Inversion of multichannel geophysical data with projected kernels

Statistical de‐noising methods such as Principal Component Analysis modify data in a way not constrained by physics. In much the same way as frequency‐filtered data must incorporate altered frequency content into numerical interpretation, so must statistically rotated data include the rotation operator in inversion processes. We propose a method of accounting for statistical reduction of data in non‐linear inversions (such as for electromagnetic data) through an incorporation of the rotation operator into the kernels and sensitivity matrix. We show a generalized linear inversion to demonstrate the necessity of rotating the inversion kernels in this abstract and will present a nonlinear parametric example from an unexploded ordnance application.