Downloaded by guest on September 29, 2021 a 77 G 37077 Germany; reversing not Brown probably Maxwell is field magnetic Earth’s ntetoms eetecrin,teLshm at Laschamp www.pnas.org/cgi/doi/10.1073/pnas.1722110115 the analysis excursions, our data recent concentrate of most geomag- we amount two the the therefore, the of time, on decreases; evolution in spatial field back and netic temporal go reversals the approaching we field describing those As the resemble whether excursions. today infer and and see excursions we behav- and the long structures reversals investigate on past to field of is the approach ior predict alternative An yet scales. cannot time they 19), (18, development reversals/excursions for feature trigger recurrent a a and be 17). field (16, to geomagnetic suggested SAA- the LLSVP, been of African have the as of structures such longevity structures like the Given field respon- (16). geomagnetic be SAA of the may occurrence (15) the Africa velocity for wave sible southern shear below seismic low (LLSVP) Furthermore, large province long- continue the (8). to as may excursion related such (CMB) structures SAA or lived boundary 2,000 the reversal core–mantle as that the a at early suggested initiate conditions as been and perhaps has grow and It to 13) (14). (9, ago 1840 y may of volcanic before intensity in measurements begun fall artifacts, current Indirect have the archeological that 1). suggest sediments fired Fig. and rocks, from in field obtained the 2015 intensity (see the (SAA) a for Anomaly Atlantic of image South movement so-called South westward to the Africa and America, southern from growth low intensity the 1840 regional to pronounced in coupled began by been field decreased has geomagnetic has obser- the the it direct in of 11), Since are (10, strength (5–9). we the excursion whether or of of reversal vations discussion a of a stages to early led has field magnetic R paleomagnetism geomagnetism is than field between assumed. geomagnetic commonly relationship the the and production in nuclide complexity cosmogenic greater not agree- This a field time. suggests this dipole during ment model global our the in significantly despite weakening production, and nuclide with beryllium coeval chlorine modulated be to geomagnetically rever- appears in ka or increases 46 excursion published at an structure also field as SAA-like will such The event field sal. extreme weakened an current without the or recover that excursion an suggests into how- This intensity develop (SAA); reversal. fields an and SAA-like Anomaly with these 49 Atlantic field, of neither at South today’s ever, today’s to centered to comparable times, similar is structure earlier field the At neither ka, field. that 46 geomagnetic show changes we the current Here, to in respectively. similar evolution cen- ka, field Lake, 34 demonstrates Mono excursion and and 41 Laschamp geomagnetic at the the the of tered asser- excursions: behavior of recent the the model reversal study most to to a two a constructed led derived ka, undergoing 30–50 have has be spanning We field may This excursion. earlier. field an geomagnetic even or the or that 1600 tion suggesting since of 2017) observations 19, rate decay indirect December with a review a 1840, for at least (received decaying 2018 at 30, from been March century has approved and field CA, geomagnetic Jolla, La The Diego, San California, of University Tauxe, Lisa by Edited nttt fErhSine,Uiest fIead 0 Reykjav 101 Iceland, of University Sciences, Earth of Institute lhuhmtost oeattegoantcfil r in are field geomagnetic the forecast to methods Although at’ itr 14,adtercn eairo h geo- the of behavior recent in the times and numerous (1–4), occurred history have Earth’s excursions and eversals tign emn;and Germany; ottingen, ¨ c colo niomna cecs nvriyo iepo,LvrolL93P ntdKingdom; United 3GP, L69 Liverpool Liverpool, of University Sciences, Environmental of School | ot tatcanomaly Atlantic South a,b,1 oiaKorte Monika , e aoaor ePlan de Laboratoire %prcnuy(2.Ti decay This (12). century per ∼5% | acapexcursion Laschamp b ihr Holme Richard , tlgee eG de et etologie ´ k Iceland; ´ ık, | %per ∼5% reversals c,d 1ka ∼41 noWardinski Ingo , oyaiu,Universit eodynamique, ´ b F emnRsac etefrGocecs eerfneg 47 Potsdam, 14473 Telegrafenberg, Geosciences, for Centre Research German GFZ | ulse nieArl3,2018. 