Inverse procedure for calibrating parameters that control land subsidence caused by subsurface fluid withdrawal: 1. Methods

Abstract

Land subsidence prediction depends on a selected theoretical model and the calibration of its parameter values. An inverse model is developed that calibrates five parameters of a compacting confined aquifer system: K′v (vertical hydraulic conductivity of the aquitards), S′skv (aquitard nonrecoverable skeletal specific storage), S′ske (aquitard recoverable skeletal specific storage), Ssk (skeletal specific storage of the aquifer), and p′max 0 (initial preconsolidation stress within the aquitards). This inverse model combines a procedure for finding an initial set of parameter values and an inverse adjustment procedure. Initial values are estimated by using a new graphic method for the analysis of field data. The follow‐up inverse procedure is a computer algorithm that combines the Newton‐Raphson method with Helm's one‐dimensional finite difference subsidence model (COMPAC). COMPAC offers two options: a constant‐parameter simulation and a stress‐dependent parameter simulation. The classical least squares criterion is employed as the objective function of this inverse procedure. Three characteristics of the objective function are considered. This inverse model is applied to calculations of an idealized compacting confined aquifer system using Helm's model. This investigation shows that the final values for the five parameters lead to simulated compaction error of less than 1%. This contrasts to the initial error of more than 60%. These results indicate that the proposed inverse procedure (model) can be applied to actual field data.