Geology Reference
In-Depth Information
from the observed total intensity data, on the
basis of a
definitive
version of the IGRF for the
survey epoch (that is, a
DGRF
).
where
n
is the number of survey lines. Then,
for each point
r
j
on the tie line
R
k
,if
T
is
the observed magnetic field intensity, then the
following transformation is performed:
T
r
j
!
T
r
j
h
©
i
k
(5.7)
5.3
Levelling Techniques
This transformation is applied to the observed
field values of all tie lines. Then, the crossover
errors are updated using the new tie line magnetic
intensities. The procedure is now repeated for
the survey lines
L
i
.Ifthereare
m
tie lines, then
we set:
The procedure of normalization of ship-track or
aeromagnetic data according to the information
given by a set of crossover points is called
level-
ling
. The objective of this technique is to reduce
systematically the
intersection errors
(difference
between two readings) at crossover points. This
is made through an iterative algorithm that dis-
tributes the errors between tie lines and survey
lines (Luyendyk
1997
). Although in origin the
method was developed as an alternative to the
use of base station data (Yarger et al.
1978
;
Nabighian et al.
2005
), today it is commonly used
even after the application of base-station diurnal
corrections, in conjunction with a survey track
design that includes tie lines. In fact, in absence
of levelling magnetic anomaly maps often show
small long wavelength artifacts aligned with the
survey lines that can be misleading during the
phase of structural interpretation. The application
of a levelling procedure is important for the
production of reliable magnetic anomaly maps,
especially in regions of severe space weather con-
ditions at high latitudes, where diurnal variations
may be as high as 100 nT (Mauring et al.
2002
).
The basic idea behind levelling is that the
crossover errors, "
ki
, form a time sequence of
data that can be used to estimate the diurnal
drift function through a regression procedure.
Although several algorithms have been designed
for the levelling of magnetic data, here we
are going to describe two simple methods
that are widespread in the applied geophysics
community: (1)
Polynomial fitting
of crossover
errors, and (2)
Median filtering
. A procedure
of polynomial fitting starts with a
zero
-
order
levelling step. Let <">
k
be the average crossover
error along tie line
R
k
(see Fig.
5.4
):
X
m
1
m
h
"
i
i
D
"
ki
(5.8)
k
D
1
In this case, for each point
r
s
on the survey line
L
i
, the following transformation is performed:
T.r
s
/
!
T.r
s
/
h
©
i
i
(5.9)
These transformations do not introduce distor-
tions in the data set, because they simply offset
the tie lines or the survey lines. However, the
resulting data set is not perfectly levelled and
an output magnetic anomaly map would show
narrow bands aligned as the survey lines. There-
fore, usually a high-order levelling procedure is
applied. This consists into a least squares re-
gression of the crossover errors as a time series
functional of the elapsed time through low order
polynomials (the typical order is 1-3). The re-
gression can be applied to tie lines, survey lines,
or to an entire flight. The resulting polynomials,
which are called
drift curves
, are then subtracted
from the corresponding data set to minimize the
crossover errors. In the simplest case, a levelling
procedure requires three steps (Mauring et al.
2002
): (1) levelling the tie lines; (2) update the
crossover errors, and (3) levelling the survey
lines. However, more complex procedures can be
used to obtain better results (e.g., see the proce-
dure described in Appendix 1 of Luyendyk
1997
),
and the regression can be also performed using
non-polynomial estimators (Sander and Mrazek
1982
). A major problem of polynomial regression
is that for a given order the degree of smoothing
X
iD1
©
ki
n
1
n
h
©
i
k
D
(5.6)
