EFFICIENT INVERSION OF MAGNETOTELLURIC DATA IN 2 DIMENSIONS

Two algorithms are presented to invert magnetotelluric data over 2D conductivity structures. Both algorithms use approximate sensitivities that arise from the 1D conductivity profile beneath each station; this avoids the large computations normally required to calculate the true 2D sensitivities. The first algorithm produces 'blocky' models by minimizing the l(1), norm of the conductivity, whereas the second algorithm produces smoother models by minimizing the l(2), norm of the model. The inversion of a large matrix in the l(2), norm minimization is obviated by using a sub-space solution. Our presentation is motivated by three goals. The first is to provide details of these algorithms and to show their efficiency compared with more commonly used techniques. The second goal is to illustrate the non-uniqueness inherent in these inversions and to illuminate the importance of choice of norm that is minimized. To accomplish this we perform l(1) and l(2) norm inversions on a synthetic model. The third goal is to show the utility, the practical importance, and the limitations of inverting determinant average data. The utility is demonstrated by the similarity that is often observed when comparing the inversion result obtained by inverting transverse electric (TE) and transverse magnetic (TM) mode data jointly with that obtained from inverting determinant average data. The importance of inverting determinant average data in field experiments arises because determinant average data are insensitive to rotations of the impedance matrix and perhaps other artefacts of processing the data. The limitations are shown by the loss of resolution in the model obtained by inverting the determinant average data compared with joint inversion of TE and TM modes. We illustrate our algorithms by inverting synthetic data and the COPROD2 data set.