ArticlePDF Available

Abstract and Figures

The geomagnetic field is subject to possible reversals or excursions of polarity during its temporal evolution. Considering that: (a) the typical average time between one reversal and the next (the so-called chron) is around 300 000 yr, (b) the last reversal occurred around 780 000 yr ago, (c) more excursions (rapid changes of polarity) can occur within the same chron and (d) the geomagnetic field dipole is currently decreasing, a possible imminent geomagnetic reversal or excursion would not be completely unexpected. In that case, such a phenomenon would represent one of the very few natural hazards which are really global. The South Atlantic Anomaly (SAA) is a great depression of the geomagnetic field at the Earth's surface, caused by a reverse magnetic flux in the terrestrial outer core. In analogy with critical point phenomena characterised by some cumulative quantity, we fit the surface extent of this anomaly over the last 400 yr with power or logarithmic functions in reverse time, also decorated by log-periodic oscillations, whose final singularity (a critical point tc) reveals a great change in the near future (2034 ± 3 yr), when the SAA area reaches almost a hemisphere. An interesting aspect that has been recently found is the possible direct connection between the SAA and the global mean sea level (GSL). That the GSL is somehow connected with SAA is also confirmed from the similar result when an analogous critical-like fit is performed over GSL: the corresponding critical point (2033 ± 11 yr) agrees, within the estimated errors, with the value found for SAA. From this result, we point out the intriguing conjecture that tc would be the time of no return, after which the geomagnetic field could fall into an irreversible process of a global geomagnetic transition that could be a reversal or excursion of polarity.
Content may be subject to copyright.
Nat. Hazards Earth Syst. Sci., 13, 3395–3403, 2013
© Author(s) 2013. CC Attribution 3.0 License.
Natural Hazards
and Earth System
Open Access
Toward a possible next geomagnetic transition?
A. De Santis1,2, E. Qamili1, and L. Wu3,4
1Istituto Nazionale di Geofisica e Vulcanologia, Sezione Roma 2, Roma, Italy
2Università “G. D’Annunzio”, Campus Universitario, Chieti, Italy
3Northeastern University, Shenyang, China
4China University of Mining and Technology, Xuzhou, China
Correspondence to: A. De Santis (
Received: 12 June 2013 – Published in Nat. Hazards Earth Syst. Sci. Discuss.: 27 September 2013
Revised: – – Accepted: 28 November 2013 – Published: 23 December 2013
Abstract. The geomagnetic field is subject to possible rever-
sals or excursions of polarity during its temporal evolution.
Considering that: (a) in the last 83 million yr the typical av-
erage time between one reversal and the next (the so-called
chron) is around 400000yr, (b) the last reversal occurred
around 780000yr ago, (c) more excursions (rapid changes
in polarity) can occur within the same chron and (d) the geo-
magnetic field dipole is currently decreasing, a possible im-
minent geomagnetic reversal or excursion would not be com-
pletely unexpected. In that case, such a phenomenon would
represent one of the very few natural hazards that are re-
ally global. The South Atlantic Anomaly (SAA) is a great
depression of the geomagnetic field strength at the Earth’s
surface, caused by a reverse magnetic flux in the terrestrial
outer core. In analogy with critical point phenomena charac-
terized by some cumulative quantity, we fit the surface ex-
tent of this anomaly over the last 400yr with power law or
logarithmic functions in reverse time, also decorated by log-
periodic oscillations, whose final singularity (a critical point
tc)reveals a great change in the near future (2034±3yr),
when the SAA area reaches almost a hemisphere. An inter-
esting aspect that has recently been found is the possible di-
rect connection between the SAA and the global mean sea
level (GSL). That the GSL is somehow connected with SAA
is also confirmed by the similar result when an analogous
critical-like fit is performed over GSL: the corresponding
critical point (2033±11yr) agrees, within the estimated er-
rors, with the value found for the SAA. From this result, we
point out the intriguing conjecture that tcwould be the time
of no return, after which the geomagnetic field could fall into
an irreversible process of a global geomagnetic transition that
could be a reversal or excursion of polarity.
1 Introduction
The magnetic field of the Earth changes in time and space,
in an irregular fashion, including dramatic manifestations
such as the geomagnetic reversals or excursions, when the
magnetic polarities exchange in sign, so that the geomag-
netic south becomes north and vice versa (e.g., Jacobs, 1994).
Over the last 83 million years we count 184 reversals (Cande
and Kent, 1995). From the facts that: (a) the typical average
time between a reversal and another (the so-called chron)
is around 400000yr, (b) the last reversal occurred around
780000yr ago, (c) more excursions (rapid changes in polar-
ity) can occur within the same chron and (d) the geomagnetic
field dipole is currently decreasing, a possible imminent geo-
magnetic reversal or excursion would not be completely un-
expected. Such a phenomenon would represent one of the
very few natural hazards that are really global, because it
would affect the whole globe, although the detailed conse-
quences over the planet, in general, and the biosphere, in par-
ticular, are not completely known. For instance, we recall a
presumed link with mass extinctions (Raup, 1985; Courtillot
and Besse, 1997; but see also Constable and Korte, 2006).
In the last 25yr, some papers have appeared suggesting
that an imminent reversal could occur (e.g., De Santis et
al., 2004 and the references therein). The recent dipole de-
crease is considered part of a trend that has continued for
the last 2000yr (Merrill and McElhinny, 1983) and a more
rapid poleward drift of the dipole axis in the past 50yr has
also been suggested (Amit et al., 2010). Analyzing the past
150yr of magnetic data, a more significant decay of the ge-
omagnetic dipole intensity was found (Gubbins, 1987; Gub-
bins et al., 2006), much faster than the rate of free decay
Published by Copernicus Publications on behalf of the European Geosciences Union.
3396 A. De Santis et al.: Toward a possible next geomagnetic transition?
in the Earth’s core (Olson and Amit, 2006). Most of this
decay stems from the Southern Hemisphere, as shown by
Gubbins (1987), who also suggested a direct correlation be-
tween the dipole decrease and the westward movements of
a pair of reverse fluxes under South Africa. Other studies
(e.g., Hulot et al., 2002; Constable, 2011) confirm the pres-
ence, at the core mantle boundary (CMB), of two reverse
flux features: in particular, one is placed inside the tangent
cylinder near the North Pole and the other is a large reverse
flux patch under the Southern Atlantic that has been asso-
ciated with the rapid decay of the field strength. Other au-
thors have concentrated their studies on understanding the
mechanism of magnetic polar reversals in dynamo numerical
models (e.g., Glatzmaier and Roberts, 1995). Flux patches
of reversed polarity appear at low or mid latitude prior to a
reversal and then migrate polewards, thus reducing the ax-
ial dipole component (Wicht and Olson, 2004; Takahashi et
al., 2005; Aubert et al., 2008; Wicht et al., 2009; Wicht and
Christensen, 2010; Christensen, 2011). All these results are
in agreement with early stages of a dipole collapse in the nu-
merical dynamo model by Olson et al. (2009). In a detailed
study of the Matuyama–Brunhes polarity reversal (Leonhardt
and Fabian, 2007) and Laschamp excursion (Leonhardt et al.,
2009) the field instability starts when reverse flux patches ap-
pear in low or mid latitude regions at the CMB and then move
poleward. In contrast, Aubert et al. (2008) found a mixed be-
havior, with reversals and excursions initiated by reversed
flux generated both outside and inside the tangent cylinder.
The same authors suggested that the appearance of the South
Atlantic reversed flux patch could be attributed to a reverse
magnetic anticyclone supplied by a strong equatorial mag-
netic upwelling.
