IEEE Geoscience and Remote Sensing Magazine - March 2021 - 179

N

j =1
N

/ ^y j - yr h2

(7)

j =1

and
1 N
yr = N /y j, (8)
j =1

RESULTS AND DISCUSSION
As detailed in the previous section,
more advanced data processing and
interpretation require an accurate
time-lag correction. Particularly for
data collected using motorized field
setups, an improper shift correction
will result in data staggering, showing characteristic " fishbone " patterns (Figure  10). For asymmetrical
configurations, after a time-lag correction, a fishbone pattern might
still occur due to differences in the
survey heading [Figures 10, 13(a),
and 14(a)], which can be addressed
equally by repeating survey lines.
Bidirectional and predicted unidirectional data collected using an
asymmetrical coil configuration are
illustrated in Figures 13 and 14 for
the largest R 2 values (see Table 1).
A clear example of a fishbone pattern, introduced by survey heading,
is visible in Figures 13(a) and 14(a).
Figure  13(c) illustrates the effect of
survey heading and the associated
instrument response along a survey line. The QP peak value in the
survey line is mirrored by predicting the opposing direction, which
results in the lateral data being corrected for the staggering pattern,
i.e., going from Figure 13(a) to (b). A
similar pattern can be distinguished
for the smaller peaks, although it
is less obvious. The ML algorithm
successfully captures all of these
MARCH 2021

+5.6752e6

1.8
1.6

UTM Y (m)

90

1.4
80

1.2
1

70

0.8
60

0

0.6

10
20
30
UTM X (m) +5.17e5
(a)

1.6

(b)

Measured in
Northeast Heading
Predicted in
Southwest Heading

1.4
QP (ppt)

where N is the number of samples
within a survey line. This method divided the observations into k groups
or folds, where every fold was a repeated survey line. The model was
then fitted to k - 1 folds, while the
predictions were validated based on
one fold. This process resulted in a
mean value for k estimates of the prediction error.

1.2
1
0.8
0.6
0

25

50
75
100
125
Measurement Along Survey Line
(c)

150

175

FIGURE 13. Removing the effect of the survey heading in the asymmetrical PRP2 configuration at Koolkerke, where (a) is the collected bidirectional data, (b) is the predicted unidirectional data, and (c) is a survey line measured in one direction [the black line, northeast,
as illustrated in (a)] and predicted in the opposing direction [the red line, southwest, as
illustrated in (b)].

3

+5.843e6

2.8

10
UTM Y (m)

	

QP (ppt)

R2 = 1 -

variations along the survey line transect and therefore also
on a lateral scale, equally reflected by the high R 2 values
listed in Table 1.
In general, the effect of survey heading for asymmetrical
configurations is more pronounced for larger coil spacings,

2.6

0
-10

2.4

-20

2.2

QP (ppt)

	

/ ^y j - yt jh2

2

-30
10

20

30 40 50 60
UTM X (m) +6.449e5
(a)

1.8
(b)

FIGURE 14. Removing the effect of survey heading in the asymmetrical PRP2 configuration
in Wervershoof, where (a) is the collected bidirectional data and (b) is the predicted unidirectional data.

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IEEE Geoscience and Remote Sensing Magazine - March 2021

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