30, April online Published 1073/pnas.1722110115/-/DCSupplemental. at online information supporting contains article This ( Ger- the Service at 1 Data deposited Geosciences been for have files) Center .txt Research containing man file .zip (a data The deposition: Data the under Published Submission. Direct PNAS a is article This interest. of wrote conflict S.G. no and declare I.W., authors R.H., The M.K., M.B., and data; analyzed research; paper. S.G. performed the and S.G. I.W., and R.H., M.K., M.K., M.B., M.B., research; designed M.B. contributions: Author ihyrmnseto h itrcladrcn ed sse in seen as field, are recent ka and 46.3 models historical and a global the 48.5 the have at of fields or reminiscent the highly 4C) However, Lake 4D). Fig. Mono the Fig. during excursion; excursion; (as dipole today Laschamp than the contribution the by dipole weaker dominated during not (as either are field field, current the 2. unlike and 1 Figs. in snapshots the spec- of some the for of in field, (movies provided observed the are is of tra what origin reflecting physical surface, the the reflecting and at CMB, spectra square the determined mean We depths: Methods). the two and are from (Materials structure derived 24) (23, field spectrum field energy the an into by insights provided Further and 3). 2), (Fig. (DM; excursion (Fig. excursion) moment Laschamp excursion dipole each in the minima of for global center with local the compared as be for can defined field maps the These similar of ka). structures 43.8 snapshots field and and have (47.25 (48.5 not snap- today do today following to two but immediately to dipole, (ii) periods the configuration field, by two similar dominated current (iii) a the and in (i) ka), field 46.3 of the maps of show shots we 1, Fig. In Results today’s with excursions field. these geomagnetic the during compare and and prior excursions field Lake geomagnetic Mono and Laschamp the covering both model harmonic spherical global continuous at temporally Lake Mono the and 21) (20, owo orsodnesol eadesd mi:[email protected]. Email: addressed. be should correspondence whom To o na al tg farvra rexcursion. or reversal a of stage is early field an magnetic in Earth’s that not analyz- infer we through excursions, however, previous centuries strongly; ing past decreasing the been over also strength has return Field a polarity. by original marked the are to excursions while retaining polarity, pole opposite the an by rapidly characterized poles the reversals magnetic with the events, polarity, and flip such decreases vari- field During extreme the excursions. most of strength field’s and the reversals changes of are Two reflect ations Earth. variations the these within and deep history, geological through- timescales different out on varied solar has harmful field from The surface radiation. Earth’s protects and liquid core convecting outer Earth’s iron in generated is field magnetic Earth’s Significance h w xusosdslycmlxfil tutrsthat, structures field complex display excursions two The b,e n ynyGunnarson Sydney and , eNne,UR61 NS -42 atsCdx3 France 3, Cedex Nantes F-44322 CNRS, 6112 UMR Nantes, de e ´ NSlicense. PNAS PNAS gufm1 .I i.4 esmaiespectra summarize we 4, Fig. In S1). Movie | d a lnkIsiuefrSlrSse Research, System Solar for Institute Planck Max a 5 2018 15, May 1)adteItrainlGeomagnetic International the and (10) 4k.I hssuy epeeta present we study, this In ka. ∼34 4k o h ooLake Mono the for ka ∼34 | doi.org/10.5880/GFZ.2.3.2018.002 o.115 vol. a www.pnas.org/lookup/suppl/doi:10. | o 20 no. | ii 5111–5116 htare that 1ka ∼41 ).