The most recent geomagnetic dipole field is decreasing
very rapidly and its temporal linear extrapolation would pre-
dict a null field at around 1000yr from now. In some parts
of the Earth’s surface this zero value would be reached even
earlier since this field is more complex than a pure dipolar
field: for instance, in the polar regions the field would be zero
in around 300yr (De Santis, 2007). Some other papers (De
Santis et al., 2004; De Santis and Qamili, 2008, 2010a) have
found clear evidence for a chaotic state of the present geo-
magnetic field. De Santis (2007, 2008) calculated the Shan-
non information, which is a measure of the spatial order, for
the field of the last 400yr. He found that the Shannon in-
formation started to decay from around 1690, and began to
decrease more rapidly at around 1775 and even more rapidly
after 1900, revealing that the field is increasing its overall
complexity. The author also found that some parts of the
globe (e.g., Antarctica) contribute more than others to this
trend, in agreement with what was found by Gubbins (1987).
All these aspects can be interpreted as a sign that the
Earth’s magnetic field might be in the early stage of a re-
versal (Hulot et al., 2002; De Santis et al., 2004; but see also
Constable and Korte, 2006). Other authors, studying the fu-
ture evolution of the field from numerical dynamos, use more
caution in interpreting these results (Hulot et al., 2010). Ana-
lyzing the exponential growth of errors in numerical models,
these authors concluded that predictions for the next reversal
will not be possible for more than one century, although bet-
ter predictions for the evolution of the field in the near future
could be possibly made.
Recently, De Santis and Qamili (2010b) focused their at-
tention on the South Atlantic Anomaly (SAA), which is a
great depression of the geomagnetic field at the Earth’s sur-
face. These authors proposed a simple model to represent the
dynamics of this feature in terms of an apparent monopo-
lar magnetic source moving at the top of the outer core. In
practice, under the frozen flux approximation in the outer
core (strong coupling between material motions and mag-
netic fields), this would represent the magnetic expression
of a vortex in the outer core, as a component of a strong
magnetic flux with reversed polarities with respect to the
surroundings. The origin of the SAA can be either due to
a decrease in the whole geomagnetic field strength or in the
dipole field, which are two typical ingredients for a possible
geomagnetic reversal. Another cause could be an increase in
the field complexity, i.e., an increase (decrease) in the corre-
sponding Shannon entropy (information), which has been re-
cently revealed as another important ingredient for a possible
polarity change (De Santis et al., 2004; De Santis and Qamili,
2008). Therefore, we could postulate that a possible immi-
nent reversal would be preceded by a significant increase in
the reversed magnetic flux in the CMB, and in turn at the
Earth’s surface, in the SAA area. In this paper we study the
surface extension of this anomaly over the last 400yr. In par-
ticular we analyze the variation in space and time of the area
included by the 32000nT isoline as deduced from GUFM1
(1590–1990; Jackson et al., 2000) and IGRF-11 (1900–2010;
Finlay et al., 2010) global models of the geomagnetic field.
The combined time series was obtained with a point every
5 yr taking the values from GUFM1 in the period 1590–1955,
and IGRF-11 afterward (at 1960 the two models agree quite
well). Then we will fit it with a nonlinear function usually
characterizing a system under a significant change of state,
the so-called “critical” or “tipping point”. The 32 000nT iso-
line was chosen as a reference because it is the lowest value
in the time interval of study, so it is easy to follow the in-
crease in the SAA extent with time. In the GUFM1 model
this isoline appears at the beginning of the interval of the
model validity; some recent papers (Gubbins et al., 2006;
Finlay, 2008) have cast some doubts on the validity of the
back linear extrapolation in time of the g0
1coefficient (related
to the axial dipole of the field) before 1840, which is just af-
ter the time Gauss introduced an absolute method to measure
the geomagnetic field intensity in 1832 (Malin, 1982). In the
following we will denote with GUFM1-G and GUFM1-F the
two models derived from the suggestions given by Gubbins
et al. (2006) and Finlay (2008), respectively, whose models
differ from GUFM1 mainly in the values of g0
1before 1840
(the other Gauss coefficients are just rescaled appropriately).
Nat. Hazards Earth Syst. Sci., 13, 3395–3403, 2013
A. De Santis et al.: Toward a possible next geomagnetic transition? 3397
In the next section we will introduce some concepts related to
critical point processes, i.e., dynamical systems coping with
dramatic changes of state, and then we will apply these con-
cepts to the temporal evolution of SAA area extension over
the last 400yr, together with the changes in the mean global
sea level (GSL) as provided by Jevrejeva et al. (2008) and
Church and White (2011) (but for an alternative view on GSL
please see Mörner, 2004, 2010). The comparison between
SAA and GSL is important because an unexpectedly close
correlation between these quantities has recently been found
(De Santis et al., 2012). Our joint analysis will confirm the
existence of a tipping point for both time series. Finally we
will present some conclusions and discussions.
2 Critical point processes and critical time
Many complex systems have “critical” thresholds (the so-
called critical or tipping points) at which the system moves
abruptly from one state to another, i.e., shifts toward a crit-
ical transition (Scheffer, 2009); the corresponding times are
also called critical times. In the literature we can find differ-
ent methods for scientific predictions of catastrophic events
based on the concepts of non-linear physics (e.g., Bunde et
al., 2002; Dakos et al., 2012). A way to attempt to recognise
these critical transitions is to detect some early warnings that
may anticipate them (Scheffer et al., 2009). This strategy has
been applied in ecology, medicine and global finance (May
et al., 2008). Another approach is related to the critical point
hypothesis for processes usually characterized by some cu-
mulative critical quantity. This approach has also found ap-
plications in such different fields as: climate dynamics, seis-
mology, material rupture, financial crashes, etc. (Sornette,
2003). It is important to note that the critical point hypoth-
esis can be used when the system is close to or moving to-
ward a critical state, in analogy with a phase transition (e.g.,
Stanley, 1971), and the capability to predict the critical point
generally improves as the latter is more approaching. With
the term “critical” we denote the state of a system between
order and disorder, and which is strongly influenced by ex-
ternal and internal factors. Examples of systems that respond
to such characteristics are some cases of liquids and mag-
nets, but many others can be found in different disciplines
(Sornette, 2006; Scheffer et al., 2012).
In analogy with standard critical phenomena of solid state
physics, it is thought that the precursory seismicity of large
events may follow power laws or alternative diverging func-
tions in time. This approach has found more applications
in the attempt to predict large earthquakes, although mostly
from a retrospective point of view. In particular, Bufe and
Varnes (1993) and Bowman et al. (1998) suggested that the
time tcof the largest main shock of a seismic sequence is
the critical time of the seismic sequence, i.e., the time when
the system drastically changes its dynamical regime. Since
the seismological phenomena are mainly earthquakes, which
are large ruptures or failures of a part of the crust, this ap-
proach has also been called the “time-to-failure” approach.
In a broad sense, also in other occasions and fields when a
general system shifts to a critical transition, the latter event
could be considered as a failure of the system to maintain its
previous typical state; thus the term failure must be taken in
this general meaning, not implying necessarily that there is a
physical failure or rupture in the system under study. Then, a
measure y(t ) of the seismic release (e.g., the seismic defor-
mation) at any preceding time treasonably close to the time
tccan be described by a power law relation of the form:
y(t ) =k(tct)n(1)
where k > 0 and 1 >n>0 are appropriate parameters.
