IEEE Geoscience and Remote Sensing Magazine - March 2021 - 176

TIME LAG OR GEOREFERENCING

t s = t + ∆t. (2)

If t s were covered by t, the geographical x- and y-coordinates
(denoted as UTM X and UTM Y, respectively) were interpolated according to their associated t s through a piecewise
cubic hermite interpolating polynomial along its Euclidean length p = ^UTM X h2 + ^UTM Y h2 to account for
survey heading and sampling location. The MAE was then
used as an objective measurement to describe the similarity
between the overlapping survey lines:
1 N
MAE = N /u m 0i ^t s, p h - m 1i ^t s, p hu , (3)
i =1

where m is the QP or IP measurement (ppm), N is the total
number of measurements in a survey
line, and 0 and 1 indicate opposing
heading directions. The final shift, Tt,
correcting all survey lines, is the value
associated with the lowest MAE obtained in (3). Assuming a stationary
time lag, more robust MAE values can
be obtained by combining multiple
repeated survey lines or multiple coil
configurations or frequencies (in the
case of multifrequency or configuration FDEM instruments).

Interline Sampling Interval (m)
2.4

1.6

0.8

METHODOLOGY
The constrained-shift method, presented here, builds
on the procedures of Delefortrie et al. [13] and Delefortrie et al. [12]. Of importance is the allocation of corrected

coordinates within the limit of the survey track and its objective estimation via repeating survey lines and the mean
absolute error (MAE).
Hereby, the original time stamps t were first shifted with
a time shift Tt :

3.2

0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06

QP (ppt)

For the anisotropic responses, we suggest a simple, data-driven approach using ML methods to transform the
collected (lawnmower) data into unidirectional data [i.e.,
from Figure 2(b) and (c)], where the repeated survey lines
act as training data. Subsequently, data sets are available for
interpretation in both acquisition directions without needing to cover the whole study area in both directions or a
time-consuming unidirectional survey.
A graphical summary of this workflow is illustrated in Figure
10 for both asymmetrical and symmetrical configurations. Note
that the former require a two-stepped correction procedure,
while the latter can be resolved with one correction.

0.26

0.51
1
1.97
Inline Sampling Interval (m)

3.75

FIGURE 8. The influence of the inter- and inline sampling intervals on a PRP1 QP map at

the test field (the black line represents the field boundary) in Kluizen. The coordinates were
removed for visualization; the exact values can be found in Figure 3(a).
176

RESULTS AND DISCUSSION
The MAE was calculated for all the
repeated survey lines for the HCP
and PRP configurations. The time
shift was sampled at 41 evenly spaced
intervals between 0 and 1 s. For the
collected FDEM data and the associated logger device and GPS, an ideal
time shift of 0.6 s was obtained for all
the configurations, effectively lowering the MAE (Figure 11). Because the
same instrument setup was used for
all the surveys, similar time-shift corrections were o
- btained.
A time-lag correction via the MAE
can be applied on both the symmetrical and asymmetrical configurations (Figure 11). In general, larger
MAE values are expected for asymmetrical configurations, especially in
highly heterogeneous environments.
These are caused by a combination of
their associated (asymmetrical) subsurface sensitivity and the opposing

IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

MARCH 2021

IEEE Geoscience and Remote Sensing Magazine - March 2021

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