We present a fast approximate method for 1D inversion of frequency domain data and apply it to frequency domain helicopter-borne data from the Bookpurnong area of the Murray River, South Australia. The method is based on fast approximate forward computation of transient electromagnetic step responses and their derivatives with respect to the model parameters of a 1D model, with the frequency domain responses and derivatives then found through Fourier transformation of the time-domain counterparts. The inversion is carried out with multi-layer models in an iterative, constrained least-squares inversion scheme including explicit formulation of the model regularization through a model covariance matrix. The method is 30 times faster than conventional full inversion for a layered earth model and produces model sections of concatenated 1D models and contoured maps of mean conductivity in elevation intervals almost indistinguishable from those of a conventional full inversion. In a theoretical forward and inverse modelling study, the fast approximate and conventional computation methods are compared demonstrating the applicability of the approximate method and its limitations. Applied to the Bookpurnong RESOLVE~FDHEM data set from South Australia, the inversion produces model sections and conductivity maps that reveal the distribution of conductivity in the area and thereby the distribution of salinity. This information is crucial for any remediation effort aimed at alleviating the salinization of the river and the degradation of floodplain vegetation and associated ecosystems.
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