Equation (1) is characterized to have a singularity at t=tc
because y(tc)= ∞. In practice, in seismology it is preferred
to integrate Eq. (1) in time to use a cumulative function s(t)
of y(t ), in order to have a finite value for s(tc), its time deriva-
tive being singular, i.e., the slope of the function s(t ) at tcis
vertical. In this way, we have:
s(t ) =Zy(t)dt=ak
m(tct)m=a+b(tct )m(2)
where a>0 is the constant of integration; b= −k/m < 0,
and m=1n > 0 are constant parameters that are found by
means of a nonlinear least regression on the available data;
m, normally 0.2<m<0.6 (Mignan, 2011), is a critical expo-
nent that represents the degree of accelerating energy release
(De Santis et al., 2010). It is clear that ais the value of the
measure related to the cumulative seismic release at the crit-
ical time, i.e., a=s(tc). In addition to the accelerating strain
release in Eqs. (1) or (2), Sornette and Sammis (1995) pro-
posed an extension of this method, finding a better fit to the
time of occurrence of large seismic events by fitting a func-
tion that included a log-periodic fluctuation:
s(t ) =a+b(tct)m·{1+d·cos[2πf ln(tct ) +ϕ]}(3)
where dis the magnitude of the fluctuations around the ac-
celeration growth, fis the frequency of the fluctuations, ϕis
the phase shift, and tcis the critical time. Note that for d=0
we have the simple power law as in Eq. (2). The equations
from Eqs. (1) to (3) have also been applied in analyzing fi-
nancial crises (Sornette, 2003).
An alternative form of diverging functions in time is that
of considering just a logarithmic function in (reversed) time
(e.g., Vandewalle et al., 1998):
s(t ) =A+Bln(tct) (4)
where A>0 and B<0 (and tc)are parameters to be found
from the experimental data, thus reducing the unknown pa-
rameters from four of Eq. (2) to only three. With respect to
Eq. (2), but as for Eq. (1), the price to pay of Eq. (4) is that
we have s(tc)= ∞ at t=tcand A=s(tc1). Since in our Nat. Hazards Earth Syst. Sci., 13, 3395–3403, 2013
3398 A. De Santis et al.: Toward a possible next geomagnetic transition?
Fig. 1. Extension of the SAA over the last 400yr and the best non-
linear fit of the function indicated in the text as Eq. (5). The “critical
time” tcwould be 2034±3 yr,where the curve will have a singular-
ity, i.e., where the curve is tangent to the vertical dashed line drawn
at the critical time in the smaller picture. Our interpretation is that
this time will represent the time of no return for a great change in the
geomagnetic field, possibly going toward a reversal or excursion. In
the inset table, DoF are the degrees of freedom and ris the correla-
tion coefficient of the nonlinear fit; for the other fitting parameters
see the text.
calculations the time is in years, the value of Ais a good ap-
proximation of the actual value that the quantity under study
will take close to its critical time (i.e., just one year before).
Equation (4) is the time integral of the limiting case of Eq. (1)
with n=1, and Ais the constant term of integration. The cor-
responding log-periodic form can be written as (e.g., Vande-
walle et al., 1998):
s(t ) =A+Bln(tct)·{1+D·cos[2πf ln(tct ) +ϕ]}.(5)
Note that for D=0 we have simple logarithmic divergence
as in Eq. (4).
It is clear that the “integral” Eqs. (2)–(5) are more appro-
priate than Eq. (1) for SAA and GSL, because they are all
cumulative processes as the seismic deformation for which
some of those equations had been introduced.
The quality of the acceleration toward the critical point can
be evaluated by the Cfactor (Bowman et al., 1998), which
measures the ratio between the root mean squares (rms) of
the diverging function (rmsdf)and the rms of the best fit line
rmsline =s1r2
line (6)
where ris the correlation coefficient of the corresponding
fit. The lower than 1 the Cfactor is, the greater (and more
significant) the acceleration toward the critical point is.
In the next section we will analyze the SAA at the Earth’s
surface, because the geomagnetic field is known there and
Fig. 2. Global sea level (GSL) rise and its best log-periodic fit with
Eq. (5). The critical time (2033±11 yr indicated by the vertical
dashed line in the smaller picture) within the given error is the same
as that estimated for the SAA. In the inset table, DoF are the degrees
of freedom and ris the correlation coefficient of the nonlinear fit;
for the other fitting parameters see the text.
any global model is more reliable at the Earth’s surface than
at that extrapolated at the CMB, where the main sources of
the geomagnetic field are placed (e.g., Merrill and McEl-
hinny, 1983): the higher harmonics, which are typically mea-
sured at the surface with a low signal-to-noise ratio, are
greatly amplified together with their errors, when extrapo-
lated downward to the CMB, contaminating any final rep-
resentation of the field at that depth (Lowes, 1974). In the
Appendix we show that the critical time tcfor the SAA is as
important at the Earth’s surface as at the CMB.
3 Application to SAA and GSL data and interpretation:
a great planetary change?
We applied all possible functions given by Eqs. (1)–(5) over
the SAA and GSL data. In our study the log-periodic ap-
proach Eq. (5) has shown the best fit over the available data
with respect to the other possible functions in terms of the
lowest χ2and the highest correlation coefficient r. Figures 1
and 2 show the corresponding results for SAA and GSL, re-
spectively. A low Cfactor (0.18 and 0.48 for SAA and GSL,
respectively) confirms a significant acceleration toward the
critical point. When we compare the couples of the same fit-
ting parameters with each other, the agreement is astonishing
for most of them: in particular, the critical time tcis prac-
tically the same (around 2034±3yr and 2033±11yr, for
SAA and GSL, respectively; please note that the indicated
errors are only statistical because they could be up to two
times greater, Gross and Rundle, 1998); when the fit is ap-
plied to GUFM1-G and GUFM1-F the results change a little,
with a critical time ranging from 2014 to 2027. In the above
Nat. Hazards Earth Syst. Sci., 13, 3395–3403, 2013
A. De Santis et al.: Toward a possible next geomagnetic transition? 3399
analyses we did not consider any error in the SAA area esti-
mates. Defining an accurate error budget for the area of the
SAA is not possible.
Not only has one to find what the accuracy of the Gauss
coefficients is, but one also has to estimate what the contri-
butions of the unknown small scales of the magnetic field
are. One also has to estimate what effect the regularization
process (if present) applied for deriving magnetic field mod-
els from geomagnetic data has on the SAA area. Neverthe-
less we expect that the greatest contribution will come from
the Gauss coefficient errors, so we try to take them into ac-
count in a simple way. Likely, errors in the Gauss coeffi-
cients change with time, say from 10% at the beginning of
the considered time interval and 1% in more recent times,
so we cannot be too wrong in supposing an average crude
error budget of 5% to propagate with the same percentage
to the SAA area values. When these errors are considered in
a weighted log-periodic fit the results (not shown here) are
not significantly different from those above (in particular, we
find a critical time of 2042). Therefore, in all cases a criti-
cal process is still compatible with model data. This means
that the overall trend that underlies both quantities (SAA and
GSL) is something real and not an artefact. This confirms
the choice of De Santis et al. (2012) to make the compari-
son of SAA and GSL (in terms of Spearman rank correlation
and relative entropy) without removing any trend (although,
when removing a trend and normalizing both time series to
unitary standard deviation, correlation still remains signifi-
cant, with the Pearson correlation coefficient r=0.62 and
P < 0.0001; this correlation increases much more when we
consider more recent data after 1800, reaching r=0.94 and
P < 0.0001). The low values of χ2/DoF (degrees of free-
dom) and the high values of the correlation coefficient r(for
both quantities r>0.98), with respect to the corresponding
fit, indicate that the acceleration of both SAA and GSL is un-
likely to be a mere coincidence, and that they are, rather, in-
dications of some physical underlying critical point process.