EARTH, ATMOSPHERIC, AND PLANETARY SCIENCES 2015 2015

48.50 ka 48.50 ka

47.25 ka 47.25 ka

46.30 ka 46.30 ka

43.80 ka 43.80 ka

Fig. 1. Intensity at Earth’s surface (Left) and radial field (Br) at the CMB (Right) for today’s field [2015 from IGRF-12 (22)], for two SAA-like times (the 49-ka SAA at 48.5 ka and the 46-ka SAA at 46.3 ka) and for two times that are dipole-dominated at Earth’s surface (47.25 and 43.8 ka). The field is truncated at spherical harmonic degree 5.

Reference Field 12 (IGRF-12; ref. 22) (Fig. 1). We refer to field falling locally, e.g., by up to 60% within the 46-ka SAA; however, structures similar to the current field with a minimum in intensity the dipole component decreases by only 10–20% globally (Fig. occurring across southern Africa, the south Atlantic, or South 3) and at a similar rate to that seen in recent Holocene field America as SAA-like. The 48.5- and 46.3-ka snapshots belong to models over the past 2,000 y (14). Although associated with a two epochs (50–47.8 and 47.2–45 ka) where SAA-like field struc- small decrease in the global DM, the SAA-like surface fields are tures are dominant. For simplicity, we refer to these epochs as linked to the growth of reversed flux patches at the CMB in the 49 and 46 ka, respectively. Following both SAA-like epochs, the Southern Hemisphere coupled to variability in the non-dipole field does not transition into an excursion or a reversal; rather, it contributions to the field. reestablishes itself, and strongly dipolar field structures become visible at Earth’s surface (e.g., at 47.25 and 43.8 ka; Fig. 1). Discussion Before the Mono Lake excursion, no apparent SAA-like struc- Comparing Excursions and the Present-Day Field. It has been sug- tures are visible at Earth’s surface (see the time-varying movie in gested that the present-day SAA may expand and deepen, lead- Movie S1). ing to an excursion or reversal (8). Although the mechanisms The spectra for the SAA-like structures at 49 and 46 ka are that initiate these events could be different, the SAA-like inten- similar to the present day (Fig. 4 A and B), with an approx- sity structures at 49 and 46 ka do not grow and spread across imately white spectrum (common energy to all degrees), but Earth’s surface to form either excursions or reversals. Rather, with greater energy in the dipole field, indicating that the largest the field remains dipole-dominated during and after SAA-like component of the field is the axial dipole, both at the surface epochs (Figs. 1 and 4). This leads us to infer that SAA-like struc- and the CMB. The global surface field morphology is strongly tures are transitory and not diagnostic of an imminent excursion altered during the SAA-like epochs, with the intensity of the field or reversal.

5112 | www.pnas.org/cgi/doi/10.1073/pnas.1722110115 Brown et al. Downloaded by guest on September 29, 2021 Downloaded by guest on September 29, 2021 vr nieteLshm xuso,tedcyi h axial the in decay the excursion, Laschamp at the state dominated unlike dipole a ever, from decay to begins not does but 3), (Fig. zero to (27). close expected reverse reduces be dipole would axial as the excursions, when locations directional many small with only showing variability is directional there however, nonuniform locations; globally reversed numerous minimum further fully at and decay its observed surface, to the are reaches across ceases directions low dipole then now and is the Intensity zero 3). ka, to covers (Fig. close 41 flux magnitude At reversed a 2). ka, with (Fig. 41 poles before at immediately both develop and, patches CMB, flux the reversed unconnected Numerous spatially new develop. Inten- and rapidly. anomalies at grow continues surface dominate dipole the to axial at the anomalies begins in sity field fall non-dipole the as the surface energy ka, components. the 41 dipole non-dipole the before the of just state, energy At the this exceeds in surface even the at as latitudes), poles equatorial geomagnetic the have at CMB now with locations associated the some (although changes