single- and double-aquifer model results showed significant differences in water temperature variations at different depths, consistent with the scarce observational data from multiple depths (Davis et al. 2001; Fulton et al. 2016; He et al. 2017). The single-aquifer model simulations indicated significant temperature variations within the aquifer and its vicinity (Figs 2a–f). However, water temperature variations beyond 5 m above or below the aquifer were identical. In contrast, when cold or hot water from the aquifers flowed into the borehole, significant temperature perturbations were confined within a few metres of the aquifer depth (Figs 2g–h). Therefore, temperature observations at multiple depths can detect the locations of aquifers or conductive fractures. If the location of the aquifer is known, a locally dense placement of temperature sensors within the aquifer is recommended, while the number of temperature sensors can be reduced further from the aquifer.
Some temperature observation data are more complex than those observed in our simulations of the single aquifer (He et al. 2017; Wang & Manga 2021). More complex temperature change patterns may be caused by multiple aquifers. Logging aquifers or conductive fractures in the well may help to constrain interpretations of measured groundwater temperature. Our simulation results showed temperatures far above the upper aquifer affected by pore pressure and permeability variations in both aquifers. Consequently, the influence of each aquifer may not be identifiable from temperature variations above the upper aquifer (Figs 3a–f). Temperature variations at the depth of the lower aquifer were sensitive to changes in pore pressure and permeability in the lower aquifer (Figs 4 and 5), allowing us to deduce lower aquifer parameter variations. To distinguish the contributions of multiple aquifers, comprehensive multidepth temperature observations are required. By measuring temperature at the depths of both aquifers, above the upper aquifer, and between the two aquifers, changes in the aquifers can be analysed comprehensively. For example, when the temperature changes were largest between the two aquifers (Figs 4c and d), this is likely due to opposite changes in pore pressure in the upper and lower aquifers. Reduced recharge temperatures may result in lower temperature variations in the upper and lower 5 m of the aquifer, if the aquifer has a positive change (Fig. S14 in the Supplementary Material). Beyond this depth, temperature variations remained consistent with those observed under unchanged recharge temperature conditions. Sensors placed in the vicinity of the aquifer and a certain distance from the aquifer (e.g. about 10 m) could reveal such behaviour.
When the bottom of the borehole is impervious, there is minimal temperature variation below the aquifer (Figs 2a–h and 3a–h). However, if the bottom of the well is permeable, temperature variations were opposite above and below the aquifer (Figs 6 and 7). Therefore, the distribution of temperature sensors varies according to the permeability conditions of the borehole.
6 CONCLUSIONS
This paper presents numerical simulations of vertical flow velocity and water temperature in well single- and double-aquifer models. We investigate the characteristics of groundwater temperature variations at multiple depths, which are induced by pore pressure and permeability variations, as well as the transient inflow of cold or hot water in the aquifer. Our field application of the model considers multidepth water temperature changes in the Chuan No. 03 well induced by the Wenchuan earthquake. The main findings are as follows:
When a single aquifer is connected to a borehole with an impermeable bottom, the maximum temperature variation occurs above the aquifer. Temperature variations in and near the aquifer vary with depth, while variations below the aquifer are minimal. The peak temperature variation increases nearly linearly with increasing pore pressure and permeability. However, if the well bottom is permeable, significant temperature variations are observed beneath the aquifer. When groundwater recharge temperature changes, the effect is most pronounced at the depth of the aquifer and within a few metres above and below it. The influence on well water temperature decreases rapidly with increasing distance from the aquifer.
When two aquifers are connected to a borehole with an impermeable bottom, significant temperature variations occurred above the upper aquifer, at the locations of the aquifers, and between the aquifers. Different pore pressure and permeability changes in the two aquifers can lead to distinct temperature variation patterns with depth. When the well bottom is permeable, notable temperature variations exist below the aquifer, but no significant temperature changes are observed between the two aquifers if their parameter changes are identical.
Based on the multidepth temperature response to the Wenchuan earthquake in the Chuan No. 03 well, we applied a well-double aquifer model, which could effectively explain the observed co-seismic temperature rise and fall at different depths. The observed temperature changes in the well may result from a transient inflow of water from the upper aquifer, combined with the drainage of water to the lower aquifer, with a permeable well bottom.
The modelling results emphasize the need to observe groundwater temperature at multiple depths to interpret temperature anomalies. Since significant temperature variations occur at and near the aquifer depth, observation density near the aquifer should be increased. Compared to the simple temperature pattern of a single aquifer model, a well-double aquifer model can better explain more complex temperature changes.
With advances in instrumental technology, analysis and interpretation, groundwater temperature observation may play a greater role in understanding subsurface fluid processes related to earthquakes.
ACKNOWLEDGMENT
This work was supported by the National Natural Science Foundation of China (42374118, 42274079), the Basic Research Funds from the Institute of Geology, China Earthquake Administration [IGCEA2416, IGCEA2002] and the National Key Research and Development Program of China [2019YFC1509202]. The water temperature and water level data of the Chuan No. 03 well used in this study were collected from the National Earthquake Data Centre of the China Earthquake Administration (https://data.earthquake.cn).
DATA AVAILABILITY
The water temperature and water level data from the Chuan No. 03 well as well as the simulation results in Section 3 can be downloaded via GitHub (https://github.com/ZhouBoCUG/GJI-Model-data-2025).