Also, the Dand fparameters are very similar in both SAA
and GSL, indicating that the fluctuations affect the acceler-
ation in almost the same way in both physical quantities. In
addition, it is interesting to note that the critical time of the
SAA will be almost the time at which the SAA area, i.e., the
parameter A, will cover a hemisphere: because of the valid-
ity of Eqs. (A2) and (A3), this is limited not only to the field
at the Earth’s surface, but would also be at the CMB, where
A0of Eq. (A4) will cover more than half of the core sur-
face. Since the SAA is usually considered the manifestation
at the Earth’s surface of a reversal magnetic flux produced at
the CMB (e.g., Hulot et al., 2002), the epoch when the SAA
may reach the area corresponding to the surface of half the
planet is a critical moment for the present geomagnetic field.
This time is not the time of the eventual geomagnetic rever-
sal, but we interpret it as the time of the point of no return,
after which the geomagnetic field could fall in the process
of a global geomagnetic transition, which could be a rever-
sal or excursion of polarities. How long after the critical time
tcthis transition will occur cannot be fully established, be-
cause what we predict is a time when the dynamical system
reaches its critical state, after which any successive time is
a potential candidate for the actual start of the reversal or
excursion. Why GSL also shows the same overall trend with
similar parameters is a question that deserves further scrutiny
and is left to future work. What we can speculate now is that
when GSL reaches its critical point it will correspond to a
significant coverage of many present coasts, implying a big
change in the land–ocean system. In addition, the similarities
found in both SAA and GLS confirm that the two quantities
are really closely related, and, if the interpretation of an im-
minent geomagnetic field reversal is correct, this would once
more support the internal hypothesis indicated among other
possibilities in De Santis et al. (2012).
4 Conclusions
In this work we analyze both SAA and GSL overall trends
in the last few centuries, finding an astonishing similarity,
further confirming previous results (De Santis et al., 2012).
These similar trends can be explained by the theory of the
critical point processes for which each dynamical system is
close to or is going toward a critical point, when the system
will undergo a dramatic change in its macroscopic proper-
ties. This interpretation comes from the analysis of the SAA
behavior, for which the critical time tcwould correspond to
practically the time at which the SAA area will exceed the
extent of a hemisphere. Since SAA is a superficial manifes-
tation of a reverse magnetic flux at the CMB, this time will
be the time of no return after which the geomagnetic field
will go to a significant transition reverse in polarity, such as a
geomagnetic excursion or a complete geomagnetic reversal.
A similar dramatic change would have to occur in the
oceans, although no clear information can be obtained from
the present work. Regarding this, only some questions can
be asked: would the entire Earth or most of it be flooded?
This seems not to be the case, because from a simple calcula-
tion (Woo, 2011), the predicted sea level rise of around 0.5m
higher than the present value (at time tc1) will cause about
3km of present coasts to be covered by water. Nevertheless,
if this is the case, the consequences will be very dramatic as
well (let us think of the many cities and mega-cities that are
close to the coasts). Or would the GSL suddenly collapse? Or
would the GSL’s abrupt increase imply an enormous change
in the land–ocean system? Or what else? In this sense, if the
model we propose for both SAA and GSL is correct, what is
in preparation will be a really global change, and many more
parts of the planet could be involved, humankind included.
Of course, this interpretation must be taken with some cau-
tion at least for three reasons, so that it will need further in-
vestigation in the coming years. First, the SAA surface in the
most recent years seems to deviate slightly from the overall Nat. Hazards Earth Syst. Sci., 13, 3395–3403, 2013
3400 A. De Santis et al.: Toward a possible next geomagnetic transition?
fit, although this could simply be due to some edge effects in
the IGRF-11 model construction that we used for the most
recent years. Second, because of its intrinsic chaotic char-
acteristics (De Santis et al., 2004), the time of predictability
of the geomagnetic field is comparable with the remaining
time to the predicted tc(e.g., De Santis et al., 2004; Hulot et
al., 2010). Thus, the prediction of the critical time should be
updated again as soon as more SAA and GSL data become
available, since any prediction based on a log-periodic func-
tion such as Eq. (5) is not stable when we are far from the
critical time, but improves its quality of prediction as soon as
we are closer to tc(e.g., Brée and Joseph, 2013). The study
of the diverging function parameters at successive predic-
tions/times together with the use of the Cfactor will also
allow one to investigate any deviation of the real behavior
from the prediction, and possibly to detect a change from the
present “catastrophic” trend: any departure from the behavior
predicted so far would be seen in terms of significant increase
of both tcand the Cfactor. Third, both SAA and GSL can
also be well fitted by some higher degree polynomial: for ex-
ample, a quintic polynomial (containing the same number of
unknown coefficients of our log-periodic function) provides,
in terms of r2and χ2/DoF, a fitting quality similar to that
obtained by the log-periodic function, although, of course,
the found polynomial behaves unrealistically outside the data
range, thereby excluding its use for forecasting purposes.
Now one might ask why we are able to predict the point
of no return from just a few hundred years of a phenomenon
that usually lasts several thousand years (Jacobs, 1994; but
see also Nowaczyk et al., 2012, where the Laschamp excur-
sion seems to change the geomagnetic polarity in a few hun-
dred years), i.e., with some analysis based on data taken over
a temporal window much shorter than the typical timescales
of the reversal or excursion process. A simple answer is that
we are analyzing a sufficient (although short) time before the
eventual critical transition: we believe that the recent accel-
eration of both SAA and GSL is nothing casual, but probably
uncovers important physical information regarding the future
of our planet in the near future, such as a possible precursor
to the eventual close critical transition of the geomagnetic
Appendix A
This appendix has the aim of showing that the results ob-
tained by means of analyses made on the SAA at the Earth’s
surface are equivalent to those made at the CMB, where the
main sources of the geomagnetic field are placed, but where
any extrapolation is difficult or even impossible.
However complicated the geomagnetic field may be at
the SAA within the 32000nT isoline, we can define a frus-
tum of quasi-cone that is confined by the lower surface
S(rCMB)at the CMB, i.e., at r=rCMB =3485 km and the
upper surface S(r0)of the SAA at the Earth’s surface, i.e., at
Fig. A1. The magnetic flux crossing both the core mantle bound-
ary (CMB) and South Atlantic Anomaly (SAA) is conserved. Thus
analyses on the SAA at the Earth surface are equivalent to those
made at the CMB.
r=r0=6371 km (Fig. A1); the lateral surface is here called
Sl. The lower surface S(rCMB)at the CMB is representative
of some typical isoline enclosing the reverse magnetic flux
(we will come back to this in the final part of the Appendix).
The divergence-free condition of the geomagnetic field
imposes a null flux through the surfaces bounding the vol-
ume :
8[S(rCMB)] − 8[S(r0)] − 8[Sl] = 0 (A1)
where 8[Si]is the magnetic flux across the surface Si(where
Siis S(r0)or S (rCMB)or Sl)that can be expressed as follows:
8[Si] = ZBi·ndSi=BicosδSi
where Bicosδis the mean component of the field perpendic-
ular to the surface Si(δis the angle between the vector field
Band the vector nnormal to Si). For the geometry of the
quasi-conical volume, Bicosδwill be Zfor the upper SAA
and the lower surface at the CMB, while it will be a compo-
nent in the horizontal plane for the lateral surface Sl. We can
safely neglect the flux across the lateral surface Slof ; thus
Eq. (A1) becomes:
Z(rCMB)S(r0)=γ S (r0),
where the γratio
γ=Z(r0)/Z(rCMB)=S (rCMB)/S(r0)(A3)
Nat. Hazards Earth Syst. Sci., 13, 3395–3403, 2013
A. De Santis et al.: Toward a possible next geomagnetic transition? 3401
Fig. A2. Surface enclosed by the isoline 200000 nT at the CMB
for an expansion of GUFM1 up to the spherical harmonic degree
N=3 and N=4. Both trends are almost monotonic and diverging
in time. A log-periodic function with critical (a priori fixed) time of
2034 yr is a reasonable fit for both cases.