at excursion directional spectrum large at energy yield degrees immediately the all begins for and dipole white rapidly, the becomes locations of more these magnitude decay below the time, to patches Through flux CMB. reversed the associated on of are growth these and over the Asia), (one SE with over simultaneously one almost and America grow large-intensity central Two surface 3). the (Fig. at slowly anomalies initiated changes are directional excursion ini- the the and are of weakens from spectra component However, dipole the day. axial events, the present the SAA-like to 46-ka similar and tially times 49- for as the excursion, Laschamp before the For mechanism. different a Excursions. of Initiation more become will continued this orbit a as Earth such with issues low and widespread. intensity, on (26), field SAA failures in the decrease electrical through to passing led satellites dipole has in the example, decrease SAA For moderate (25). current a implications practical even Amer- have that the could to noted for strength continues been consequences SAA has greatest the It 3B) the If icas. (Fig. have values. will epochs these this least SAA-like at deepen, 46-ka to and drop 49- could for and the higher persevere is both DM may global during This current than The intensity. time. of in amount uncertain decrease some current its tinue 5. degree harmonic spherical at truncated is field The excursion. Lake Mono 2. Fig. rw tal. et Brown o h ntaino h ooLk xuso,teaildipole axial the excursion, Lake Mono the of initiation the For con- not will field today’s that imply not does finding This nest tErhssrae(Left surface Earth’s at Intensity h eeaino h xusosfollows excursions the of generation The 2k Fg ) hsde not does This 4). (Fig. ka ∼42 n ailfil (Br field radial and ) 3k onward, ka ∼43 6k.How- ka. ∼36 tteCB(Right CMB the at ) 42 ka 34.20 40.95 ka odvlpatr3 a ihrvre u tmdt ihlati- high to mid at at flux appearing reversed SAA- hemispheres with both resemble ka, in not 35 tudes S1 after do and (Movie develop and short-lived to structures are evolution field they spatial but and like their onward, mid in ka at 36 appear erratic before from anomalies just latitudes intensity occurring and DM surface low 3) sig- the Multiple (Fig. in ka. remaining minimum surface a 34 energy the with 4), at dipole (Fig. energy CMB with non-dipole short-lived, above nificantly only is dipole rgnlpbiain 2,2).Teiecore ice The 29)]. (28, and from [data publications ( Materials records nuclide original (DT) cosmogenic from tilt derived strength dipole field magnetic and DM (C B) ( Methods). Methods ). and (Materials face 3. Fig. eod eefitrda rqec f180yt eoeteinfluence at the fields (28). SAA-like remove the production to of times y nuclide the 1/800 are cosmogenic areas of Shaded modulated frequency nongeomagnetically a at of filtered were records C B A .(Upper ). nrya at’ sur- Earth’s at Energy (A) ka. 50 and 30 between series time Model ipito h acapecrin (Lower excursion. Laschamp the of Midpoint ) ita xa ioemmn VD)a esr fgeo- of measure a as (VADM) moment dipole axial Virtual ) PNAS | a 5 2018 15, May 40.95 ka 34.20 ka .Rvre u ace start patches flux Reversed ). 10 | e and Be- 5k steenergy the as ka ∼35 o.115 vol. 9ad4 ka. 46 and ∼49 36 ipito the of Midpoint ) ldrvddipole Cl-derived | o 20 no. | 5113

EARTH, ATMOSPHERIC, AND PLANETARY SCIENCES ABwhereas across the Mono Lake, reversed flux is located primar- ily over the North Pole (Fig. 2) for only a few hundred years (Movie S1). Although today’s dipole is weakening, it is still substantially stronger than the higher-degree components of the field and exceeds the dipole moment from our model through the major- ity of 40–50 ka. Today’s secular variation is instead comparable to the SAA-like states at 49 and 46 ka, which did not lead to an excursion. Similar arguments apply to the Mono Lake excur- sion; although it does not reach the magnitude and extent of the Laschamp excursion, it still starts from a more geographically spread weak state than from a single SAA-like feature.

