Abstract Sensitivity maps of drawdown observations on spatial hydraulic parameters are essential information for hydraulic tomographic analysis. It can guide us to design the optimal cross-hole pumping test strategy. In this study, we show how the sensitivity equation method can be employed to derive analytical sensitivity maps of drawdown observations on spatially variable hydraulic parameters during cross-hole pumping test in a two-dimensional, unbounded aquifer. Unlike previously used adjoint state method, the analytical solutions of the sensitivity maps are not in the forms of complex integration and the properties can be evaluated readily. Moreover, we provide discussions on the essess of adjoint method by comparing the derivation of the close-form solution via the sensitivity equation method and the adjoint equation method.

中文翻译：

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通过灵敏度方程方法对非均质水力参数进行水头观测的分析灵敏度图

摘要 空间水力参数下降观测的灵敏度图是水力层析分析的重要信息。它可以指导我们设计最优的跨孔抽水试验策略。在这项研究中，我们展示了如何在二维无界含水层中进行跨孔抽水测试期间，如何使用灵敏度方程方法来导出对空间可变水力参数的压降观测的分析灵敏度图。与以前使用的伴随状态方法不同，灵敏度图的解析解不是复杂积分的形式，并且可以很容易地评估属性。此外，我们通过比较敏感方程法和伴随方程法的近似解的推导，讨论了伴随法的重要性。