can be taken as constant in time. This means that an equation
of the same form as Eq. (4) (but this would also be valid for
Eq. 5) can also be written for s0(t) of S(rCMB):
s0(t) =A0+B0ln(tct), (A4)
with A0=γ A and B0=γ B. Thus, the results we find at the
Earth’s surface are also representative of the deep dynamics
of the geomagnetic field; in particular, the critical time tces-
timated at the Earth’s surface will also be the same for the
Unfortunately it is difficult to verify the constancy of γ
with any global model (such as GUFM1) that is based on ob-
servational data taken at the Earth’s surface. This difficulty is
twofold: (i) the area S(rCMB)is impossible to determine, and
(ii) it is difficult or even impossible to estimate Z(rCMB)be-
cause of the eventual explosion of errors when continuing the
vertical component from the Earth’s surface to the CMB, be-
cause of their multiplication by a factor [r0/rCMB]n+2(nis
here the spherical harmonic degree of the geomagnetic field
To reasonably circumvent most of the problems, we can
simply look at an isoline at the CMB that could act as the
32 000 nT at the Earth’s surface. By applying a simple dipolar
downward continuation of the 32 000nT isoline to CMB (just
multiplying by [r0/rCMB]3)we obtain about 200 000 nT.
Therefore, looking at the surface enclosed by the latter iso-
line at the CMB for an expansion of the GUFM1 model up to
N=3 and N=4 (Fig. A2), we notice an almost monotonic
trend for both cases where a log-periodic behavior pointing
to a critical (a priori fixed) time of 2034 is something really
possible (Cfactor is always much less than 1 for both cases:
0.52 and 0.23 for N=3 and 4, respectively). By the way, the
area of the enclosed surfaces 1yr before the critical time for
N=3 and N=4 are 64 % and 84%, respectively, so in both
cases the surface of this isoline at the critical time will cover
more than half of the entire core surface. We limit our anal-
ysis made at the CMB to N=4, because for larger values of
N, the expected downward continuation errors would be too
large to reliably detect the 200000 nT (or any other) isoline.
Acknowledgements. Part of this work has been realised in the
frame of the SAGA-4-EPR project co-funded by the Italian Foreign
Office, the Istituto Nazionale di Geofisica e Vulcanologia (Italy)
and Northeastern University of Shenyang (China). We thank
G. Hulot, G. Balasis and P. Lurcock, whose constructive comments
helped us to improve a preliminary version of this manuscript.
We also thank two anonymous referees for their comments and
Edited by: R. Lasaponara
Reviewed by: two anonymous referees
Amit, H., Leonhardt, R., and Wicht, J.: Polarity reversals from
paleomagnetic observations and numerical dynamo simulations,
Space Sci. Rev., 155, 293–335, 2010.
Aubert, J., Aurnou, J., and J. Wicht, J.: The magnetic structure
of convection-driven numerical dynamos, Geophys. J. Int., 172,
945–956, 2008.
Bowman, D. D., Ouillon, G., Sammis, C. G., Sornette, A., and Sor-
nette, D.: An observational test of the critical earthquake concept,
J. Geophys. Res., 103, 24359–24372, 1998.
Brée, D. S. and Joseph, N. L.: Testing for financial crashes using the
log periodic power law model, International Review Financial
Analysis, 30, 287–297, 2013.
Bufe, C. G. and Varnes, D. J.: Predictive modelling of the seismic
cycle of the Greater San Francisco Bay region, J. Geophys. Res.,
98, 9871–9883, 1993.
Bunde, A., Kropp, J., and Schellnhuber, H. J.: The Science of Dis-
asters. Climate disruptions, heart attacks, and market crashes,
Springer Berlin, 2002.
Cande, S. C. and Ken, D. V.: Revised calibration of the geomag-
netic polarity timescale for the late Cretaceous and Cenozoic, J.
Geophys. Res., 100, 6093–6095, 1995.
Christensen, U. R.: Geodynamo models: Tools for understanding
properties of the Earth’s magnetic field, Phys. Earth Planet. Int.,
187, 157–169, 2011.
Church, J. A. and White, N. J.: Sea-level rise from the late 19th to
the early 21st century, Surv. Geophys., 32, 585–602, 2011. Nat. Hazards Earth Syst. Sci., 13, 3395–3403, 2013
3402 A. De Santis et al.: Toward a possible next geomagnetic transition?
Constable, C. G.: Modelling the geomagnetic field from syntheses
of paleomagnetic data, Phys. Earth Planet. Int., 187, 109–117,
Constable, C. G. and Korte, M.: Is Earth’s magnetic field reversing?,
Earth Planet. Sci. Lett., 246, 1–16, 2006.
Courtillot V. and Besse J.: Magnetic Field Reversals, Polar Wander,
and Core-Mantle Coupling, Science, 237, 1140–1145, 1987.
Dakos, V., Carpenter, S. R., Brock, W. A., Ellison, A. M., Guttal, V.,
Ives, A. R., Kéfi, S., Livina, V., Seekell, D. A., van Nes, E. H.,
and Scheffer, M.: Methods for detecting early warnings of critical
transitions in time series illustrated using simulated ecological
data, PLoS One, 7, e41010, doi:10.1371/journal.pone.0041010,
De Santis, A.: How persistent is the present trend of the geomag-
netic field to decay and, possibly, to reverse?, Phys. Earth Planet.
Int., 162, 217–226, 2007.
De Santis, A.: Erratum to “How persistent is the present trend of
the geomagnetic field to decay and, possibly, to reverse?”, Phys.
Earth Plan. Int., 170, p. 149, 2008.
De Santis, A. and Qamili, E.: Are we going towards a global
planetary magnetic change? 1st WSEAS International Confer-
ence on Environmental and Geological Science and Engineering
(EG’08), 149–152, 2008.
De Santis, A. and Qamili, E.: Shannon information of the geomag-
netic field of the past 7000years, Nonlin. Proc. Geophys., 17,
77–84, 2010a.
De Santis, A. and Qamili, E.: Equivalent monopole source of the ge-
omagnetic South Atlantic Anomaly, Pure Appl. Geophys., 167,
339–347, 2010b.
De Santis, A., Tozzi, R., and Gaya-Piqué, L.R.: Information content
and K-Entropy of the present geomagnetic field, Earth Planet.
Sci. Lett., 218, 269–275, 2004.
De Santis, A., Cianchini, G., Qamili, E., and Frepoli, A.: The 2009
L’Aquila (Central Italy) seismic sequence as a chaotic process,
Tectonophysics, 496, 44–52, 2010.
De Santis, A., Qamili, E., Spada, G., and Gasperini, P.: Geomag-
netic South Atlantic Anomaly and global sea level rise: a direct
connection?, J. Atmos. Sol. Terr. Phys., 74, 129–135, 2012.
Finlay, C. C.: Historical variation of the geomagnetic axial dipole,
Phys. Earth Planet. Int., 170, 1–14, 2008.
Finlay, C. C., Maus, S., Beggan, C. D., Hamoudi, M., Lowes, F.
J., Olsen, N., and Thebault, E.: Evaluation of candidate geomag-
netic field models for IGRF-11, Earth Planets Space, 62, 787–
804, 2010.
Glatzmaier, G. A. and Roberts, P. H.: A three-dimensional self-
consistent computer simulation of a geomagnetic field reversal,
Nature, 377, 203–209, 1995.
Gross, S. and Rundle, J.: A systematic test of time-to-failure analy-
sis, Geophys. J. Int., 133, 57–64, 1998.
Gubbins, D.: Mechanism for geomagnetic polarity reversals, Na-
ture, 326, 167–169, 1987.
Gubbins, D., Jones, A. L., and Finlay, C. C.: Fall in Earth’s Mag-
netic Field is erratic, Science, 312, 900–902, 2006.