CDRelationship Between SAA-Like Structures and Cosmogenic Nuclide Production. The above inferences depend on the robustness of our model; however, there is evidence from a complementary source: variations in cosmogenic nuclide production. Peaks in nuclide production (10Be and 36Cl) coincide with the intensity lows of the Laschamp (29, 31) and Mono Lake (31, 32) excur- sions (Fig. 3C). However, there are also peaks in production that do not match known excursions. One production peak of partic- ular note occurs at 46 ka and is coeval with one of our SAA-like structures, supporting our observation of a weakened field at this time. This peak is evident as a low in the 1/800 y filtered 10Be- and 36Cl-derived dipole variations obtained from Greenland ice core records (7, 28) and is hinted at in the stacks of sediment 10Be/9Be records from the Portuguese margin and west equato- Fig. 4. (A–D) Mean square field energy spectrum variations through spher- rial Pacific (29) (Fig. 3C). There are two other times when there ical harmonic (SH) degrees 1–5 (Materials and Methods). SH degree 1 is the are decreases in both the 10Be- and 36Cl-derived dipole data. dipole term. ( – ) Red symbols are times preceding the 46-ka SAA epoch B D ∼ (B), the Laschamp excursion (C), and the Mono Lake excursion (D). Blue sym- The low at 31 ka is approximately coeval with a decrease in DM bols are for times during the 49- and 46-ka SAA epochs and at the midpoints in our model. The low at ∼37 ka does not appear to be correlated of the two excursions. Gray symbols are for the 2015 IGRF-12 (22) field as a with any field behavior in our model; however, this low appears reference for today’s field spectrum. negligible in the same records filtered at 1/3,000 y (31). The ori- gin of the anticorrelation of the 10Be- and 36Cl-derived dipole ice core records between 49 and 50 ka is currently unknown (31), in the octupole term matches the energy of the dipole term. and we do not consider cosmogenic nuclide data before 48 ka in However, the Mono Lake excursion is not driven into a more our analysis. substantial excursion, and by 33 ka, the field regains its dom- Cosmogenic nuclide records reflect globally averaged produc- inantly dipolar appearance at the surface, although increased tion through postproduction atmospheric mixing processes (33). energy in some of the higher-order components post-33 ka cre- Numerous factors can influence cosmogenic nuclide production ates greater spatial complexity in both intensity and Br than for and concentration (31). On time scales longer than hundreds today’s field. of years, production results primarily from variations in the geomagnetic field, although possible millennial-scale solar activ- A Mechanism for Excursion and Reversal Generation. A possible ity and climate influences may complicate estimates of dipole interpretation for excursions is that field contributions of all change (31). It is commonly assumed that production is related scales vary with time, but with a weaker base state (a weaker axial to changes in the dipole component of the field. This is based on dipole), variations in the axial dipole are sufficient to produce an the altitude of modulation of cosmic rays and the rapid fall-off of excursion (27). Excursions can therefore be considered a part of non-dipole components with distance from the CMB (31). How- normal secular variation, but with a weaker axial dipole contribu- ever, we observe only a minor reduction in DM at 46 ka in our tion and a greater chance of producing a zero or reversed dipole model (Fig. 3) and suggest instead that localized areas of weak field. We argue that the field has two possible mean states, one in intensity, such as SAA-like structures, might additionally allow which the axial dipole is dominant at the CMB, which is broadly cosmogenic nuclides to penetrate the geomagnetic field. We do stable, and one in which the axial dipole matches the