648
Bleil and von Dobeneck
resolve any details, however. Most plausible ages
for the Norwegian-Greenland Sea and the Blake
events should be around 70 and 110 ka, respectively. Similar adverse conditions during oxygen
isotope stage 3 may have prevented a more distinct recording of the Laschamp event and also
conceal the onset of the Mono Lake event.
Lock-in Model
Based on the simple concept of delayed remanence
acquisition (e.g., Denham and Chave 1982; Hyodo
1983; Mazaud 1996; Meynadier and Valet 1996)
we designed a model that accounts for all characteristic features ofthe polarity and relative paleointensity records in the Ceara Rise sediments. As
carrier of remanence we presume a magnetic mineraI assemblage remaining unchanged in concentration, composition and grain-size distribution over
time (its maximum PDRM is normalized to 1). A
layer now at core position z was progressively
buried under a sediment cover of thickness S
(Fig. 8). The fraction oflocked magnetic momentum, the cumulative 10ck-infunctionA«(, c(z)), only
depends on burial depth and a lithology related
variable c(z) disceming sediments of different lockin properties. The model exclusively relies on the
assumption that magnetic minerals are either
blocked or free to adjust their magnetic momentum parallel to the direction of an external field.
The lock-in depth is hence no explicit function of
field strength, i.e., strong fields will notre-mobilize
more minerals than weak fields (Otofuji and Sasajima 1981). Although a respective ..1((, c(z), H)
could be formulated, the lack of relevant experimental data precludes its quantitative application.
The initial lock-in depth do represents the
lower limit ofthe bioturbated layer which does not
preserve a remanent magnetic signal due to benthos
activity. As do is difficult to quantify from accessible information, it was set zero at this stage. The
median lock-in depth dv, is reached, where half of
the available magnetic momentum has definitely
been fixed. Assuming a constant increase of the
lock-in rate, the total lock-in depth d l will be at
twice dv,. According to the above discussed
observations in the Ceara Rise sediments plausible, but rather conservative estimates of d l = 15
and d I = 35 cm have been chosen to span the range
between purely terrigenous (c = 1) and biogenic
(c = 0) endmembers. For intermediate sediment
compositions (O
piecewise linear lock-in function
Ak,c} = {d,~e) for ( < d, (e)
1
for s~ d,(e)
(1)
Since lock-in depends on burial depth and not
on burial time, the model calculations are performed
in the depth domain. H(z) therefore describes the
geomagnetic field vector, when core position z
was the surface layer. We now follow the lock-in
process at z, while the burial depth S successively
increases at discrete steps i = 1 ... n. The incremental magnetization acquired atz from S;-I to S; is
proportional to the rise of the lock-in function
LlA = A[S;, e(z)]- A[Si_l, e(z)]
and the average magnetic field during this interval
Y,·[H(z- Si) + H(z- (i-I)]
By multiplying these two terms and summing
up the partial remanences of all n steps, which
takes C; to the present burial depth C;n = z, yields
the total PDRM
Mpdr(z) = t {A[s"e(z)] - A[Cpe(z)]}
i=l
H(z-()+H(z-Si_')
2
(2)
Equation (2) describes a discrete convolution
of the differential lock-in profile and the geomagnetic field record in the depth domain. This form
applies for numerical computations. An analytical
analogue, the continuous convolution integral
Mpdr(z) = )J :A[(,e(z)l} H(z - s)ds
d,{z}
1
)0 d, [c(z)] H(z - s)ds
(3)
is better apt for systematic analyses. The second
transformation is valid only for A as defined in equa-
Bleil and von Dobeneck
resolve any details, however. Most plausible ages
for the Norwegian-Greenland Sea and the Blake
events should be around 70 and 110 ka, respectively. Similar adverse conditions during oxygen
isotope stage 3 may have prevented a more distinct recording of the Laschamp event and also
conceal the onset of the Mono Lake event.
Lock-in Model
Based on the simple concept of delayed remanence
acquisition (e.g., Denham and Chave 1982; Hyodo
1983; Mazaud 1996; Meynadier and Valet 1996)
we designed a model that accounts for all characteristic features ofthe polarity and relative paleointensity records in the Ceara Rise sediments. As
carrier of remanence we presume a magnetic mineraI assemblage remaining unchanged in concentration, composition and grain-size distribution over
time (its maximum PDRM is normalized to 1). A
layer now at core position z was progressively
buried under a sediment cover of thickness S
(Fig. 8). The fraction oflocked magnetic momentum, the cumulative 10ck-infunctionA«(, c(z)), only
depends on burial depth and a lithology related
variable c(z) disceming sediments of different lockin properties. The model exclusively relies on the
assumption that magnetic minerals are either
blocked or free to adjust their magnetic momentum parallel to the direction of an external field.
The lock-in depth is hence no explicit function of
field strength, i.e., strong fields will notre-mobilize
more minerals than weak fields (Otofuji and Sasajima 1981). Although a respective ..1((, c(z), H)
could be formulated, the lack of relevant experimental data precludes its quantitative application.
The initial lock-in depth do represents the
lower limit ofthe bioturbated layer which does not
preserve a remanent magnetic signal due to benthos
activity. As do is difficult to quantify from accessible information, it was set zero at this stage. The
median lock-in depth dv, is reached, where half of
the available magnetic momentum has definitely
been fixed. Assuming a constant increase of the
lock-in rate, the total lock-in depth d l will be at
twice dv,. According to the above discussed
observations in the Ceara Rise sediments plausible, but rather conservative estimates of d l = 15
and d I = 35 cm have been chosen to span the range
between purely terrigenous (c = 1) and biogenic
(c = 0) endmembers. For intermediate sediment
compositions (O
piecewise linear lock-in function
Ak,c} = {d,~e) for ( < d, (e)
1
for s~ d,(e)
(1)
Since lock-in depends on burial depth and not
on burial time, the model calculations are performed
in the depth domain. H(z) therefore describes the
geomagnetic field vector, when core position z
was the surface layer. We now follow the lock-in
process at z, while the burial depth S successively
increases at discrete steps i = 1 ... n. The incremental magnetization acquired atz from S;-I to S; is
proportional to the rise of the lock-in function
LlA = A[S;, e(z)]- A[Si_l, e(z)]
and the average magnetic field during this interval
Y,·[H(z- Si) + H(z- (i-I)]
By multiplying these two terms and summing
up the partial remanences of all n steps, which
takes C; to the present burial depth C;n = z, yields
the total PDRM
Mpdr(z) = t {A[s"e(z)] - A[Cpe(z)]}
i=l
H(z-()+H(z-Si_')
2
(2)
Equation (2) describes a discrete convolution
of the differential lock-in profile and the geomagnetic field record in the depth domain. This form
applies for numerical computations. An analytical
analogue, the continuous convolution integral
Mpdr(z) = )J :A[(,e(z)l} H(z - s)ds
d,{z}
1
)0 d, [c(z)] H(z - s)ds
(3)
is better apt for systematic analyses. The second
transformation is valid only for A as defined in equa-