Hulot, G., Eymin, C., Langlais, B., Mandea, M., and Olsen, N.:
Small-scale structure of the geodynamo inferred from Øersted
and Magsat satellite data, Nature, 416, 620–623, 2002.
Hulot, G., Lhuillier, F., and Aubert, J.: Earth’s dynamo
limit of predictability, Geophys. Res. Lett., 37, L06305,
doi:10.1029/2009GL041869, 2010.
Jackson, A., Jonkers, A. R. T., and Walker, M. R.: Four centuries
of geomagnetic secular variation from historical records, Philos.
Trans. R. Soc. Lond. A, 358, 957–990, 2000.
Jacobs, J. A.: Reversals of the Earth’s magnetic field, 2nd Edition,
Cambridge University Press, Cambridge, UK, 346 pp., 1994.
Jevrejeva, S., Moore, J. C., Grinsted, A., and Woodworth, P. L.: Re-
cent global sea level acceleration started over 200years ago?,
Geophys. Res. Lett., 35, L08715, doi:10.1029/2008GL033611,
Leonhardt, R. and Fabian, K.: Paleomagnetic reconstruc-
tion of the global geomagnetic field evolution during the
Matuyama/Brunhes transition: iterative Bayesian inversion and
independent verification, Earth Planet. Sci. Lett., 253, 172–195,
Leonhardt, R., Fabian, K. Winklhofer, M. Ferk, A. Kissel, C., and
Laj, C.: Geomagnetic field evolution during the Laschamp excur-
sion, Earth Planet. Sci. Lett., 278, 87–95, 2009.
Lowes, F. J.: Spatial power spectrum of the main geomagnetic field,
and extrapolation to the core, Geoph. J. R. Astr. Soc., 36, 717–
730, 1974.
Malin, S. R. C.: Sesquicentenary of Gauss’s first measurement of
the absolute value of magnetic intensity, Philos. Trans. R. Soc.
Lond. A, 306, 5–8, 1982.
May, R. M., Levin, S. A., and Sugihara, G.: Ecology for bankers,
Nature, 451, 893–895, 2008.
Merrill, R. T. and McElhinny, M. W.: The Earth’s Magnetic Field
(Its History, Origin and Planetary Perspective), Academic Press,
San Diego, 1983.
Mignan, A.: Retrospective on the Accelerating Seismic Release
(ASR) hypothesis: controversy and new horizons, Tectono-
physics, 505, 1–16, 2011.
Mörner, N.-A.: Estimating future sea level changes from past
records, Global Planet. Change, 40, 49–54, 2004.
Mörner, N.-A.: Some problems in reconstruction of mean sea and
its changes with time, Quatern. Int., 221, 3–8, 2010.
Nowaczyk, N. R., Arz, H. W., Frank, H. W., Kind, J., and Plessen,
B.: Dynamics of the Laschamp geomagnetic excursion from
Black Sea sediments, Earth Planet. Sci. Lett., 351, 54–69, 2012.
Olson, P. and Amit, H.: Changes in earth’s dipole, Naturwis-
senschaften, 93, 519–542, 2006.
Olson, P., Driscoll, P., and Amit, H.: Dipole collapse and reversal
precursors in a numerical dynamo, Phys. Earth Planet. Int., 173,
121–140, 2009.
Raup D. M.: Magnetic Reversals and Mass extinctions, Nature, 314,
341–343, 1985.
Scheffer, M.: Critical Transitions in Nature and Society. Princeton
Univ. Press, 2009.
Scheffer, M., Bascompte, J., Brock, W., Brokvin, V., Carpenter, S.
R., Dakos, V., Held, H., van Nes, E. H., Rietkerk, M., and Sug-
ihara, G.: Early-warning signals for critical transitions, Nature,
461, 53–59, 2009.
Scheffer, M., Carpenter, S. R., Lenton, T. M., Bascompte, J., Brock,
W., Dakos, V., van de Koppel, J., van de Leemput, I. A., Levin, S.
A., van Nes, E. H., Pascual, M., and Vandermeer, J., Anticipating
critical transitions, Science, 338, 344–348, 2012.
Sornette, D.: Why stock markets crash. Critical events in complex
financial systems, Princeton Univ. Press, Oxford, 2003.
Sornette, D.: Critical Phenomena in Natural Sciences, Second Ed.
Springer, Berlin, 2006.
Nat. Hazards Earth Syst. Sci., 13, 3395–3403, 2013
A. De Santis et al.: Toward a possible next geomagnetic transition? 3403
Sornette, D. and Sammis, C.: Complex critical exponents from
renormalization group theory of earthquakes: implications for
earthquake predictions, J. Phys. I France, 5, 607–619, 1995.
Stanley, H. E.: Phase transition and critical phenomena, Clarendon
Press, New York, 1971.
Takahashi, F., Matsushima, M., and Honkura, Y.: Simulations of a
quasi-Taylor state geomagnetic field including polarity reversals
on the Earth simulator, Science, 309, 459–461, 2005.
Vandewalle, N., Ausolos, M., Boveraus, P., and Minguet, A.: How
the financial crash of October 1997 could have been predicted,
Eur. Phys. J. B., 4, 139–141, 1998.
Wicht, J. and Christensen, U. R.: Torsional oscillations in dynamo
simulations, Geophys. J. Int., 181, 1367–1380, 2010.
Wicht, J. and Olson P.: A detailed study of the polarity reversal
mechanism in a numerical dynamo model, Geochem. Geophys.
Geosyst., 5, Q03H10, doi:10.1029/2003GC000602, 2004.
Wicht, J., Stellmach, S., and Harder, H.: Numerical models of the
geodynamo: from fundamental Cartesian models to 3-D simula-
tions of field reversals, edited by: Glassmeier, K. H., Soffel, H.,
and Negendank, J. F. W., Geomagnetic field variations. Springer,
Berlin, 107–158, 2009.
Woo, G.: Calculating Catastrophe, Imperial College Press, 355 pp.,
2011. Nat. Hazards Earth Syst. Sci., 13, 3395–3403, 2013
... The rate of decrease of the field intensity during the first part of the Laschamp excursion shows a significant acceleration. This is reminiscent of the acceleration of the increase in the geographical extent of the SAA observed by De Santis et al. (2013) and which, according to these authors, would ultimately leads to the SAA extending over almost one hemisphere, setting the grounds for a geomagnetic reversal or excursion. Also, Leonhardt et al. (2009) have reconstructed the evolution of the global morphology of the geomagnetic field during the Laschamp excursion by using a Bayesian inversion of several high-resolution paleomagnetic records used in the GLOPIS-75 stack. ...
... 10 22 Am 2 , i.e., about one half of its non-transitional value, at the moment when the rate of decrease attains its maximum value. When extrapolated to the present field, at the present rate of decrease it would take some 1000 years to reach half of its value, less if an acceleration takes place, as suggested by the acceleration of the rate of the increase of the geographical extent of the SAA (De Santis et al., 2013). But, in this case, even assuming an increase of a factor of 2, which seems to be an extreme upper limit to us, some 500 years would be needed for the directional changes to start to be significant. ...
Full-text available
The rapid decrease of the geomagnetic field intensity in the last centuries has led to speculations that an attempt to a reversal or an excursion might be under way. Here we investigate this hypothesis by examining past records of geomagnetic field intensity obtained from sedimentary cores and from the study of cosmogenic nuclides. The selected records describe geomagnetic changes with an unprecedented temporal resolution between 20 and 75 kyr B.P. We find that some aspects of the present-day geomagnetic field have some similarities with those documented for the Laschamp excursion 41 kyr ago. Under the assumption that the dynamo processes for an eventual future reversal or excursion would be similar to those of the Laschamp excursion, we tentatively suggest that, whilst irreversible processes that will drive the geodynamo into a polarity change may have already started, a reversal or an excursion should not be expected before 500–1000 years.
