Geology Reference
In-Depth Information
depends from the number of crossover errors to
be fitted. For example, fitting a second order
function to 5 points will generally produce a
lower smoothing than fitting the same function
to 20 points. Therefore, a direct manual assess-
ment of the required polynomial degree could be
necessary. Alternatively, it should be possible to
use spline regression techniques or other forms of
piecewise low-order polynomials to generate drift
curves.
Levelling by median filtering of crossover
errors is a valid alternative technique to
polynomial fitting (e.g., Mauring et al.
2002
).
This approach is especially convenient for the
removal of random noise and does not require
pre-processing procedures such as despiking. A
median filter is a non-linear filter based on the
following algorithm:
value of the group. If
i
b
r
/2
c
, then the set
S
cannot be filled with
r
values whose central
position has index
i
C
r
/2, thereby, the set is
filled with a series of "
k
1
. For example, if
r
D
5
and the data set is represented by the sequence:
f
21,5,-8,12,4,-3,10,14,:::
g
, then for
i
D
1weset
S
f
21,21,21,5,-8
g
, because the set
S
must
contain five values. A similar procedure is used
at the end of the sequence, for
i
>
n
-
b
r
/2
c
.Inthis
case (at step #3), the set will be completed by a
series of "
kn
. This algorithm is particularly useful
for removing spikes, although it preserves sharp
edges in the input data set.
The levelling procedure described above gen-
erally produces good results, but small “corru-
gations” aligned as the survey lines may be still
observed on the output magnetic anomaly maps.
In this instance, an additional
microlevelling
fil-
tering algorithm is applied, which will remove
the residual levelling errors (e.g., Minty
1991
;
Mauring and Kihle
2006
).
Algorithm 5.1: (Median Filtering Algorithm)
Input: A time-ordered sequence of crossover
errors
f
"
k
1
,"
k
2
, :::,"
kn
g
; filter size
r
(
r
od
d)
Output:
A
median-filtered sequence
f
"
k1
;"
k2
;
:::;"
kn
g
;
f
1)
i
1;
2) if
i
b
r
/2
c
then set
S
f
"
k
1
, "
k
1
, "
k
1
,
:::, "
k
1
, "
k
,
i
, "
k
,
i
C 1
, :::, "
k
,
i
C
r
g
(fill miss-
ing values with "
k
1
);jump#6;
3) if
i
>
n
b
r
/2
c
then set
S
f
"
ki
, "
k
,
i
C 1
,
:::, "
kn
, "
kn
, "
kn
, :::, "
kn
g
(fill missing
values with "
kn
);
4) jump #6;
5)
S
f
"
ki
,"
k
,
i
C1
, :::,"
k
,
i
C
r
g
;
6) ©
k;iCr=2
median
(
S
);
7)
i
i
C
1;
8) if
i
n
-
r
C
1 then jump #2;
5.4
Modelling of Marine
Magnetic Anomalies
In general, dating the ocean floor, constructing
isochron maps that describe the sea floor spread-
discovering the plate kinematics of continents
during the geological time, have a common
starting point in the modelling of oceanic crust
magnetization through the identification of
marine magnetic anomalies. Such identification
requires in turn calculation of the “anomalous”
field
F
D
F
(
r
) associated with an assumed
distribution of magnetized blocks of oceanic
crust. Then, total field magnetic anomalies are
computed for the survey time and compared with
the observed anomalies. A best match is found
by trial and errors varying the spreading rate
function, hence the width of crustal blocks having
normal or reversed magnetization according to a
Let us consider first the problem of calculating
the gravitational or magnetic field generated by
g
In this algorithm, the function
median
() per-
forms a sorting of the input sequence, then it
returns the median of the resulting distribution
of values. The algorithm uses a running win-
dow of size
r
over the input data set, which
is moved from position
i
D
1 to position
i
D
n
-
r
C
1. Given the group of crossover errors
in the window at position
i
, it simply replaces
the middle value of the array by the median
