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On the possibility of recovering paleo-diurnal magnetic variations in transitional lava flows: I. Constraints from
thermoremanence modelling for an experimental protocol
Michael Winklhofer, Karl Fabian, Roman Leonhardt, Christian Vérard
To cite this version:
Michael Winklhofer, Karl Fabian, Roman Leonhardt, Christian Vérard. On the possibility of recover- ing paleo-diurnal magnetic variations in transitional lava flows: I. Constraints from thermoremanence modelling for an experimental protocol. Physics of the Earth and Planetary Interiors, Elsevier, 2008, 169 (1-4), pp.108. �10.1016/j.pepi.2008.07.019�. �hal-00532166�
Accepted Manuscript
Title: On the possibility of recovering paleo-diurnal magnetic variations in transitional lava flows: I. Constraints from thermoremanence modelling for an experimental protocol Authors: Michael Winklhofer, Karl Fabian, Roman Leonhardt, Christian V´erard
PII: S0031-9201(08)00180-5
DOI: doi:10.1016/j.pepi.2008.07.019
Reference: PEPI 5011
To appear in: Physics of the Earth and Planetary Interiors Received date: 15-2-2008
Revised date: 11-7-2008 Accepted date: 12-7-2008
Please cite this article as: Winklhofer, M., Fabian, K., Leonhardt, R., V´erard, C., On the possibility of recovering paleo-diurnal magnetic variations in transitional lava flows: I.
Constraints from thermoremanence modelling for an experimental protocol,Physics of the Earth and Planetary Interiors(2007), doi:10.1016/j.pepi.2008.07.019
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Accepted Manuscript
On the possibility of recovering paleo-diurnal magnetic variations in transitional lava flows:
I. Constraints from thermoremanence modelling for an experimental protocol
Michael Winklhofera,∗ Karl Fabianb Roman Leonhardta,c Christian V´erarda,d
aDepartment of Earth and Environmental Science, Ludwig-Maximilians-University Munich, Theresienstr. 41, D-80333 Muenchen, Germany
bNGU, Geological Survey of Norway, 7491 Trondheim, Norway
cDepartment of Applied Earth Sciences and Geophysics, Montanuniversity, 8700 Leoben, Austria
dInstitut de G´eologie et Pal´eontologie (IGP), University of Lausanne, CH - 1015 Lausanne, Switzerland
Abstract
One of the tenets in paleomagnetism is that perturbations of the ground mag- netic field due to magnetospheric or ionospheric current systems are too small to leave a detectable paleomagnetic signature in lava flows. As suggested by recent work in paleomagnetosphere modeling, however, external field perturbations may be significantly enhanced during periods of transitional field behaviour, particularly when the dipole-field axis is strongly tilted towards the equator, which then leads to an extremely dynamic magnetosphere on the diurnal time scale even for quiet solar wind conditions. We here demonstrate that thin (rapidly cooled) lava flows (∼50 cm thick) with high magnetic blocking temperatures (within ∼50−100◦C below the Curie temperature) indeed have the potential to record such diurnal perturbations.
Further, an experimental protocol is suggested to paleomagnetically extract these perturbations. Our proof-of-concept is based on numerical modelling of thermore- manence (TRM) acquisition and simulation of thermal demagnetization surfaces for discrete temperature steps in function of vertical position in the flow. The TRM direction recovered at a given thermal demagnetization step varies with vertical position in the flow and reflects the wave form of the external field variation. Char- acteristically, the vertical position of a captured signal changes systematically with unblocking temperature, which reflects the oblique orientation of cooling isochrons, along which the signals are blocked. The signals have their largest amplitudes at the maximum unblocking temperatures, but decay away at lower temperatures. It is by these systmatic trends that external field perturbations, if trapped, can be
* Manuscript
Accepted Manuscript
paleomagnetically identified and distinguished from a secondary overprint. The ex- perimental procedure requires a sample spacing of 1 cm (with 1 cm drill cores) and small thermal demagnetization steps (15◦C) at elevated temperatures.