... However, previous SAA characterizations which are useful in the context of space safety, can be improved and designed to be more useful for exploring its core dynamical origin. In this paper, we will show that SAA area estimates based on a fixed threshold (De Santis et al. 2013;Pavón-Carrasco and De Santis 2016;Campuzano et al. 2019) are affected by global variations and as such might not represent adequately regional morphological changes of the geomagnetic field. Furthermore, SAA center estimates based on surface minimum positions (e.g. ...
Full-text available
The South Atlantic Anomaly (SAA) is a region at Earth’s surface where the intensity of the magnetic field is particularly low. Accurate characterization of the SAA is important for both fundamental understanding of core dynamics and the geodynamo as well as societal issues such as the erosion of instruments at surface observatories and onboard spacecrafts. Here, we propose new measures to better characterize the SAA area and center, accounting for surface intensity changes outside the SAA region and shape anisotropy. Applying our characterization to a geomagnetic field model covering the historical era, we find that the SAA area and center are more time dependent, including episodes of steady area, eastward drift and rapid southward drift. We interpret these special events in terms of the secular variation of relevant large-scale geomagnetic flux patches on the core–mantle boundary. Our characterization may be used as a constraint on Earth-like numerical dynamo models.
... On the Earth's surface, the SAA is delimited by the area where the intensity of the geomagnetic field has lower values than would be predicted by a field with more symmetrical characteristics. Different authors have suggested intensity values to define the SAA limit: e.g., Hartmann and Pacca (2009) suggested the limit at 28 μT, while De Santis et al. (2013) and Pavón-Carrasco and De Santis (2016) used 32 μT in their analyses. Another way to define the SAA limit on the surface can be from the area with values lower than that predicted by an essentially dipolar and axial geomagnetic field (Hartmann et al., 2019). ...
In the depths of planet Earth there is a layer composed essentially by molten iron, which moves in a complex and constant manner on a planetary scale (Earth's outer core). This movement is responsible for the generation of the magnetic field that encompasses the planet, which in turn has (today) a predominantly dipolar geometry. Asymmetries in the dynamics of the Earth's outer core, provided by its (magneto)hydrodynamics and the physical heterogeneities of the structures above and below this fluid layer, can be observed on Earth's surface via non-dipolar features in the geomagnetic field. Studying these features is a passport to understand the unreachable interior of our planet, and some multidisciplinary correlations. For this purpose, we need to comprehend the magnetic field at present (e.g., via geomagnetic observatories and satellites), as well as its fossil record in archaeological and geological materials collected on the surface, especially in regions where non-dipolar behaviour are significantly expressed. Currently, an outstanding feature that displays a major non-dipolar contribution is mostly located over the southern portion of South America, where the intensity manifests remarkably low values – called South Atlantic Anomaly. In this context, the region of the Jequitinhonha and Mucuri river valleys (Southeast Brazil) emerges as an excellent natural laboratory since it is located within this outstanding non-dipolar feature of the modern geomagnetic field. In this article, I present a brief review of the Earth's magnetic field for the past four centuries and discuss some of its main features from the perspective of the valleys region. At the end, I emphasize the advantage of the valleys region in the study of the Earth's magnetic field in geographical, archaeological, and geological terms. This article contains an available Portuguese version in Supplementary material 1.
... Reversed flux patches are formed from the expulsion of horizontal magnetic field (e.g. Bloxham, 1986;Troyano et al., 2020) and may yield low intensity field at Earth's surface (Olson and Amit, 2006;De Santis et al., 2013;Aubert, 2015;Tarduno et al., 2015;Pavón-Carrasco and De Santis, 2016;Terra-Nova et al., 2017). Aubert (2015) assimilated historical geomagnetic data with an Earth-like numerical dynamo model. ...
It has been proposed that magnetic flux expulsion due to outer core fluid upwellings may affect the geomagnetic secular variation on the core-mantle boundary (Bloxham 1986). In this process intense horizontal field lines are concentrated below the outer boundary, introducing small radial length scales and consequently strong radial diffusion. Here we explore such magnetic boundary layers in numerical dynamo simulations with heterogeneous outer boundary heat flux inferred from a tomographic model of lower mantle seismic shear waves velocity anomalies. Our scheme associates magnetic boundary layers to peak horizontal magnetic fields at the top of the shell. In our models mean magnetic boundary layer thickness ranges ≈200 − 400 km and decreases with increasing magnetic Reynolds number. Extrapolation or interpolation to Earth's core conditions based on total core flow amplitude or its poloidal part gives mean magnetic boundary layer thickness of ≈220 and ≈260 − 330 km, respectively. We find magnetic boundary layers associated with the azimuthal field at the equatorial region, whereas magnetic boundary layers associated with the meridional field are found at mid latitudes. Negative outer boundary heat flux anomalies yield preferred locations of expulsion of azimuthal field below Africa and the Pacific, while positive outer boundary heat flux anomalies yield preferred locations of expulsion of meridional field below the Americas and East Asia. Furthermore, we find a tendency of the azimuthal field to low latitudes of the Northern Hemisphere. Our results suggest that the local diffusion time is on the order of several kyr and the local magnetic Reynolds number is on the order of ≈10, both much smaller than classical estimates.
... The fixity and existence of the SAA for times prior to the historical record remains controversial (12). Additionally, since the growth of the SAA is associated with an overall decay of the dipole field (7,(13)(14)(15), it has been interpreted by some as a precursor to a geomagnetic reversal (16)(17)(18). ...
Significance Earth’s magnetic field is generated in the outer core by convecting liquid iron and protects the atmosphere from solar wind erosion. The most substantial anomaly in the magnetic field is in the South Atlantic (SA). An important conjecture is that this region could be a site of recurring anomalies because of unusual core−mantle conditions, but this has not previously been tested on geological timescales. With paleodirectional data from rocks from Saint Helena, an island in the SA, we show that the directional behavior of the magnetic field in the SA did indeed vary anomalously between ∼8 million and 11 million years ago. This supports the hypothesis of core−mantle interaction being manifest in the long-term geomagnetic field behavior of this region.
... According to paleomagnetic data, the mean chron duration depends on the total time period, i.e. the reversals happened every about 300 kyr for the last 5 million years, every about 400 kyr for the last 83 Myr (not including the duration of CNS; e.g. De Santis et al., 2013), every about 500 kyr for the last 166 Myr. Such different estimations are probably due to the increasing of inaccuracy by enlarging the geological time and to the presence of CNS 0031-9201/Ó 2015 Elsevier B.V. All rights reserved. ...
... Due to the apparently rapid increase of this anomaly, some authors have postulated that a new reversal is impending (e.g. De Santis et al., 2013) Fig. 11. Comparison between palaeointensity data from this study and different geomagnetic field model predictions at Däbsan coordinates (12.26°N, 37.65°E). ...
Full-text available
The historical trend in the axial dipole is sufficient to reverse the field in less than 2 kyr. Assessing the prospect of an imminent polarity reversal depends on the probability of sustaining the historical trend for long enough to produce a reversal. We use a stochastic model to predict the variability of trends for arbitrary time windows. Our predictions agree well with the trends computed from paleomagnetic models. Applying these predictions to the historical record shows that the current trend is likely due to natural variability. Furthermore, an extrapolation of the current trend for the next 1 to 2 kyr is highly unlikely. Instead, we compute the trend and time window needed to reverse the field with a specified probability. We find that the dipole could reverse in the next 20 kyr with a probability of 2%.