higher not claim that the apparently coveal timing of one our SAA-like degrees, when fluctuations in the axial dipole can produce an structures with a period of increased cosmogenic nuclide produc- excursion. The question remains: Are random fluctuations suffi- tion unequivocally links the two events; however, this observation cient for a full reversal? To answer this question, a reexamination would be worth pursuing by researchers in the future. This con- of the most recent reversal, the Matuyama–Brunhes, building on jecture could be tested by incorporating the geomagnetic model previous modeling (30), but with an expanded dataset, will be presented here into models of cosmogenic nuclide production necessary. for this time. We infer that for excursions to occur, a weakening of the field across much of the globe spreading from multiple sources Materials and Methods is required, and not just localized weakening expanding from an SAA-like feature. They also require the growth of reversed The data used for modeling can be found at doi.org/10.5880/GFZ.2.3.2018. 002. Our analysis derives from a model of the time-dependent geomag- flux patches in both hemispheres, with reversed flux transit- netic field spanning 30–50 ka. The model was constructed from the largest ing the poles. However, the amount and duration of reversed compilation of sediment and volcanic paleomagnetic data for this period to flux across the poles differs for the Laschamp and Mono Lake date (SI Appendix), exceeding the amount of data used in the only previous excursions. Reversed flux occurs simultaneously across both attempt to model the Laschamp excursion (34). An inverse model was con- poles during the Laschamp (Fig. 2) and is present for ∼2 ka, structed by using a spherical harmonic decomposition of the scalar potential

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Walker ART, Jonkers A, Jackson 10. is 4S n S10–S12 and S4–S6 reasonably Figs. than Appendix, the variability (SI that temporal data such more the show by predictions, required not model did and regularization average data temporal present- on of of model the comparison strength of visual the models a for chose through than We lower field. be geomagnetic will day method), energy mechanisms variation sampling/measurement other secular and/or and the acquisition rate sedimentation remanence on affecting (depending data sediment (see struc- 5 field and radial test). The with 4 this degrees. 2, degrees degree harmonic at at appearing spherical even tures different visible is truncated to anomaly we 2015 intensity is 5, surface for degree model to our model up whether IGRF-12 structures test the To field in 5. SAA-like output degree resolving model to of All capable truncated been degrees. have insufficient these are figures beyond data the resolution the that model suggesting effective beyond 5, rapidly for or off 4 falls degrees spectrum harmonic the spherical With (37). constraint, field regularization present-day chosen the for our the than higher with substantially excursion not degree was Laschamp main-field for degree that the the ensured after This comparing and spectrum. by before (37), present-day times chosen modeling at was spectra data. field parameter energy the geomagnetic damping to fit spatial Holocene given the a previous through following model the Instead, of smoothness appropriate the S1.) Movie losu opo asbt ftefil bevda at’ ufc n the and surface Earth’s at observed of field the ( of field description magnetic both This radial maps model (37). plot convergence The to ensure iteratively. us to found steps allows iteration solution 35 the on based and was linearized therefore, was coefficients; model problem the and the to inclination, related nonlinearly Declination, were approach. data least-squares intensity The a regularization time. the using in under by component data constraints field the from radial determined the in were