IEEE Geoscience and Remote Sensing Magazine - March 2019 - 80

Function forward modeling (sensor, model)
1 calculate magnetic fields [(1)-(14)]
2
→ use Function magnetic Fields
3 calculate normalized response H [(15) or (16)]
4 calculate and REtuRn IP (17) and QP (18) response
EnD

Function magnetic fields (sensor, model)

1 get sensor coil configuration (from sensor)
2 cASE coil configuration (XX, XY, XZ, YX, YY, YZ, ZX, ZY, ZZ)
3
calculate and REtuRn secondary magnetic field H S [(1)-(9)]
4
→ use Function digital filtering
5
calculate and REtuRn free-space magnetic fields H 0 [(12)-(14)]
6
→ use Function digital filtering
7 EnD
END

Function digital filter [sensor, model, K (29), Bessel order (29)]

1 cASE Bessel order (0 or 1)
2
from Appendix Table 1-4 in [26]:
3
load filter abscissa a
4
load filter spacing s
5
load filter weights W n
6 EnD
7 calculate lambda values m n (30)
8 evaluate sampled function K for every lambda m n
9
→ use Function primary and/or secondary sampled functions
10 Calculate and REtuRn weighted output (31)
EnD

Function primary sampled functions (sensor, lambda m n)

1 calculate u 0 (25)
2 calculate and REtuRn H P [(1)-(9), primary part; see (10)]
EnD

Function secondary sampled functions (sensor, model,
lambda m n)

1 calculate u 0 (25)
2 calculate reflection coefficient rTE (or propagation matrix; see "Propagation
matrix")
3
→ use Function reflection coefficient (or propagation matrix)
4 calculate and REtuRn H S [(1)-(9), secondary; see (11)]
EnD

Function reflection coefficient (sensor, model, lambda m n)

1 calculate magnetic permeability of each layer n n (28)
2 calculate for each layer the wavenumber u n (25)
Yn
3 calculate for each layer the admittance (23)
4 set admittance equal at basement (22)
5 FoR each layer n starting at basement layer to top layer (N -1 $ n $ 1)
6
calculate for each layer Ytn (21)
7 EnD
8 calculate and REtuRn reflection coefficient rTE (19)
EnD

80

fields, 3) digital filter, 4) primary sampled functions, 5) secondary sampled functions, and 6) reflection coefficient (or,
alternatively, propagation matrix; see "Propagation Matrix").
The pseudocode of the sensitivity modeling is given in
its simplest form, i.e., by iteratively solving the whole forward model for a perturbed profile. Increased performance
of the sensitivity modeling can be obtained if the perturbation is located closer to the function of interest, i.e., the
reflection coefficient or propagation matrix. However, the
method indicated below is the most practical; hence, no
other is provided here.
COMPUTER PROGRAMS
Four different programs are presented: FDEM1DFWD RC,
FDEM1DFWD PM, FDEM1DSENS RC, and FDEM1DSENS PM,
where FDEM1DFWD calculates the theoretical EM response
of a loop-loop system located on or above a layered earth
and FDEM1DSENS is used to obtain the sensitivity distribution within the considered model. Note that further distinction is made between the wave propagation approach, i.e.,
reflection coefficient or propagation matrix.
The presented software theoretically calculates, with
each execution, the forward response and/or sensitivity
for one layered half-space (i.e., model) and one instrument
setup. However, this can be easily adjusted by adding more
dimensions to the modeling process.
MATLAB
In MATLAB R2016a (MathWorks, Natick, Massachusetts),
the four aforementioned programs were implemented as
four different functions: FDEM1DFWD_RC.m, FDEM1DFWD_PM.m, FDEM1DSENS_RC.m, and FDEM1DSENS_
PM.m. The forward modeling programs have an input structure with the governing variables embedded in two different
structures, one for the half-space (or model characteristics)
and one for the instrument setup (or sensor characteristics;
see the section "Pseudocode"). The sensitivity modeling
program has the same input and an extra string indicating
the physical property for the sensitivity analysis.
Up-to-date MATLAB code (with comments passed alongside) and examples can be found in [45].

Function sensitivity modeling (sensor, model, physical
property)
1 calculate forward response of original profile H (m)
2
→ use Function forward modeling
3 FoR each layer n of the model
4
set perturbation Tm n
5
add perturbation Tm n to nth layer physical property m n
to alter profile
6
calculate forward response of altered profile H (m + Dm n)
7
→ use Function forward modeling
8
calculate approximate sensitivity in layer n (33)
9 EnD
10 REtuRn approximate sensitivity
EnD

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IEEE Geoscience and Remote Sensing Magazine - March 2019

Table of Contents for the Digital Edition of IEEE Geoscience and Remote Sensing Magazine - March 2019
