Abstract
We present a new approach that allows for the inversion of quantities
derived from the observed data using non-diagonal data covariance
matrices. For example, we can invert approximations of apparent
resistivity and phase instead of magnetotelluric impedance using this
methodology. Compared to the direct inversion of these derived
quantities, the proposed methodology has two advantages: i) If an
inversion algorithm allows for the specification of a full data
covariance matrix, users can invert for arbitrary derived quantities by
specifying the appropriate covariance matrix instead of having to rely
on the inversion code to have implemented this feature. ii) It is fully
compatible with the assumptions of least-squares optimization and thus
avoids potential issues with bias when inverting quantities that are
non-linear functions of the original data, We discuss the theory of this
approach and show an example using magnetotelluric data. However, the
same method can be applied to other types of geophysical data, for
example gravity gradient measurements.