An adaptive inversion algorithm for one-dimensional magnetotelluric problems

      As we know, the traditional one-dimensional (1-D) magnetotelluric (MT) regularization inversion needs the geometry model of the 1-D Earth conductivity model, i.e., the number of layers and the thickness of each layer to be given in advance and cannot be changed during the inversion. In this way, too few layers cannot approximate the 1-D conductivity model accurately, while too many layers will increase the non-uniqueness of the inversion problem and hence may result in unreasonable results. Aiming to solve this issue, an adaptive inversion algorithm has been proposed for 1-D MT problems, where the layer number and the thickness of each layer can be adjusted automatically during the inversion process. To this end, three pseudo a-posterior error estimators has been proposed to guide the adjustment of the 1D geometry model, which are based on the gradient of the data misfit term of the penalty function, the diagonal elements of the model resolution matrix, and the weighted elements of the sensitivity matrix, respectively. The inversion results of the synthetic and field data by using our proposal adaptive inversion algorithm and the traditional regularization inversion not only validate the proposed algorithm, but also show that our proposed algorithm can obtain more accurate and reasonable results than traditional one. Subsequently, the proposed algorithm will be extended for 3-D magnetotelluric inversion problems soon.