Key words: paleomagnetosphere, Paleomagnetosphere, diurnal variations, transitional field geometry, geomagnetic impulses, numerical modelling of thermoremanence acquistion
1 Introduction
1
High-resolution paleomagnetic records have provided detailed insight into the
2
spatio-temporal behavior of the main field during the last polarity transition
3
(Valet et al., 1999; Clement, 2004; Singer et al., 2005) and during the most
4
recent geomagnetic excursions (Lund et al., 2005; Channel, 2006; Laj et al.,
5
2006). The decent spatial coverage of these events by well-dated high-quality
6
paleomagnetic records has made it possible for the first time to reconstruct the
7
evolution of the global main-field morphology across the last reversal (780 ka)
8
and the Laschamp excursion (∼ 41 ka) (Leonhardt and Fabian, 2007; Leon-
9
hardt et al., 2008). For example, at the climax of the last reversal, when
10
the axial-dipole field reversed sign, the strongly diminished surface field was
11
dominated by contributions from the quadrupolar and equatorial dipole terms
12
(Leonhardt and Fabian, 2007). It was already realized in the mid-1970s that
13
such a transitional field configuration would generate a qualitatively different
14
magnetosphere that produces large-scale daily perturbations of the ground
15
field (Siscoe and Crooker, 1976; Saito et al., 1978). Siscoe and Chen (1975)
16
estimated that even a reduced, but still axial-dipole dominated main-field
17
would lead to more frequent and stronger magnetic storms. The effect of vari-
18
ations in axial-dipole strength on the external field contributions was recently
19
explored in more detail on the basis of scaling relationships and the assump-
20
tion of a present-day field geometry (Vogt and Glassmeier, 2001; Glassmeier
21
et al., 2004). The strongest effect here was predicted for the equatorial electro-
22
jet (EEJ) system, the strength of which decreases with decreasing magnetic
23
dipole momentM only asM−2/3 (Glassmeier et al., 2004), which implies that
24
its relative strength increases with decreasing internal field. Since the EEJ is
25
confined to a narrow latitudinal band about the geomagnetic equator, the as-
26
sociated effects therefore are not expected to be seen worldwide. If, however,
27
∗ To whom correspondence should be addressed
Email addresses: michael@geophysik.uni-muenchen.de(Michael Winklhofer), karl.fabian@ngu.no(Karl Fabian),roman.leonhardt@mu-leoben.at(Roman Leonhardt),Christian.Verard@unil.ch(Christian V´erard).
Accepted Manuscript
the dipole axis comes to lie in the equator plane, then drastic diurnal per-
28
turbations can be expected (Saito et al., 1978). In such a scenario, as shown
29
by state-of-the-art magnetohydrodynamic (MHD) simulations (Zieger et al.,
30
2004), the magnetosphere reconfigures on the diurnal time scale, particularly
31
its openness varies over the course of the day, which entails a regular diur-
32
nal variation of a number of phenomena like substorms, geomagnetic activ-
33
ity, etc, even under solar quiet conditions. MHD calculations for non-dipolar
34
transitional field topologies (Vogt et al., 2004) also predicted a continuously
35
changing, highly dynamic magnetosphere.
36
Taken together, these results suggest that ground-field perturbations of ex-
37
ternal origin can be expected to be significantly enhanced and to occur on
38
diurnal time scales during transitional field states that deviate strongly from
39
the axial dipole configuration. As such, they would have an effect on the ther-
40
moremanence recorded in rapidly cooled lava flows. It is an altogether different
41
question whether enhanced external perturbations can be identified at all by
42
means of paleomagnetic techniques. Before we present our solution to that
43
paleomagnetic challenge further below, we give a short review of the Steens
44
Mountain controversy, the only case in the paleomagnetic literature where
45
external perturbations were taken into consideration to explain the observed
46
rapid movements of virtual geomagnetic pole (VGP) positions.
47
The Miocene Steens Mountain lava sequence provides one of the most detailed
48
records of transitional field behavior. Mankinen et al. (1985) found evidence
49
of astoundingly rapid angular changes (50◦/yr) in transitional VGP position,
50
referred to as ’geomagnetic impulses’ (Pr´evot et al., 1985a) or ’transitional
51
impulses’ (Coe and Pr´evot, 1989). The first impulse occurred during a com-
52
plete polarity reversal, the second and third one during a normal-transitional-
53
normal rebound after the reversal. A reinvestigation of flow B51, in which
54
the first impulse was suspected, showed that the observed variations in rema-
55
nence direction along a vertical profile in the flow reflected a thermochemical
56
overprint due to the overlying flow (Camps et al., 1995a,b). However, there
57
was no evidence of any thermochemical overprint in the remanence of flow
58
A41-2, which contained the second impulse. Using a numerical cooling model
59
to assign a time-temperature pair to each vertical position in the flow, Camps
60
et al. (1995a,b) calculated change rates of 4◦-8◦ per day for the second im-
61
pulse. In a later reinvestigation of the critical parts of the Steens mountain
62
record, previous evidence for rapid field changes in the transitional record was
63
essentially corroborated (Camps et al., 1999).
