IEEE Geoscience and Remote Sensing Magazine - March 2021 - 177

size of 0.2 m via natural-neighbor interpolation [53], and the
measured locations were sampled according to a 5 # 5 pixel
kernel to create the input variable xv train. The kernel was rotated
180° depending on the survey heading.
We defined xv train as a subset of xv, where output variables
y train were present. Then, a Bayesian ridge regression model
f was used to fit xv train to y train:

y train = f ^ xv train h . (4)

The implementation of the model f in scikit-learn [57] was
used, based on the algorithm described by Tipping [58],
where updates of the regularization parameters are implemented, as suggested by MacKay [59]. Next, unidirectional
data were predicted via the fitted model in the previous step:

yt = f ^ x h . (5)

As such, unidirectional data were predicted for the
complete area, even though the area was surveyed in a

3.2

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2

IP (ppt)

Interline Sampling Interval (m)
2.4

1.6

0.8

survey direction. Under highly heterogeneous conditions,
this might even result in an erroneous correction of the
time lag, although we did not encounter this in any of the
presented studies. To minimize the risk of such an error, we
propose an MAE measure to quantify the time-lag error as
opposed to, e.g., squared measures to avoid the exponential
influence of signal peaks.
A time-lag correction is important when integrating auxiliary
spatial data and should therefore be performed prior to data
calibration. By collecting overlapping survey lines in immediate succession (and thus within a relatively short time frame),
the effect of signal drift can be neglected. This assures that a
time-lag correction can be performed before calibration, ensuring correct spatial offsets in the (relative or absolute) calibration
that follows.
For instruments providing both QP and IP data, whereby
the time lag can be assumed to be equal for both responses,
the signal component offering the strongest response amplitude is preferred for lag correction. However, as with
most commercially available instruments, QP data are
the most drift resilient [13] and provide the optimal basis for evaluating temporal lag. In the presented
cases, the time shift remained stationary throughout each individual
survey and constant (0.6 s) over all
the obtained data sets. Although
the latter relates to uniform instrumental properties, setup, and output, the former cannot be guaranteed as it also depends on, e.g., the
speed of the software, memory card,
and so forth.
A time-lag correction can be performed either via QP and/or IP data
for each repeated survey line individually or together. The same applies to multiple configurations or
frequencies for FDEM instruments
that record them simultaneously. In
general, adding more data will increase the robustness of the time-lag
correction, but configuration-specific details might get lost.

METHODOLOGY
First, the collected survey data were
deduplicated by removing one heading direction of the repeated survey
lines. The extracted survey lines in
the opposing direction were used as
(target) output variable y train (see Figure 12). Next, the lawnmower pattern
was interpolated to a grid with a cell
MARCH 2021

ANISOTROPIC RESPONSES

0.26

0.51
1
1.97
Inline Sampling Interval (m)

3.75

FIGURE 9. The influence of the inter- and inline sampling intervals on a PRP1 IP 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).

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IEEE Geoscience and Remote Sensing Magazine - March 2021

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