In this work, a new analytical solution to describe tide‐induced head fluctuations in aquifers of variable thickness is presented. The proposed model assumes a finite and confined aquifer with a thickness that increases or decreases quadratically with the distance to the coast. A closed‐form analytical solution is obtained by solving a boundary‐value problem with both a separation of variables method and a change of variables method. This solution is a generalization of the solution obtained by Cuello et al., Hydrogeological Journal, 2017, 25, 1509–1515. The analytical solution is expressed in terms of the wedging parameter, a parameter that depends on the length and thicknesses at the coast and at the inland edge of the aquifer. Positive values of the wedging parameter describe aquifers with increasing thickness towards land and negative values describe aquifers with a decreasing thickness in the inland direction. The comparison of the new solution and the solution for a finite aquifer with constant thickness indicates that the sign of the wedging parameter enhances or decreases the amplitude of the tide‐induced signal. However, the differences in time‐lag between both solutions are negligible near the coast. The slope factor, which quantifies the inconsistencies between aquifer diffusivities estimated from attenuation and time‐lag data, is computed and analysed. Near the coast, slope factor values greater than one are obtained for negative wedging parameters while slope factor values less than one are obtained for positive wedging parameters. The analysis of the new solution also indicates that more reliable estimates of the hydraulic diffusivity can be obtained from time‐lag data.

中文翻译：

---

潮汐引起的厚度变化的沿海含水层的水头波动

在这项工作中，提出了一种新的分析解决方案，用于描述潮汐引起的厚度变化的含水层中的水头波动。所提出的模型假设一个有限的密闭含水层，其厚度随着到海岸的距离呈二次方增加或减少。通过同时使用变量分离法和变量更改法解决边值问题，可以获得封闭形式的解析解。该解决方案是Cuello等人在《水文地质杂志》上获得的解决方案的概括。，2017，25，1509-1515。分析解决方案用楔形参数表示，该参数取决于含水层海岸和内陆边缘的长度和厚度。楔形参数的正值表示向陆地增加的厚度的含水层，负值表示向内陆方向减小的厚度的含水层。新解与具有恒定厚度的有限含水层解的比较表明，楔形参数的符号增强或减小了潮汐诱发信号的幅度。但是，两种解决方案之间的时滞差异在海岸附近可以忽略不计。计算并分析了斜率因子，该因子量化了根据衰减和时滞数据估算的含水层扩散率之间的不一致性。在海岸附近，对于负的楔入参数，获得的坡度系数值大于1，而对于正的楔入参数，获得的坡度系数值小于1。对新解决方案的分析还表明，可以从时滞数据中获得更可靠的水力扩散率估计值。