64
The origin of the rapid field changes was controversially discussed and still
65
remains enigmatic for the lack of present-day analogues of comparable magni-
66
tude. A geomagnetic jerk may bear the comparison with rapid field impulses
67
as far as the time scales are concerned, but falls short of explaining the magni-
68
tude of the changes. By analogy with the famous 1969 jerk in secular variation
69
Accepted Manuscript
(Courtillot et al., 1978; Mizuno, 1980), which was shown to be of internal ori-
70
gin (Malin and Hodder, 1982), Pr´evot et al. (1985b) consider the transitional
71
impulses as impulses of the first-order time derivative of the field, due to large
72
and possibly global changes of the (internal) magnetic-field configuration with
73
time constants of the order of 1-2 yr. Coe et al. (1995) proposed a highly en-
74
ergetic magnetic field perturbation in the outer core, of dodecapolar order
75
(spherical harmonic degree n = 6) or higher with a period of 7 days. Shorter
76
periods or lower-degree harmonics of the same period would be screened out
77
effectively by the electrically conducting lower mantle (Merrill, 1995).
78
A completely different viewpoint was put forward by Ultr´e-Gu´erard and Achache
79
(1995), arguing that the ambient field variations recorded in Steens Mountain
80
flow A41-2 were unlikely to be of internal origin but rather caused by external-
81
field perturbations. The rationale goes back to the proposition by Siscoe and
82
Chen (1975): As the internal field is weakened, the magnetosphere shrinks
83
and so delivers stronger external fields to the Earth’s surface. In combination
84
with a reduced internal field, strong external perturbations, for example due
85
to a large magnetic storm, may well give rise to local large-intensity variations
86
as observed in flow A41-2 (Starchenko and Shcherbakov, 1991). However, as
87
Jackson (1995) points out, the directional jump observed in A41-2 can only be
88
explained by assuming a rather improbable coincidence of the direction pro-
89
duced by the magnetic storm and the post-jump direction, which are physically
90
unrelated. Nevertheless, the possibility that external field perturbations may
91
be paleomagnetically captured in a rapidly cooling lava flow is worthwhile
92
exploring. As we shall show below, however, the paleomagnetic identification
93
of such signals requires a sampling and measurement strategy which goes far
94
beyond the usual paleomagnetic method.
95
2 Towards identifying variations of external origin: Preliminary
96
considerations
97
To obtain detailed transitional records and to demonstrate their fidelity is al-
98
ready at the limits of paleomagnetism (Fuller, 1989). These limits are further
99
stretched when it comes to reconstructing fast field changes from directional
100
changes within an individual lava flow: The usual palaeomagnetic method of
101
assessing the fidelity of the obtained direction, that is, calculation of 95%
102
confidence limits about a flow-mean VGP from several samples randomly dis-
103
tributed over the flow, would average out not only random, but also systematic
104
variations of remanence direction with depth due to an external field variation.
105
On the basis of our theoretical analysis below, we show that palaeomagnetic
106
direction has to be extracted as a function of both unblocking temperature
107
and vertical position within the flow in order to identify systematic variations
108
in remanence if recorded in the flow.
109
Accepted Manuscript
In the following, we explore the conditions under which external field variations
110
can be trapped in a cooling lava sheet in order to derive some preselection
111
criteria for candidate flows. We then model acquisition of thermoremanence
112
(TRM) for a vertical profile of a lava flow cooling under diurnal field variations
113
and numerically simulate continuous thermal demagnetization curves. This
114
will help us to devise and optimise the sampling strategy and measurement
115
protocol.
116
2.1 Cooling scenario
117
A lava sheet of thickness D and solidus temperature T1 is emplaced upon an
118
old flow at time t= 0. The depth coordinate z is positive downward, its zero
119
is defined by the upper surface of the flow. The temperature above the flow
120
(z < 0) is T0 (air), the initial temperature below the flow (z > D) is T0 (old
121
flow). Provided that the extension of the flow in x and y direction is much
122
larger than the thickness, we can obtain the cooling history (away from the
123
edges) by solving the one-dimensional heat equation,
124
∂T(z, t)
∂t =−κ∂2T(z, t)
∂z2 (1)
125
where κ is the thermal diffusivity, which for rocks is ∼10−6 m2/s. A generic
126
solution to Eq. 1 has the form erf(z/√
4κt), where √
κt is the characteristic
127
thermal diffusion length. The special solution now depends on the boundary
128
conditions. We assume that heat from the basal part of the flow is transmitted
129
by conduction into the underlying rock and that the surface of the flow is
130
isothermal, that is T(z = 0) =T0 for allt >0. The prescribed temperature at
131
the surfaces implies that heat is efficiently transported away from the surface
132
(such as by convection). With this, the solution to Eq. 1 writes
133
Θ(z >0, t) = T −T0
(T1−T0) = erf z 2√
κt
!
−1
2 erf z−D 2√
κt
!
+ erf z+D 2√
κt
!!