of coefficients norm model derivative dissipation second phys- Ohmic the used and the those We space i.e., data. constraints: the models, regularization describe smooth motivated to against invoked structure ically data were of recover the amount time to to least and fit the expected requiring reasonable space This we a y. in off than 50 Regularizations trade model every to data. harmonic the placed available spherical were in the to points complexity from expanded knot more spline was for and series allowed 10, spatial order The and 36). Holocene degree and 35, (10) historical (14, the for field used methods following B-splines, cubic field the for rw tal. et Brown .PltiW ignA,Tidd I atanG,TraNv 21)Continuous (2018) F Terra-Nova GA, Hartmann RI, Trindade AJ, Biggin W, Poletti past. 9. the from Hints transition? geomagnetic Pav impending An 8. (2015) C Kissel C, reversing? Laj field 7. magnetic Earth’s the Is of (2006) structure M Small-scale Korte (2002) C, N Constable Olson M, 6. Mandea B, Langlais C, Eymin G, scale. Hulot time 5. instability geomagnetic scale. Quaternary A time (2014) BS polarity Singer 4. Geomagnetic (2012) excursions. J Geomagnetic Ogg (2007) 3. JET the Channell for timescale C, geomagnetic the Laj of 2. calibration Revised (1995) DV Kent SC, Cande 1. ie h neettmoa mohn fteploantcsga in signal paleomagnetic the of smoothing temporal inherent the Given constrain to used be to defined insufficiently are uncertainties data The Br o-oncnrlo h geodynamo. the on control top-down Science years. 000 10 1840. least at to for hemisphere prior southern in dipole the of decay 304:13–21. rapid implies tensity 902. records. historical records. historical from variation dipole. axial magnetic earth’s the 274:72–86. of decrease millennial reversal. geomagnetic possible Sci Earth Front 246:1–16. data. satellite Magsat and Oersted from inferred geodynamo 85–113. pp 21:29–52. Boston), (Elsevier, GM Ogg MD, Schmitz JG, Ogg FM, Gradstein 373–416. pp Amsterdam), (Elsevier, G Schubert Cenozoic. and Cretaceous late tteCBadttlfil tegha at’ ufc r rvddin provided are surface Earth’s at strength field total and CMB the at nCrac J eSni 21)TeSuhAlni nml:Tekyfra for key The Anomaly: Atlantic South The (2016) A Santis De FJ, on-Carrasco ´ 320:626–628. B = 3:61. ∇Φ e Geophys Rev ihec ofcetepne ntm nabssof basis a on time in expanded coefficient each with , Br tteCB h eino h edsoii.(Movies origin. field’s the of region the CMB, the at ) epy Res Geophys J rn at Sci Earth Front 41:1006. hlsTasRScLn A Lond Soc R Trans Philos a Commun Nat IAppendix SI 100:6093–6095. 4:40. at lntSiLett Sci Planet Earth 6:7865. eds Scale, Time Geologic The ed Geophysics, on Treatise ≥ 358:957–990. o ute eal on details further for ,teeeg neach in energy the 2, hsErhPae Inter Planet Earth Phys Nature at lntSiLett Sci Planet Earth at lntSiLett Sci Planet Earth ). utGeochronol Quat Science 416:620–623. 453:78–86. 312:900– 8 a ,GiluH islC(04 yaiso h at antcfil nte10- the in field M magnetic 29. earth the of Dynamics (2014) and C excursions Kissel field H, geomagnetic Guillou for C, model Laj simple Anomaly A 28. Atlantic (2016) South M Korte Ever-present MC, (2002) Brown DC 27. Wilkinson JH, Allen dipole. earth’s JR, in Changes Heirtzler (2006) H 26. Amit P, Olson 25. 4 oe J(94 pta oe pcrmo h angoantcfil,and field, geomagnetic main the of spectrum power Spatial (1974) fields. FJ vector harmonic Lowes spherical of 24. sphere on values Mean-square (1966) FJ Lowes 23. 1 ac ,Fibr M oaeJ,CegH dad L(06 g fteLaschamp the of Age Th (2016) 22. RL Edwards H, Cheng JA, Dorale JM, Feinberg I, Lascu 21. (2009) al. et modern BS, on Singer data model in field 20. predictability archeomagnetic of and Impact (2018) assimilation W data Kuang A, to Tangborn introduction 19. An (2010) al. et A, reversals. polarity Fournier geomagnetic for 18. Mechanism (1987) D Gubbins 17. 