Numerical Algorithms for Cooperative Imaging of Complex Geological Regions

为了对底土进行成像，收集了许多不同类型的数据。通常独立使用相应的建模技术来表示不同的地质特征并计算模型响应。我们的目标是发展一种方法，使之成为一项合作事业。首席研究员已经开发了地震反演技术，对材料界面进行了相当复杂的三维建模。他还没有在包括大地电磁反演在内的其他方法上取得类似的能力。多目标优化是我们方法的数学基础。当模型间存在耦合的未知参数时，为多个模型对相应数据集的协同拟合提供了一个自然的设置。通常，当独立运行时，这些不同的技术将产生相互冲突的结果。我们的多目标算法采用二次规划来计算权重，将失配函数向量缩放，同时尝试根据一组提议的参数向量对用户偏好进行建模。该算法试图生成帕累托最优参数向量供用户考虑。

Many different types of data are collected in order to image the subsoil. Corresponding modeling techniques are used, generally independently, to represent different geological features and calculate model responses. Our aim is to develop a methodology to make of this a cooperative enterprise. The principal investigator has already developed seismic inversion techniques, with fairly sophisticated three dimensional modeling of material interfaces. He is nor achieving similar capabilities for other methods, including magnetotelluric inversion. Multiobjective optimization is the mathematical technique on which we are basing our approach. It provides a natural setting for the cooperative fitting of multiple models to corresponding data sets, when the models have coupling unknown parameters. Usually, when run independently, these different techniques will produce conflicting results. Our multiobjective algorithm employs quadratic programming to calculate weights that scalarize the vector of misfit functionals, while trying to model the user's preferences with respect to a set of proposed parameter vectors. The algorithm attempts to generate Pareto optimal parameter vectors for the user's consideration.