.(2)
134
The first term describes the temperature diffusion due to an infitetely thin
135
layer of excess temperature T1 − T0 emplaced at t = 0. The second term
136
accounts for the finite thickness of the flow and satisfies the boundary con-
137
dition that the intitial contact temperature at the interface z = D shall be
138
(T1 −T0)/2, where we assume that lava flow and underlying rock have the
139
same thermal effusivity. The third term in Eq. 2 is introduced to satisfy the
140
boundary condition that the flow surface be isothermal. It thus exactly cancels
141
out the second term atz = 0 (note the first term is always zero forz = 0 since
142
erf(0) = 0). By analogy with electric mirror charges, the third term can be
143
Accepted Manuscript
construed as a mirror heat sink. Eq. 2 can be expanded to account for a finite
144
width of the flow. Let y be the horizontal coordinate in the flow (one side at
145
y = 0, the other side at y = ∞), then the solution to the two-dimensional
146
heat equation is given by
147
θ(y, z, t) =θ(z, t)1
2 1 + erf y 2√
κt
!!
. (3)
148
A simple calculation shows that edge effects need not be considered as long
149
asy >5D.
150
We have neglected the effect of latent heat, which raises the contact tempera-
151
ture at the interface to the underlying rock and slows down the early cooling
152
process. However, as shown by Jaeger (1961), latent heat does not greatly
153
affect the general pattern of the isotherms. In other words, the effect of latent
154
heat can also be compensated for by a slightly thicker lava sheet. Also, since we
155
already prescribe the temperature at the surface to beT0, we need not include
156
the radiative cooling of the surface, which is very efficient at high tempera-
157
tures, but not so at low temperatures. Another simplification was made by
158
assuming that the thermal diffusivity has no temperature dependence. Camps
159
et al. (1995a) used a sophisticated cooling model which includes all these ef-
160
fects to reconstruct the cooling history of a given flow to be able to assign
161
time marks to the directions isolated at each depth level. As opposed to the
162
inversion-type approach by Camps et al. (1995a), where all these details mat-
163
tered to obtain a good estimate of the rates of field change, the task here is to
164
understand at a more conceptual level what kind of paleomagnetic signature
165
a lava flow may acquire when cooled in a periodic magnetic field variation.
166
From the temporal evolution of the cooling isotherms versus depth (Fig. 1)
167
it can be seen that the time at which a given temperature is reached varies
168
considerably along the depth coordinate, which implies that a given phase of
169
an external field perturbation will be magnetically blocked at different times
170
in different depths (assuming that each temperature is a blocking tempera-
171
ture). Whether or not that phase is recorded equally well in different depths,
172
however, depends both on cooling rate and the magnetic blocking temperature
173
spectrum. For a given (blocking) temperature, the cooling rate, |dT /dt| and
174
with it the temporal resolution decrease strongly from the top to the bottom
175
of the flow (Fig. 1).
176
2.2 Blocking process and temporal resolution
177
It is well known that cooling rate has an important influence on the mag-
178
netic blocking process. Firstly, the effective blocking temperature is a func-
179
Accepted Manuscript
tion of cooling rate (Stacey, 1963), and it has been shown that lowered effec-
180
tive blocking temperatures due to slower cooling rates lead to a few per cent
181
higher pTRM acquired at a factor of 10 decrease in cooling rate (Dodson and
182
McClelland-Brown, 1980; Fox and Aitken, 1980; Halgedahl et al., 1980). This
183
effect, however, turns out to be irrelevant in the case studied here. Secondly,
184
and more importantly, the cooling ratedT /dtis inversely proportional to the
185
transition time from the unblocked to the blocked state. The time interval t95
186
between 5% and 95% blocking of a given component of the blocking spectrum
187
is approximately
188
t95 ≈7.2 Θ, (4)
189
(Dodson, 1973), where Θ is the cooling time constant, that is, the time in
190
which the magnetic relaxation time increases by a factor e (Dodson, 1973;
191
York, 1978). Thus, t95 defines the temporal resolution at a given blocking
192
temperature. Θ itself can be estimated on the basis of the following first-order
193
approximation derived by Dodson and McClelland-Brown (1980),
194
1 Θ = 1
kT dEa
dT −Ea
T
!dT
dt , (5)
195
where Ea is the activation energy to magnetization switching, k is the Boltz-
196
mann constant and T is the absolute temperature. As a general rule, the
197
closer the temperatures gets to the Curie temperature, the more pronounced
198
is the variation of the activation energy with temperature (first term in Eq. 5)
199
and the shorter the blocking time interval becomes. Provided that a certain
200
type of anisotropy (for example, due to particle shape) prevails over the tem-
201
perature interval of interest, Ea(T) can be factorized into Ea(T0) (ms(T))r,
202
whereEa(T0) is the activation energy at a given reference temperatureT0 and
203
ms(T) =Ms(T)/Ms(T0). Then, Eq. 5 simplifies to
204
1
Θ = Ea(T0)
kT rmr−s 1
dms
dT − ms
T
!dT
dt , (6)
205
(Dodson and McClelland-Brown, 1980). When computing Θ (or t95) for pure
206
magnetite (Curie temperatureTc= 580◦C), we assume that the energy barrier
207
for magnetite is dominated by shape anisotropy at high temperatures (Dodson
208
and McClelland-Brown, 1980; Halgedahl et al., 1980), so that r= 2 in Eq. 6.
