Inversion of electromagnetic data processed by principal component analysis

Abstract

Statistical de-noising and compressive inversion methods based on Principal Component Analysis can reduce random noise, separate desired signals from correlated noise, and improve the efficiency and results of airborne EM inversions. However, inversion of PCA-processed data with standard kernels produces inaccurate results due to the improper forward mapping operators used. These inversions must incorporate the PCA rotation in the inversion process for accurate results. In order to appropriately apply these operators to the inversion kernels, the statistical distribution of the noise before and after processing and its effect on the data misfit must be understood. We can then develop compressive inversion techniques utilising PCA. In this presentation, we demonstrate the need for incorporation of rotation into the inversion kernels through linear examples and show the utility of principal component analysis in compressive inversion. We then examine the statistical distribution of TEM data and noise and show that the noise follows a multivariate t-distribution both before and after processing with PCA. We conclude by introducing a compressive inversion technique formulated in the principal component domain.