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

电磁（EM）反问题是非唯一的，即如果有任何模型符合数据，则有无限多个模型。解决这个问题的一种方法是生成在某种意义上最大程度平滑的模型，从而确保真实的地球比模型更粗糙。因此，这些模型不太可能包含地球上没有的结构元素。同时，平滑的反演结果反映了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种技术，并且有一个为二维MT问题生成模型的初始代码。pi将扩展一维反演，包括二维电阻率问题，并使用这些代码来检查二维MT、电阻率和联合反演的分辨率。与模型生成同样重要（或更重要）的是，在维度假设下，是否存在适合数据的模型。而t;一维大地电磁法和电阻率法的存在性问题已经得到了解决，而二维存在性判据的存在性问题尚未得到解决。一旦存在性问题得到解决，平滑反演方案就变得更加强大，因为迭代反演可以从可行解开始。

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.