209
For comparison, we also study a titanomagnetite containing 50 mole per cent
210
ulv¨ospinel (TM50, Tc = 250◦C), the latter being a frequent composition in
211
alkali basalts (Petersen, 1976). In titanomagnetites, magnetoelastic anisotropy
212
contributes significantly to the coercivity, i.e., Ea(T) ∝ λ, where λ is the
213
characteristic magnetostriction constant. The temperature dependence of λ
214
Accepted Manuscript
for intermediate titanomagnetites can be approximated by Ms(T)r with r
215
about 3 (Moskowitz, 1993; Sahu and Moskowitz, 1995). Since λ decreases
216
fast with increasing temperatures, shape anisotropy may eventually supplant
217
magnetoelastic anisotropy as the prevailing anisotropy term, in which caset95
218
values would be higher by about 40% (dashed lines in Fig. 2). We further
219
assume that Ms(T) ∝ (Tc −T)p with p = 0.5 and note that the resulting
220
t95 values do not critically depend on whether a value of 0.4 or 0.5 is used
221
for the exponent p (solid lines in Fig. 2). From Fig. 2, it can be clearly seen
222
that the blocking time intervalt95decreases strongly as blocking temperatures
223
approach the Curie temperature, which reflects the fast decay of Ms(T) for
224
T →Tc(largedms/dT in Eq. 6). Sincet95defines the temporal resolution, the
225
best TRM recording fidelity to time-dependent signals can thus be realized
226
with high blocking temperatures,
227
When dealing with time-dependent signals, the physical meaning oft95 is that
228
of an averaging time. It is clear that t95 needs to be small compared to the
229
characteristic period Pω of the signal in order to enable precise recording. We
230
invoke filter theory to assess the smoothing effect when t95 is of the same
231
order of magnitude as Pω. Let us assume that the blocking process can be
232
described by a boxcar filter of length t95. The filter has a symmetric weight
233
function, therefore its phase spectrum is unity, that is, it will not produce a
234
phase shift. However, it acts as a low-pass filter. The amplitude response of
235
the boxcar filter of length t95 to a sine wave of period Pω is|sin(x)/x|, where
236
x=πt95/Pω. The amplitude response between x= 0 and x= 0.4 decays with
237
1−x2/6 and has zeros at x = n with n = 1,2,3, . . .. Small local maxima
238
occur at x= (n+ 1/2)·Pω, but dwindle quickly in amplitude. Therefore, t95
239
should be shorter than 1 hours in order to achieve a decent recording fidelity
240
to an external variation ofPω = 4 h. At a cooling rate of 10◦C/hr, this can be
241
achieved with blocking temperatures within ∼50◦C below Tc (Fig. 2), while
242
at 5◦C/hr, that range narrows to within∼25◦C belowTc. For TM50 particles
243
dominated by magnetoelastic anisotropy, that blocking temperature range is
244
roughly twice as broad than for magnetite particles.
245
In the flow described above (Fig. 1), the cooling rate can vary considerably
246
with temperature and vertical position. ThedT /dt(z, T) distribution is there-
247
fore plugged into Eqs. 4-6 to obtain the full range of t95 values for the flow.
248
The resulting t95(z, T) diagrams (Fig. 3) for magnetite and TM50 now show
249
the combined effect of blocking temperatue and cooling rate on the tempo-
250
ral resolution. Compared to the isallotherms in Fig. 1, the duration isochrons
251
in Fig. 3a are steeper in the high temperature range (effect of blocking tem-
252
perature on t95). Conversely, in the low-temperature range, the slope of the
253
duration isochrons is similar to that of the isallotherms, which emphasizes the
254
effect of cooling rate on t95 here. In other words, for blocking temperatures
255
well below Tc, the cooling rate limits the temporal resolution by imposing
256
longer averaging times.
257
Accepted Manuscript
It is interesting to ask how thet95distribution looks like for a flow of different
258
thickness ˜D, with ˜D = f D, which cooled under the same conditions. Since
259
the solutions of the heat equation have the form erf(z/√
4κt), we obtain
260
t95(f z, T;f D) = f2t95(ζ, T;D). (7)
261
This means that thet95values for a 40 cm thick flow are only a fourth of those
262
for the 80 cm thick flow.
