Combined meshless modelling and inversion of electromagnetic data

在这个项目中，将开发一种新的无网格方案，用于地电和电磁数据的反演和模拟。与常用的离散技术如有限差分(FD)或有限元方法(FEM)不同，在离散过程中不使用固定网格或网格。对于这个项目，我们使用了一个已经可用的算法，该算法是在科隆大学的一篇论文框架内开发的，能够模拟大地电磁实验，并将其扩展到处理地电和有源电磁模拟。将开发一种新的逆算法，该算法直接受益于这两种不同方法的无网格离散。为了实现这一点，将开发一种基于高斯-牛顿算法的新数学公式的联合反演。这里，这两种方法将以数学的方式联系在一起，以增强地下的图像。为了验证新开发的算法，将对合成数据和实际数据进行反演，以研究地下增强后的图像。

In this project, a newly meshless scheme for the inversion and simulation of geoelectric and electromagnetic data will be developed. In contrast to commonly used discretization techniques like finite differences (fd) or the finite element method (fem), no fixed mesh or grid will be used during the discretization. For this project we use an already available algorithm, developed within the framework of a dissertation at the University of Cologne, which is capable to simulate magnetotelluric experiments and extend it to handle geoelectrical as well as active electromagnetic simulations. A new inverse algorithm will be developed which directly benefit from the meshless discretizations of the two different methods. To achieve this, a joint-inversion will be developed which is based on a new mathematical formulation of the Gauss-Newton algorithm. Here, the two methods will be linked in a mathematical way to enhance the image of the subsurface. To validate the newly developed algorithm, synthetic as well as real data will be inverted to study the enhanced image of the subsurface.