地下水潮汐现象的物理机制和统一数学方程

用新的分层承压含水层模式 ,不但考虑含水层的力学压缩性质 ,而且考虑含水层的渗流特性 ,并结合扰动信息源的频率特性 ,分别研究扰动源地球固体潮、大气潮和地表负荷潮对承压井水位和流量的影响机理 ,给出相应的偏微分方程。从方程的解释或数值解讨论扰动源与承压井含水层的力学压缩参数、渗流特性参数及与频率特性频数的关系 ,进而给出承压井水位和流量对地球固体潮、大气潮和地表负荷潮汐响应的统一数学方程及其潮汐响应函数 ,并揭示了上述几类潮汐扰动信息源对承压井水位和流量影响的物理机理

PHYSICAL MECHANISM AND UNITARY MATHEMATICAL EQUATION FOR TIDAL PHENOMENA OF GROUND WATER

A new model of layering confined aquifer, which takes both the mechanical compressibility and permeability of the aquifer into account, is proposed in this paper. This model combined with the frequency characteristics of the disturbance signal source, is used to analyze the mechanism of the effects of the disturbance signal sources including earth tide, atmospheric tide and loading tide of surface water, on the water level and rate of discharge of the confined well. Moreover, the corresponding partial differential equations for these effects are given. On the basis of numerical and analytical solutions of the equations, the relation between the disturbance signal source and the parameters of the mechanical compressibility, permeability and frequency characteristic of the aquifer in the confined wells are discussed, and then the unitary mathematical equation and response function of the water level and discharge of the confined well to tidal phenomenon are given. The results of the present study reveals the physical mechanism of the effects of the disturbance signal source, such as earth tide, atmospheric tide and loading tide of surface water, on the water level and discharge of the confined water well. We find that although the effects of earth tide, atmospheric tide and loading tide of surface water on the confined aquifer are different, they produce similar effect of stress on the aquifer. Therefore, they can be defined by a unitary partial differential equation. The tidal phenomena of the level, discharge and temperature of the confined water have the same physical mechanism, and they are the result of volumetric strain of the aquifer due to earth tide. In consideration of the seepage between the well and the aquifer, it is concluded that the function of response amplitude and the phase lag of the aquifer in the well to the effects of three different tidal phenomena bear a relation to the variation period of the parameters and signal of the aquifer. The response of the aquifer system in the well to long period signal is the same as that of the aquifer with discharge. They have the same response amplitude without phase lag.