0 enad ,Fba 20)Ploantcrcntuto ftegoa geo- global the of reconstruction Paleomagnetic (2007) K Fabian R, Leonhardt 30. ie by given (R degree, dipole each at energy quantity the this and to l degree, contributions harmonic the 4 spherical Fig. by In separated Earth. are solid the of radius mean the amncdegree harmonic where by given is 24) (23, field square mean The h ioeai D)potdi i.3i ie by given is 3 Fig. in plotted (DT) axis dipole the yaGusPoesrhpfo h kdmedrWseshfe zu Wissenschaften der Akademie supported the was from (Marmite). R.H. ANR-13-BS05-0012 Professorship BR4697/1. Forschungsge- Gauss Project Deutsche G 1488 a by supported PlanetMag by was who SPP studies work and meinshcaft Nowaczyk individual This Norbert of Leonhardt. with authors discussions Roman acknowledges the M.B. and data. compilations provided data their viding ACKNOWLEDGMENTS. where spotdaantta ere h nryo h ioe(R dipole the of energy The degree. that against plotted is , tign ..wsspotdb gneNtoaed aRceceProject Recherche la de Nationale Agence by supported was I.W. ottingen. ¨ h Ma at’ ufc lte nFg sgvnby given is 3 Fig. in plotted surface Earth’s at DM The follows. as are evolution field magnetic describe to used parameters The and 5krpro opiigteLshm n ooLk xusos e results New excursions: Lake Mono and 184–197. Laschamp Cha French the the comprising from period kyr 75 observations. palaeomagnetic for inferences spacecraft. damages xrplto otecore. the to extrapolation Res Geophys generation. emgei ioelwfo h lblatmospheric authigenic global of the bution from low dipole geomagnetic from record geomagnetic speleothem a of dating America. U-Th North by determined excursion chronologies. climate and core ice Lett for tie-point radioisotopic A sion: forecasts. geomagnetic era geomagnetism. antcfil vlto uigteMtym/rne rniin Iterative transition: verification. Matuyama/Brunhes independent the and 172–195. during inversion evolution Bayesian field magnetic Res enabr ´ butE ta.(05 nentoa emgei eeec ed h 12th The field: reference geomagnetic International (2015) al. et E, ebault ´ 117:B11101. g 286:80–88. µ l m = nd a ,Bourl L, eaz ´ and Z edpotdi i.3aelmtdt ereadodr5adare and 5 order and degree to limited are 3 Fig. in plotted field ) 4π R at,PaesSpace Planets Earth, B(r nd 71:2179–2179. · h 10 l m = Geology ) pc c Rev Sci Space 2 r h cmd-omlzdGuscefiinso spherical of coefficients Gauss Schmidt-normalized the are −7 l d X l n order and =2 sD,Tovn 21)Apiueadtmn fteLaschamp the of timing and Amplitude (2012) N Thouveny DL, es = Ω ` DM 5 o,TasA epy Union Geophys Am Trans Eos, R n e usi lblperspective. global a in Puys des ˆ ıne sA,tepreblt ffe pc.Telttd of latitude The space. free of permeability the Vs/Am, 10 DT d 40   Be/ etakSnaPnvk n iaTuefrpro- for Tauxe Lisa and Panovska Sanja thank We PNAS = = l Ar/ 44:139–142. 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EARTH, ATMOSPHERIC, AND PLANETARY SCIENCES 31. Muscheler R, Beer J, Kubik PW, Synal HA (2005) Geomagnetic field intensity during 34. Leonhardt R, et al. (2009) Geomagnetic field evolution during the Laschamp the last 60,000 years based on 10Be and 36Cl from the Summit ice cores and 14C. Quat excursion. Earth Planet Sci Lett 278:87–95. Sci Rev 24:1849–1860. 35. Korte M, Constable C, Donadini F, Holme R (2011) Reconstructing the Holocene 32. Wagner G, et al. (2000) Chlorine-36 evidence for the Mono Lake event in the Summit geomagnetic field. Earth Planet Sci Lett 312:497–505. GRIP ice core. Earth Planet Sci Lett 181:1–6. 36. Constable C, Korte M (2015) Centennial- to millennial-scale geomagnetic field 33. Masarik J, Beer J (1999) Simulation of particle fluxes and cosmogenic variations. Treatise on Geophysics (Elsevier, Amsterdam), 2nd Ed. nuclide production in the Earth’s atmosphere. J Geophys Res 104:12099– 37. Korte M, Donadini F, Constable CG (2009) Geomagnetic field for 0-3 ka: 2. A new 12111. series of time-varying global models. Geochem Geophys Geosyst 10:Q06008.

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