When the structure of an aquifer is complex and unknown, determining the complexity of model structure and identifying its spatially distributed parameters become very difficult. This two-paper series describes an approach for objective-oriented model construction that can identify a model with simplified structure and assure its reliability for predetermined model applications. The theoretical basis of the methodology includes the definition of structure error, the conditions of structure reducibility, the calculation of the worst-case parameter (WCP), and the solution of a generalized inverse problem. In the first paper of the series we extend the basic theory established in our previous works from zonation parameterization to any kind of parameterization. The extension makes the methodology more general and complete. We present an effective direct search algorithm that can form a nonnested structure series with an optimized pattern for solving the generalized inverse problem. We use numerical examples to show how the WCP depends on the structure complexity, prior information, boundary conditions, and the objectives of model application. Generally speaking, with more prior information, simpler boundary conditions, fewer objectives, and lower accuracy requirement, the WCP will have a simpler shape. As a result, a reliable model can be identified with less observation data. In part 2 of this series we will give the conditions of structure reducibility and the method for robust experimental design. A robust experimental design is independent of the true parameter and can provide sufficient information for identifying an objective-oriented model.