1. Geodetic Implications of Mass Transfer in the Deep Earth David Crossley St. Louis University Acknowledgements: GGP, NASA

2. Mass transfer whole earth motions – normal modes, wobbles, differential rotations - periodic (frequency domain) time-varying density variations – convection, secular e.g. growth of IC (time domain) – wave motion, periodic (freq domain) geodetic implications: gravity changesEOP, LOD (m 1, m 2, 1+m' 3 )

3. Gravity Instruments SG AG

4. Typical AG data (J9, Strasbourg)

5. J9 AG-SG comparison

6. Typical SG residual gravity subtract: tides, nominal pressure, IERS polar motion, linear drift (GGP database, ICET)

7. Moxa double-sphere data

8. Strasbourg frequency domain noise level filtered

9. SG-AG spectral comparison 1 day SG AG

10. Summary of data properties SG’s sampling: 1-5 s, continuous, quantisation 0.1 ngal time domain accuracy: 0.1 gal frequency domain accuracy: 1 ngal (or less) for periods 1s – 1 d 1 gal for periods > 1 yr AG’s sampling: ~20 s, 2 weeks max continuous, intermittent at most sites time domain accuracy: 1-2 gal frequency domain accuracy: variable (depends on measurements)

11. Gravity effect of LOD, EOP LOD gravity + centrifugal acceleration about existing axis U = V - ½  2 r 2 sin 2  g = 8   r sin 2  / T 3 latitude 45º: 40 ngal = 1 ms EOP (polar motion) gravity + centrifugal acceleration about new axis G = 0.016 m 0 cos(t+ 0 -l) gal m 0 = amplitude mas e.g. CW: m 0 = 300 mas,  g = 4.8  gal

12. LOD: C-M Coupling; torsional oscillations period ~ 65 yr seen in LOD data axisymmetric zonal MHD oscillations governed by Lorentz force (Alven waves) present in dynamo models under subseismic assumption (no elastic restoring forces) damping due to ohmic dissipation – primarily in D’’ gravity effect ~ 0.1 gal

13. LOD – torsional oscillations Tangentially geostrophic core flow used to infer core angular momentum torques from EM and topographic coupling Ponsar et al. (2003) LOD from VLBI Pais and Hulot (2000) Jackson et al. (1993) Holme and Whaler (2001) Jault et al. (1988)

14. Correlation of LOD with Core Angular Momentum correlation for model with cylindrical shells q=1 (polar tangent cylinder), q=20 (equator) velocities below CMB from secular variation and Taylor Proudman Theorem map of correlation as a function of latitude Hide et al. (2000) Time lag (yr)

15. LOD: Core–Mantle Coupling; tides Zonal tides induce changes in LOD and in seasonal changes in the ‘static’ global gravity field (e.g. C 20, Dickman, 2001). Observation of response function at M9, Mf, Ssa and Sa (monthly and annual periods) can determine C-M coupling, if we allow for oceanic and atmospheric responses. M9 torque = 1.5 x 10 16 N m, Mf = 2.4 x 10 17 N m Gravity data set is improved by GRACE, but oceanic response still a problem for annual tide

16. Free Wobbles (and nutations) 5 modes predicted theoretically: Nearly Diurnal Free Wobble - NDFW FCN (Ret) Nearly Diurnal Free Inner Core Wobble - NDFICW FICN (Prog) Tilt Over Mode - TOM ? (Ret) - not observable Chandler Wobble - CW Free Eulerian Nutation (Prog) Inner Core Wobble - ICW ? (Prog) + historical prediction: Markowitz Wobble (24 yr IC libration, Busse 1970) - inconclusive

17. FCN – rotation of OC wrt mantle nutation period (sd) Smith (1977)DG579-453.5 Matthews et al. (1991)PREM-like-457.0 de Vries & Wahr (1991)PREM-like-457.0 Dehant et al. (1993)PREM-like-463.0 Matthews et al. (2002)PREM-like-430.2 adjusted* ~100 as (variable) Rogister (2003)PREM-458.6 *mixed model adjusted to observed nutation series

18. FICN – rotation of IC vs OC and mantle nutation period (sd) Smith (1977)/CrossleyPREM474.0 Matthews et al. (1991)PREM-like476.8 de Vries & Wahr (1991)PREM-like471.0 Dehant et al. (1993)PREM-like463.0 Matthews et al. (2002)PREM-like1035.0 adjusted* Rogister (2003)PREM473.9 (2 nd order theory) *mixed model adjusted to observed nutation series

19. Chandler Wobble - CW Easily seen in both EOP and gravity period –465 sd (theoretical) –430 sd (observed) amplitude –~ 5 Gal, variable (gravity) Q – 10 5 Florsch et al. (2000), in agreement with VLBI

20. Inner Core Wobble - ICW Smith (1977)/ Crossley (unpub) PREM 1066A ~ 674 sd ~ 682 sd theory inadequate* Rochester / Crossley (unpub) PREM~ 621s d Dehant et al. (1993) PREM-like2965 sd Matthews et al. (2002) etc. PREM-like2412 sd (6.6 yr) Guo (unpub)PREM-like6.6 yramplitude ~5 gal for IC obliquity of 1º * At periods >> 1 year, motion in OC becomes parallel to IC tangent cylinder (T-P theorem), cannot be represented by T 1 1 +S 2 1 +T 3 1 Busse (1970), Smith (1977).

