IEEE Geoscience and Remote Sensing Magazine - March 2021 - 173

^y max - y min h2

HCPH

, (1)

HCP1

0

HCP2

0

PRPH

0

PRP1

25
0

FDEM Response (ppt)

-50

-50

-50

0

0

-2.5

-2.5

10

2

0

PRP2

25
0
-25

25
0
-25

10

10

0

0

0
1

-10

1

0.5
0

0

1

1

0.5

0

0

0

0.1

0.25

0
-1

0.5
0.1

0.25

0
-2.5

0

2.5

0
-2.5

0

2.5

0
-2.5

0

2.5

0
-2.5

0

RRMSE =

0.25

	

0.25
0

0

2.5

0
-2.5

Lateral Offset (m)

N

1
^ yt n - y n h2
N n/
=1

0.5

DETERMINING SAMPLING INTERVALS
Goodness of fit between continuous theoretical and discretely sampled FDEM response curves were estimated using the RRMSE:

where N is the total number of points; y max and y min are the
maximum and minimum values encountered, respectively;
yt is the predicted value; and y is the theoretical value
for 1# n # N.
Figure 7 illustrates the rising RRMSE associated
with increasing the inline sampling interval and the
decreasing--response amplitude associated with the expanding interline distance. In general, analogous to
Figure 6, the larger inline sampling intervals associated
with larger interline sampling intervals result in a lower
RRMSE due to the response's less complex signature shape
but might fall beneath the noise levels (red hatched area).
The maximum response amplitude is achieved for an interline sampling interval of 0 and decreases exponentially,
ultimately dropping below the noise levels (red full line).
The main difference between the QP and IP responses is
the maximum total absolute response amplitude, which
is larger for IP and not reflected here due to its normalization. A tradeoff between survey efficiency and the inline
and interline sampling interval must be made. A minimum response amplitude (a factor larger than noise levels) is needed to guarantee sufficient contrast between
the background and the object-induced response, while
the inline sampling interval should be sufficiently small
to guarantee a low RRMSE, making the accurate reconstruction or interpretation of the response possible.
For high-resolution surveys over large areas, one should
determine the exact value of the interline sampling interval

0.75

small to prevent the object from doing the following (see
Figure 6 for examples):
◗◗ rendering a response that occurs at an offset from the
true object position
◗◗ rendering a response that deviates too strongly from
the expected theoretical response curve and impeding
further reliable data processing (e.g., accurate data
inversion)
◗◗ rendering no response (e.g., for the 4-m inline sampling
intervals displayed in Figure 6).
The inline sampling is determined indirectly by the
sampling frequency and acquisition speed and should
therefore be sufficiently large (depending on the application) to guarantee a time-efficient survey. However, lower
sampling frequencies and acquisition speeds are advantageous to data quality, i.e., less instrument noise and tilt.
These should be taken into account equally when setting
the inline sampling interval and are mainly determined by
the FDEM instrument.

0

2.5

-0.25
-2.5

0

2.5

Distance Along Transect (m)
FIGURE 5. The influence of different sphere offsets on the DUALEM-21HS configuration. The FDEM signatures of the QP (blue) and IP

(red) responses of a theoretical sphere located at a depth of 0.25 m below the instrument. This depth was chosen because it contained
the most complex response shapes in Figure 4. The position along the transect (m) is given as the distance from the intercoil center of the
coil configuration.
MARCH 2021

IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

173
IEEE Geoscience and Remote Sensing Magazine - March 2021

Table of Contents for the Digital Edition of IEEE Geoscience and Remote Sensing Magazine - March 2021