263
2.3 TRM acquisition in a time-dependent field
264
Using the previous considerations about the phyiscal aspects of the blocking
265
process and the time scales involved, we can now formulate a mathematical
266
model for the thermoremanence (TRM) acquired during cooling in a time-
267
dependent magnetic field B(t). Let χ(T, z) denote the blocking temperature
268
spectrum at depth z, then the total thermoremanence (TRM) acquired be-
269
tween the Curie-temperature Tc and ambient temperature T0 at depth z > 0
270
can be written as
271
MTRM(z) =
Tc
Z
T0
χ(T, z)hB(t(T, z))it95dT, (8)
272
where hB(t(T, z))it95 is the magnetic field averaged over the 95% blocking
273
range [t(T), t(T) +t95] for a given component in the interval [T, T+dT] of the
274
blocking temperature spectrum. The time course of the cooling front (blocking
275
front),t(T, z) can be obtained by numerical inversion of the temperature pro-
276
file T(z, t) (see above, Section 2.1). The remanence remaining after thermal
277
demagnetization up to temperatureTE can be written as
278
tMTRM(z, TE) =
Tc
Z
TE
χ(T, z)hB(t(T, z))it95dT. (9)
279
Eq. 9 strictly holds for the case that the unblocking temperature Tub of each
280
partial TRM (pTRM) is equal to its blocking temperatureTb. Less ideal cases,
281
e.g., in which pTRM unblocking temperatures differ from the corresponding
282
blocking temperatures, can be treated analoguosly by adopting the Preisach-
283
type TRM model developed by Fabian (2000).
284
The time dependency of B(t) is not known, but from the modelling results
285
reviewed in the introduction, we expect a highly dynamic magnetosphere that
286
reconfigures on diurnal time scales. We use the waveform depicted in Fig. 4 and
287
Accepted Manuscript
assume that the pulse repeat period is 1 day, that is,Bω(t) =Bω(mod(t,24 h)).
288
Such waveforms are seen in magnetograms (of the H component) during a
289
magnetic storm at high geomagnetic latitudes (Bolshakova et al., 1995). We
290
scale the periodic field perturbation such that the resulting directional vari-
291
ation has a peak-to-trough amplitude of 10◦. The rate of directional change
292
amounts to 2.5◦/h at the rising slope of the wave and is maximum (10◦/h) be-
293
tween the peak and the trough. From the point of view of temporal resolution,
294
the imporant parameters now are the rise time (∼ 2 h) and the pulse dura-
295
tion (∼4 h). Given the filter properties of the blocking process (see previous
296
section), the recording of such a signal requires blocking times oft95≤1 hr.
297
Without loss of generality, we now apply this directional perturbation only
298
to the declination in order to be able to present the results in compact form.
299
Nevertheless, our simulations are based on the full vector form of Eq. 9. We
300
also use a simplfied blocking spectrum, which is uniform in T and constant
301
along the vertical profile, that is, χ(T, z) = 1/(Tc−T0) for T ∈ (T0, Tc) and
302
z ∈(0, L). This choice allow us to better isolate the role of temperature and
303
cooling rate on recording ability. The effects of a depth dependent blocking
304
temperature spectrum are of second order and will be discussed later.
305
3 Simulated demagnetization surfaces
306
Continuous thermal demagnetization surfaceD(z, TE) simulated for a vertical
307
profile of a 80 cm thick flow are shown in Fig. 5a (for magnetite) and Fig. 5b
308
(for TM50). For better comparison with experimental data (V´erard et al.
309
(2008), in this issue), we resample the demagnetization surface at discrete
310
temperature steps as shown on the right in Fig. 5.
311
Most importantly, the simulations shows that external-field variations are
312
clearly imprinted in the flow and can, in principle, be extracted paleomagneti-
313
cally. However, it is only at high unblocking temperatures or in the upper part
314
of the flow that the full peak-to-trough amplitude of the original declination
315
perturbation (10◦) and its waveform can be recovered. With lower blocking
316
temperatures and deeper positions in the flow, the recording fidelity contin-
317
uously deteriorates because of the longer averaging time experienced there
318
(compare with Fig. 3). This low-pass filtering leads to smoothed waveforms
319
(devoid of the trailing trough) and subdued amplitudes. As a consequence, the
320
periodic signal variations would not be recognizeable when just plotting the
321
total TRM as a function of depth coordinate. This means that closely spaced
322
thermal demagnetization steps at high unblocking temperatures are needed to
323
isolate the field variation of external origin.
