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Holistic inversion of time-domain airborne electromagnetic data

Ross Brodie and Malcolm Sambridge

Research School of Earth Sciences, Australian National University, Canberra, ACT 0200, Australia


Figure 1.

Since the research on this project resumed in August 2008 we have been investigating the feasibility of applying our holistic inversion technique to time-domain airborne electromagnetic (AEM) data.  Holistic inversion was originally developed to invert frequency-domain AEM data to solve for continuous 3D survey wide conductivity model while simultaneously solving for systematic calibration errors (e.g., scaling effects, phase shifts and zero-level bias) which often degrade frequency-domain data (Brodie and Sambridge, 2006).

One of the challenging 'calibration' issues in fixed-wing time-domain AEM is the fact that the position and attitude of the receiver coils, which are towed ~120m behind and ~40m below the aircraft, cannot be accurately measured under normal operating conditions.  This receiver geometry information is a critical input into quantitative modelling and inversion routines.  Conventionally the receiver coils' position are estimated from the measured AEM data during the routine data processing.  However this requires assumptions to be made about the conductivity of the subsurface and the attitude of the receiver coils.  When these assumptions are poor the estimated receiver position is not accurate, which results in the data not being able to be fitted and/or inaccurate conductivity models being estimated from subsequent inversions.  More recently it has been demonstrated that a better approach is to simultaneously invert for the system geometry and the conductivity model (Lane et al., 2004).

The fixed-wing time-domain holistic inversion we improve on this by inverting not just one sample of AEM data at a time but a whole flight line of data.  Figure 1 shows a schematic outline of the elements of the inversion formulation.  We solve for layer conductivities, the transmitter to receiver in-line (Dx) and vertical separations (Dz), and the receiver pitch (Rp).  All of these are parameterized as along line 1D cubic B-splines.  Splines are an ideal choice because they are able to naturally represent the smooth and continuous along line variation of receiver geometry that occurs in reality.  In doing so we are able to exploit the along line coherency, which is not accessible to the conventional sample by sample inversion, to improve upon the accuracy and stability of the inversion.

As a demonstration of the improvement that the new method offers, we have inverted a flight line of data that was acquired with the TEMPEST system using the two techniques.  Figure 2 shows the results using a conventional inversion in which we solve for the layer conductivities independently for each airborne sample point and stitch the results together post-inversion to form a conductivity section.  We did not solve for the receiver geometry.  Figure 3 shows the results for the holistic method where we inverted the whole line at once to solve for the layer conductivities and three receiver geometry parameters, each parameterized as along line splines.

Figure 2

In the holistic inversion the data was able to be fitted to the expected misfit value of 1. However they were not able to be fitted in the conventional inversion due to inaccurate receiver geometry estimates made during the data processing.  The holistic inversion conductivity section does not have the numerous vertical artefacts that are apparent in the conventional inversion section.  This makes it more geologically realistic and continuous, and thus easier to interpret/trace subtle features.  As a means of gauging the relative accuracy of the methods via independent ground truth two downhole conductivity logs (GW800232 and LMQ03) are plotted over the conductivity sections in the same color lookup scheme.  It can be seen that in the vicinity of both logs the holistic inversion more accurately reproduces the downhole logs.

Figure 2

Brodie RC, Sambridge M (2006) A holistic approach to inversion of frequency-domain airborne EM data. Geophysics 71: G301–G312

Lane R, Brodie RC, Fitzpatrick A (2004) Constrained inversion of AEM data from the Lower Balonne Area, Southern Queensland, Australia. CRC LEME open file report 163