Fast approximate inversion of FDHEM data

Abstract

Despite advances in computer speed and code efficiency, the most often employed interpretation method for frequency domain helicopterborne electromagnetic (FDHEM) data is still inversion with one-dimensional (1D) models. In areas where the lateral rate of change of conductivity is small, inversion with 1D models is justified and can be sufficient. These conditions are often found in hydrogeophysical investigations in a sedimentary environment. Even for 1D inversion, the task of inverting a survey volume of 100,000s of data points can be time-consuming, and more or less sophisticated approximate methods have been developed. These are often included in software packages used for data and model display and handling of geographical information, e.g. EMflow (Macnae et al., 1998), EMax (Fullagar and Reid, 2001), etc. A fairly comprehensive comparison between different inversion and transformation techniques used for FDHEM data is published in Sattel (2005). We present a fast approximate method for one-dimensional (1D) inversion of frequency domain data and apply it to frequency domain helicopterborne 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, and the frequency domain responses and derivatives are found through Fourier transformation of the time domain counterparts using Fast Hankel Transform filters. The inversion is carried out with multi-layer models in a state-of-the-art formulation of a least-squares iterative inversion scheme including explicit formulation of the model regularisation through a model covariance matrix. The approximate and ordinary 1D inversion approaches thus share the inversion formulation, the difference lying only in the forward mapping. The method is 30 times faster than ordinary 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 ordinary inversion.