324
Each trapped magnetic perturbation event leaves a characteristic fingerprint in
325
Accepted Manuscript
the thermal demagnetization surface by tracking a particular cooling isochron.
326
This produces a systematic ”‘phase shift”’, which becomes more pronounced
327
in the middle part of the flow, where cooling isotherms and isochrons become
328
steeper. In the z −T range below the white stippled line in Fig. 1, cooling
329
isotherms and isochrons are directed downward since heat is still transported
330
into the underlying flow unit. When an event is frozen in at the right time,
331
it can thus be recorded simultaneously in two parts of the the flow, along
332
the upper and lower branch of the same cooling isochron (see Fig. 5a). The
333
recording on the lower branch is mirror symmetric to the one on the upper
334
branch.
335
As far as the difference between a high-Tc phase (magnetite, Fig. 5a) and
336
an intermediate-Tc phase (TM50, Fig. 5b) are concerned, it can be observed
337
that five events (over five consecutive days) are trapped when TM50 is the
338
remanence carrier (compared to two events plus a mirrored one in the case
339
of magnetite). The higher number of events recorded with TM50 is due to
340
the fact that the first blocking sets in much later than in magnetite, that is,
341
when slower cooling rates are prevailing and cooling isochrons are more closely
342
spaced. This, however, implies a tradeoff between number of events trapped
343
and the spatial resolution at which each individual event is sampled. Indeed,
344
the spikes in Fig. 5 are so narrow that even a sample spacing of 1 cm appears
345
too coarse. Also, the temperature range over which the events can be extracted
346
is narrower in the case of TM50, which requires finer thermal demagnetization
347
steps, or preferably, continuous thermal demagnetization.
348
3.1 Effect of flow thickness
349
Next we consider the role of flow thickness on the recording process. From
350
Eq. 7, it is obvious that the temporal resolution (and with it the spatial reso-
351
lution at which an event is sampled), is the better the thinner the flow, which
352
is due to faster cooling rates. Fig. 6 shows the thermal demagnetization sur-
353
face for a 0.4 m thick flow, with otherwise unchanged parameters compared to
354
Fig. 5. Due to the on-average faster cooling rates, only one event is captured in
355
the flow, which however is clearly expressed and can therefore be conveniently
356
extracted with a sample spacing of 1 cm. Again, the original signal amplitudes
357
are well preserved at the high-temperature end, but become subdued with de-
358
creasing temperatures. The phase shift amounts to 5 cm per 100◦C in Fig. 6a
359
and to 5 cm per 30◦C in Fig. 6b for the case of TM50.
360
However, the higher potential recording resolution in thin flows comes with
361
the risk that the flow cools through the optimum range in the T −z space
362
before the magnetic storm event sets in. The event then is recorded in a less
363
effective region of theT −z space, with a strongly damped signature (Fig. 7).
364
Accepted Manuscript
4 Discussion
365
As pointed out in Section 2.3, we deliberately used blocking spectraχconstant
366
in T and uniform over z to better bring out the first-order characteristics of
367
time-dependent TRM acquisition in lava flows. If the blocking spectrum varies
368
along the depth coordinate, the recorded field perturbations will still track
369
cooling isochrons. However, the trace of the trapped signal will be interrupted
370
in those parts of the flow where Tc is lower than the temperature that is
371
being intersected by a cooling isochron. Conversely, the amplitude of the signal
372
variation may be enhanced in the next (later) isochron that runs through
373
the high blocking-temperature range of the lower Tc phase. Either way, the
374
variation of the amplitude with depth along a given isochron is not monotonic
375
any longer.
376
It is also important to discuss the effect of a blocking spectrum that is con-
377
centrated in the high-temperature part, but vanishes elsewhere (for exam-
378
ple, due to a thermoviscous overprint, which renders the low-temperature
379
part of the spectrum useless for this kind of study). Of course, nothing will
380
change in that temperature interval where blocking occurs. However, the
381
propagation of the external perturbation through the thermal demagnetiza-
382
tion surface will come to a halt at the lowest unblocking temperature, that
383
is, tM(z, T < min(Tub)) = tM(z,min(Tub)), and therefore only the interval
384
[min(Tub),max(Tub)] remains for the identification of a periodic external sig-
385
nal, which still may be feasible, provided that fine demagnetization steps are
386
used. What is much more detrimental, of course, is the truncation of the block-
387
ing spectrum at the high-temperature side, be it due to poor TRM carriers,
388
be it due to overprint.
