Model Construction, Existence, and Resolution in 2D Electromagnetic Sounding

电磁(EM)逆问题不是唯一的，也就是说，如果有模型符合数据的话，会有无限数量的模型符合数据。解决这个问题的一种方法是生成在某种意义上最平滑的模型，从而确保真正的地球比模型更粗糙。这就是说，这些模型不太可能包含地球上没有的结构元素。此外，光滑的反演反映了EM方法的真实分辨能力。我们已经为大多数一维问题开发了这项技术，并有一个为2D MT问题生成模型的初始代码。PI将扩展一维反演以包括2D电阻率问题，并使用这些代码来检查2D MT、电阻率和联合反演的分辨率。与模型生成一样重要(或更重要)的是模型的存在问题，该模型符合维度假设下的数据。虽然一维大地电磁测深和电阻率的存在问题已经得到解决，但对二维存在准则的研究却很少。一旦解的存在性问题得到解决，由于迭代求逆可以从一个可行解开始，使得光滑求逆变得更加强大。

The electromagnetic (EM) inverse problem is nonunique, that is an infinite number of models fit the data if any do at all. One approach to this problem is to generate models which are maximally smooth in some sense, thereby assuring that the true Earth is rougher that the models. This it is unlikely that the models contain elements of structure which do not feature in the Earth. Also, the smooth inversions reflect the true resolving power of the EM method. We have developed this technique for most 1D problems and have an initial code which generates models for the 2D MT problem. The PIs will extend 1-D inversion to include the 2D resistivity problem, and to use these codes to examine resolution for 2D MT, resistivity and joint inversion. As important (or more so) as models generation is the matter of existence of a model which fits the data under the assumptions of dimensionality. While t;he existence problem has been solved for 1D MT and resistivity, little has been done for 2D existence criteria. Once the existence problem has been solved, the smooth inversion scheme is made more powerful, as the iterative inversions can be started from a feasible solution.