Untitled Document
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