389
Therefore, lava flows have to be examined carefully for secondary alterations,
390
for example due to baking caused by overlying flows or to hydrothermal fluid
391
activity. Also, we have assumed that the unblocking temperature Tub of each
392
partial TRM is equal to its blocking temperatureTb. Tb depends on the orig-
393
inal cooling time, butTub in the thermal demagnetization procedure depends
394
on heating time. With laboratory heating rates of 10◦C/min and geological
395
cooling rates of 5−10◦C/hr, unblocking temperatures may be slightly, but con-
396
sistently higher than blocking temperatures (by 10◦ to 20◦C for single-domain
397
and lower pseudo-single-domain magnetite, depending on grain size and elon-
398
gation, see relaxation time vs. blocking temperature nomogram in Winklhofer
399
et al. (1997). Therefore, the effect of slightly, but consistently higher laboratory
400
heating rates than geological cooling times will not vitiate the applicability
401
of the protocol. However, the reciprocity assumption that Tub = Tb, may be
402
violated by several other effects. Although magnetite with its high Curie tem-
403
perature is the desired TRM carrier, magnetite is not the primary magnetic
404
mineral in terrestrial lava flows but form via (oxy)exsolution of primary titano-
405
Accepted Manuscript
magnetite, which may happen at temperatures below the equilibrium solvus
406
temperature. Therefore it is vital for the paleomagnetic investigation that the
407
exsolution temperatureTex is at least larger than the highest unblocking tem-
408
perature observed, max(Tub), but ideally higher than the Curie temperature.
409
If on the other hand, the exsolution happened at Tex < max(Tub), then the
410
maximum blocking temperature cannot exceed Tex and thus the reciprocity
411
assumption is violated. The original field variation in the temperature interval
412
[Tex,max(Tub)] cannot be recovered during stepwise thermal demagnetization
413
from [Tex,max(Tub)]. Thus, ore microscopic investigations are necessary to
414
identify the degree of deuteric oxidation and to determine the width of the il-
415
menite lamellae to put constraints onTex. The reciprocity betweenTb and Tub
416
will also be violated if multi-domain (MD) rather than single-domain/pseudo-
417
single-domain particles are the TRM carriers, and thermal demagnetization
418
will not reflect remanence acquisition (Fabian, 2001). Appropriate experimen-
419
tal methods like the IZZI protocol (Yu et al., 2004) or tail-check analysis
420
(Leonhardt et al., 2004) can be used to experimentally test for MD contribu-
421
tions to the TRM carrying fraction.
422
5 Conclusions
423
The magnitude of diurnal field perturbations relative to the static ground
424
field can be expected to be significantly enhanced under various transitional
425
field geometries. Here we have shown that rapidly cooling lava flows with high
426
blocking temperatures (close to the Curie temperature), have the potential
427
to record such perturbations. Since the transformation of a field perturbation
428
from the time domain into the depth domain happens along cooling isochrons,
429
a trapped perturbation has a unique fingerprint by which it can be identified
430
as a temporal field variation (as opposed to overprint). The recording process
431
is most accurate at blocking temperatures close to the Curie temperatures
432
(short blocking intervals) and for fast cooling rates, but deteriorates at lower
433
blocking temperatures and slow cooling rates.
434
To paleomagnetically extract such a signal, closely spaced samples (1 cm spac-
435
ing of 1 cm drill cores) from a vertical profile of a thin flow (∼ 50 cm) need
436
to be thermally demagnetized in small steps (15◦ at elevated temperatures).
437
The recovered directions are best represented in the form of a thermomagnetic
438
surface, which allows one to test if directional variations vary systematically
439
with depth coordinate and if their amplitude grows with increasing blocking
440
temperatures.
441
The fact that large signal variations are observed mainly at high temperatures
442
should not be a serious limitation to a paleodirectional study, provided that the
443
real flow has high blocking temperatures. If such variations can be recovered,
444
Accepted Manuscript
then (with the aid of a realistic cooling model) the spatial wavenumbers can be
445
translated into periods to eventually determine the time course of the external
446
field variations.
447
The experimental protocol suggested here has the robustness necessary to
448
convincingly identify rapid variations of external origin, if present in the fist
449
place and not erased by secondary processes. Although the number of suitable
450
lava flows is probably small, the prospect of experimentally reconstructing the
451
paleomagnetosphere should provide enough motivation for such studies.
452
Acknowledgements
453
The idea to this project originated on a colloquium within the DFG prior-
454
ity programme Geomagnetic Variations SPP 1042. We would like to thank
455
Joachim Vogt, Karl-Heinz Glassmeier, and Heather McCreadie for stimulat-
456
ing discussions about the paleomagnetosphere and magnetic storms. We ac-
457
knowledge two anonymous referees, whose constructive comments helped us
458
to improve the manuscript. Research was funded by the Deutsche Forschungs-
459
gemeinschaft (DFG grants Wi 1828/3-1 & 4-1).
460
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461
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