Geology Reference
In-Depth Information
Furthermore,
The first two conditions are the same of the
gravity case, whereas the third one is now,
@Z
n
@x
D
.Ÿ
n
C
1
Ÿ
n
/.—
n
C
1
—
n
/
R
2
if (Ÿ
n
D
Ÿ
n
C1
)then
f
@Z
n
—
n
C
1
—
n
r
n
.™
nC1
™
n
/
.—
n
C
1
—
n
/
2
R
2
Ÿ
nC1
Ÿ
n
log
r
n
C
1
@
z
D
P;
@Z
n
log
r
n
C
1
r
n
C
Q
(5.54)
@x
D
.
n
C
1
n
/
2
R
2
@X
n
@
z
D
Q;
@X
n
C
Q
I
@x
D
.
nC1
n
/
C
P
g
The results obtained in this section allow cre-
ating and testing magnetization models of the
oceanic crust. In fact, observation suggests that
the pattern of magnetization in oceanic basins
generally consists of assemblages of long prisms
having uniform remnant magnetization, normal
or reversed, running parallel to the spreading
imated by 2-D bodies, for which the previous
solutions allow to determine the resulting crustal
field and the corresponding anomaly at any point.
The size of these blocks in the
x
direction is not
arbitrary, but depends from the spreading velocity
and the duration of chrons in a geomagnetic po-
larity time scale. In the next section we shall see
the procedures that must be followed to analyse
and interpret the observed magnetic signal.
.Ÿ
n
C
1
Ÿ
n
/
2
R
2
@X
n
@
z
D
log
r
n
C
1
Ÿ
nC1
Ÿ
n
.™
nC1
™
n
/
—
n
C
1
—
n
r
n
C
C
Q
(5.55)
Finally,
@X
n
@x
D
.Ÿ
n
C
1
Ÿ
n
/.—
n
C
1
—
n
/
R
2
log
r
n
C
1
Ÿ
nC1
Ÿ
n
.™
nC1
™
n
/
—
n
C
1
—
n
r
n
C
C
P
(5.56)
where,
R
2
D
.Ÿ
nC1
Ÿ
n
/
2
C
.—
nC1
—
n
/
2
(5.57)
Ÿ
n
—
n
C
1
Ÿ
n
C
1
—
n
R
2
P
D
Ÿ
n
.Ÿ
n
C
1
Ÿ
n
/
—
n
.—
n
C
1
—
n
/
r
n
5.5
Forward Modelling
Procedures
#
Ÿ
n
C
1
.Ÿ
n
C
1
Ÿ
n
/
—
n
C
1
.—
n
C
1
—
n
/
r
nC1
The analysis and interpretation of marine total
field anomalies can be performed using either
forward modelling
or
inversion techniques
(e.g.,
Blakely
1996
). A forward modelling algorithm
assumes a “reasonable” initial magnetization pat-
tern of the oceanic crust, which is built starting
from a geomagnetic polarity time scale and a
spreading rate function of time
t
,
v
D
v
(
t
). Then,
a specialized computer program generates model
anomalies,
T
0
, that can be compared with the
observed data
T
. Generally, the magnetization
pattern is modified in a trial and error procedure
through successive adjustments of the spread-
ing rate function
v
D
v
(
t
), until a good fit of
the model anomalies to the observed data is
(5.58)
Ÿ
n
—
n
C
1
Ÿ
n
C
1
—
n
R
2
Q
D
Ÿ
n
.—
n
C
1
—
n
/
C
—
n
.Ÿ
n
C
1
Ÿ
n
/
r
n
#
Ÿ
n
C
1
.—
n
C
1
—
n
/
C
—
n
C
1
.Ÿ
n
C
1
Ÿ
n
/
r
nC1
(5.59)
Also in this case the evaluation of angles ™
n
through the
atan2
() C library function must take
into account of three special situations.