Full-text available
An innovative information-theoretic tool, transfer entropy, has been applied to measure the possible information flow and sense between two real time series: the South Atlantic Anomaly (SAA) area extent at the Earth's surface and the Global Sea Level (GSL) rise anomalies for the last 300 years. This connection was previously suggested considering only the long term trend. Now we study the possibility of that this relation also happens in shorter scales. The new results seem to support again this hypothesis, with more information transferred from the SAA to the GSL anomalies, with about 90 % of confidence level. This could provide a new clue on the existence of a link between the geomagnetic field and the Earth's climate in the past.
Book Launch of Calculating Catastrophe Calculating Catastrophe has been written to explain, to a general readership, the underlying philosophical ideas and scientific principles that govern catastrophic events, both natural and man-made. Knowledge of the broad range of catastrophes deepens understanding of individual modes of disaster. This book will be of interest to anyone aspiring to understand catastrophes better, but will be of particular value to those engaged in public and corporate policy, and the financial markets. The author, Dr. Gordon Woo, was trained in mathematical physics at Cambridge, MIT and Harvard, and has made his career as a calculator of catastrophes. His diverse experience includes consulting for IAEA on the seismic safety of nuclear plants and for BP on offshore oil well drilling. As a catastrophist at Risk Management Solutions, he has advanced the insurance modelling of catastrophes, including designing a model for terrorism risk.
The scientific study of complex systems has transformed a wide range of disciplines in recent years, enabling researchers in both the natural and social sciences to model and predict phenomena as diverse as earthquakes, global warming, demographic patterns, financial crises, and the failure of materials. In this book, Didier Sornette boldly applies his varied experience in these areas to propose a simple, powerful, and general theory of how, why, and when stock markets crash.Most attempts to explain market failures seek to pinpoint triggering mechanisms that occur hours, days, or weeks before the collapse. Sornette proposes a radically different view: the underlying cause can be sought months and even years before the abrupt, catastrophic event in the build-up of cooperative speculation, which often translates into an accelerating rise of the market price, otherwise known as a "bubble." Anchoring his sophisticated, step-by-step analysis in leading-edge physical and statistical modeling techniques, he unearths remarkable insights and some predictions--among them, that the "end of the growth era" will occur around 2050.Sornette probes major historical precedents, from the decades-long "tulip mania" in the Netherlands that wilted suddenly in 1637 to the South Sea Bubble that ended with the first huge market crash in England in 1720, to the Great Crash of October 1929 and Black Monday in 1987, to cite just a few. He concludes that most explanations other than cooperative self-organization fail to account for the subtle bubbles by which the markets lay the groundwork for catastrophe.Any investor or investment professional who seeks a genuine understanding of looming financial disasters should read this book. Physicists, geologists, biologists, economists, and others will welcomeWhy Stock Markets Crashas a highly original "scientific tale," as Sornette aptly puts it, of the exciting and sometimes fearsome--but no longer quite so unfathomable--world of stock markets.
A three-dimensional, self-consistent numerical model of the geodynamo is described, that maintains a magnetic field for over 40,000 years. The model, which incorporates a finitely conducting inner core, undergoes several polarity excursions and then, near the end of the simulation, a successful reversal of the dipole moment. This simulated magnetic field reversal shares some features with real reversals of the geomagnetic field, and may provide insight into the geomagnetic reversal mechanism.
Scitation is the online home of leading journals and conference proceedings from AIP Publishing and AIP Member Societies
Recent studies provide evidence for a possible imminent change of polarity or an excursion of the geomagnetic field. In this paper we explore the possibility that the present trends are persistent, looking at the behaviour of some physical quantities of the recent geomagnetic field with particular attention to the last century. Analysis of the mean square value of the field over the last 400 years shows a linear decay that if extrapolated will be zero in around 1000 years, while if we extrapolate the field over Antarctica it will go to zero in around 300 years. The information content of the geomagnetic field has been decaying from around 1690, but began to decrease more rapidly at around 1775 and even more rapidly after 1900. An intermittent synchronicity between the exponential field decay and the increase latitudinal speed of the south geomagnetic pole with similar (decaying or growing) timescales can be interpreted as evidence for a present persistent turbulence of the geomagnetic field. From this work it emerges that the present situation is likely to persist further into the future, probably for another century, but longer predictions are not possible. published 217-226 3.4. Geomagnetismo JCR Journal
The geomagnetic field and its changes with time are major tools for probing the Earth’s deep interior. It is therefore particularly appropriate that the Royal Society Discussion Meeting on the Earth’s core should coincide with the 150th anniversary of the first absolute measurement of the intensity of the geomagnetic field. This was only one of Carl Friedrich Gauss’s many contributions, both direct and indirect, to geomagnetism. For example, it was Gauss who devised the methods of least squares and of spherical harmonic analysis. With Weber, he applied these to the geomagnetic field to show that it was nearly all of internal origin. Gauss was also the initiator of, and an active participant in, the ‘Gottingen Magnetic Union’, a scheme for the simultaneous observation of the magnetic field at widespread sites from which has developed the present worldwide network of magnetic observatories. The particular achievement that we commemorate here was the determination by Gauss of the horizontal intensity of the geomagnetic field in units related to the millimetre, milligram and second. (This was one tenth of the unit that subsequently bore his name.) At that time he was working towards a universal system of units for all physical quantities and conceived the original idea that magnetic intensity can be measured in terms of mass, length and time.
The history of geomagnetism and palaeomagnetism is examined, and an analysis and description of the present geomagnetic field is presented. The magnetic compass is discussed along with declination, inclination, secular variation, magnetic charts and the search for the poles, fossil magnetism and the magnetic field in the past, transient magnetic variations regarding the external magnetic field, the origin of the earth's magnetic field, magnetic elements and charts, a spherical harmonic analysis description of the earth's magnetic field, uniqueness and other mathematical problems, geomagnetic secular variation, and the external magnetic field. Other topics explored are elated to the fundamentals of palaeomagnetism, palaeomagnetic observations regarding the recent geomagnetic field, reversals of the earth's magnetic field, the time-averaged palaeomagnetic field, the origin of the earth's magnetic field, advanced dynamo theory, the origin of secular variation and field reversals, lunar magnetism, and magnetic fields of the sun, planets, and meteorites.
The hypothesis that large earthquakes may be preceded by a period of accelerating seismicity, or Accelerating Seismic Release (ASR), was proposed about twenty years ago. A compilation of almost one hundred peer-reviewed publications on this topic since the late 1980s to the present day shows that the rate of ASR studies increased gradually until 2004 but decreased afterwards. This negative trend is amplified by a recent increase in the number of negative results and criticisms of the ASR hypothesis. The author suggests that much of the recent negativity regarding this topic is due to the formulation of this hypothesis as a power-law fit to cumulative seismicity series. This approach is intrinsically linked to the consensus for criticality, evident from an overview of the ASR literature, to explain the emergence of power-laws in earthquake populations. The holistic view of the earth's crust as a complex system restricts seismicity pattern analyses to the study of main features such as power-laws, while a reductionist view would allow for more refined ones. Such a paradigm shift, or ‘sea change’, might be under way in the ASR literature where in 2007 a new approach was proposed to explain the ASR power-law from combined concepts of elastic rebound and geometry. Reductionism versus holism is a fundamental problem that not only applies to the study of ASR but also to the broader field of earthquake physics and earthquake predictability science.
Earth's magnetic field is currently decreasing, reducing the protection it offers against charged particles coming from space and increasing space weather hazards within the near-Earth environment. Modeling the future evolution of the field is thus of considerable interest. But how far in the future this can conceivably be done is still an open question. Here we report on the first systematic investigation of the limit of predictability of fully consistent 3D numerical dynamo simulations, and suggest that the Earth's dynamo is likely unpredictable beyond a century, making decade timescale forecasts of the main magnetic field conceivable, but rendering longer-term predictions, such as the timing of the next reversal, totally unpredictable.