21. Precessions and nutations as gravity changes LOD Loyer, Bizouard et Dehant (1995) period (d)LOD (ms)centrifugal effect (ngal) 13.630.14812 13.660.35728 27.560.18815 182.620.16613 365.250.0262 6790.36 (18.6 yr) 0.1495

22. Precessions and nutations as gravity changes EOP Loyer, Bizouard et Dehant (1995) nutation period corresponding tide gravity variations (ngal) x sin 2 18.6 yr19 0.5 yrP149 27.5 d +,-M1, J18, 8 13.66 d +,-O1, OO1113, 4 13.63 d 21 9.13 dQ122

23. Slichter triplet

24. ICB density jump ICB is a phase boundary ICB is the source of compositional convection due to freezing of OC fluid part of ICB density jump is due to solidification (~ 0.2 gm cm -3, Alfe et al., 2000) remainder of ICB density jump is due to composition (Fe to Fe + alloy) both parts contribute to energy release and functioning of the geodynamo

25. Spring gravimeter observation of a single oscillation: period T86 min amplitude0.64 gal (10 -9 g) Simple calculation, motion of inner core alone: displacement48 cm  (ICB)3.125 gm cm -3 Gravitational restoring force is dominant Slichter mode (1961)

26. Superconducting gravimeters – no confirmed observations (yet): triplet 1 S 1 m m = -1, 0, 1 period range: 4 - 8 hr amplitude ~ 1 nanogal (10 -12 g) Motion of inner core, outer core, and mantle IC displacement:~ mm  (ICB) range: 0.3 – 0.8 gm cm -3 Elasticity of IC, mantle contribute to period Slichter triplet

28. Recent IC results: theoretical AuthorsModelTechniqueResults Smylie and McMillan (2000) Cal8 (Bolt and Urhammer, 1985) [ICB density jump 1.170 gm cm -3, BL thickness 370 km] Not stated (static Love numbers, subseismic approximation, viscosity) Periods 3.5839 (retrograde), 4.0167 (prograde) ICB viscosity 1.225 x 10 11 Pa s. Rieutord (2002) ‘PREM-like’direct integration (full rotation), neutral, viscous fluid periods 4% less than Crossley et al. (1992), viscosity too high to match Courtier et al. periods. Rogister (2003) PREM, 1066Adirect integration (rotation + ellipticity; S1 to S5, no viscosity) agree within 0.3% to Crossley (1993)

29. Recent IC results: observational AuthorsDataTechniqueResults Courtier et al. (2000) GGP SG observations 6 stations Parzen averaging / product spectrum Periods 3.5822 h (retrograde) 3.7656 h (axial) 4.0150 h (prograde) Masters and Gubbins (2003) PREM, 1006A, etc. (starting models) free oscillations (50 IC modes) density jump 0.82 ± 0.18 gm cm -3 Koper et al. (2003) ~ 300 TT observations PKIKP / PcP amplitude ratios density jump 0.3 gm cm -3

30. Density resolution from normal modes 0.5% target error level 1% 5% 10% ICB CMB Masters and Gubbins (2003)

31. PKIKP trade-offs for ICB parameters Koper and Pyle (2003)

32. New ICB density limits …

33. … new Slichter triplet period limits

34. Dynamic product spectrum - Strasbourg Select 1 month of 1 min residual gravity data, Hanning window, FFT Shift N days forward, repeat Geometric mean (product spectrum) of all 4 years Crossley, Pagiatakis, Rosat (unpublished)

35. Stacking of multi-station GGP data - 1 Sun et al. (2003)  21 series from 14 GGP stations  product spectrum  problem of non-linear tides around 4 hr, 6hr  detection limit 0.7 nGal Rosat et al. (2003) Search for the Slichter mode …  need quietest GGP stations  individual stations have noise levels above 1 nGal  Stacking method in Courtier et al. can detect signals weaker than 1 nGal

36. Stacking of multi-station GGP data - 2 Rosat et al. (2003) non-linear tides

37. Stacking of multi-station GGP data - 3 Rosat et al. (2003) noise 2 nGal amplitude injected level 0.1 nGal

38. Conclusions – short periods Slichter triplet 4-8 hr ICB density jump ICB+ viscosity VLBI – unlikely, gravity - possible FICN, prograde ~ 12 hr [940 day] IC densityVLBI - yes, gravity - unlikely FCN, retrograde ~ 12 hr [430 day] CMB ellipticityVLBI and gravity – yes, done

39. Conclusions – long period Core modes (inertia – gravity) 12-36 hr density gradient under CMB LOD – unlikely gravity - unlikely IC Wobble 2-6 yrICB density contrast, flattening EOP – yes gravity - possible IC-mantle gravitational coupling, 2-20 yr IC density, viscosityLOD – possible gravity – only if short period core/mantle torsional oscillations (65 yr) CMB topography, magnetic field, conductivity D” LOD - yes gravity - unlikely