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Gravimeters for seismological broadband monitoring: Earth’s free oscillations Michel Van Camp Royal Observatory of Belgium

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What is a free oscillation? 3 rd Harmonic etc. 2 nd Harmonic 1 st Harmonic Fundamental L x Free oscillation = stationary wave Interference of two counter propagating waves (see e.g.

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Seismic normal modes Periods < 54 min, amplitudes < 1 mm Observable months after great earthquakes (e.g. Sumatra, Dec 2004) Few minutes after the earthquake Constructive interferences free oscillations (or stationary waves) Few hours after the earthquake ( 0 S 20 ) (Duck from Théocrite, © J.-L. & P. Coudray)

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Travelling surface waves Richard Aster, New Mexico Institute of Mining and Technology

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Historic First theories: First mathematical formulations for a steel sphere: Lamb, 1882: 78 min Love, 1911 : Earth steel sphere + gravitation: eigen period = 60 minutes First Observations: Potsdam, 1889: first teleseism (Japan): waves can travel the whole Earth. Isabella (California) 1952 : Kamchatka earthquake (Mw=9.0). Attempt to identify a « mode » of 57 minutes. Wrong but reawake interest. Isabella (California) 22 may 1960: Chile earthquake (Mw = 9.5): numerous modes are identified Alaska 1964 earthquake (Mw = 9.2) Columbia 1970: deep earthquake (650 km): overtones IDA Network

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On the sphere… n = radial order n = 0 : fundamental n > 0 : overtones l, m = surface orders l = angular order -l < m < l = azimuthal order Radial eigenfunction Surface eigenfunction Vibrating string: On the sphere:

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Why studying normal modes? n A m l : excitation amplitude from d one can have info on the source if all n y l and x m l known Conversely: from A one can predict d : modes form the basis vectors, their combination describe the displacement (synthetic sismograms)

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Why studying normal modes ? Frequencies of the eigen modes depend on : The shape of the Earth and its density, (resistance to acceleration) shear modulus, (resistance to a change of shape) compressibility modulus (resistance to a change of volume).

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Toroidal and spheroidal Using spherical harmonics (base on a spherical surface), we can separate the displacements into Toroidal (torsional) and spheroidal modes (as done with SH and P/SV waves): T : S : Radial eigenfunction Surface eigenfunction

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Characteristics of the modes No radial component: tangential only, normal to the radius: motion confined to the surface of n concentric spheres inside the Earth. Changes in the shape, not of volume Not observable using a gravimeter (but…) Do not exist in a fluid: so only in the mantle (and the inner core?) Horizontal components (tangential) et vertical (radial) No simple relationship between n and nodal spheres 0 S 2 is the longest (“fundamental”) Affect the whole Earth (even into the fluid outer core !) Toroidal modes n T m l : Spheroidal modes n S m l :

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n, l, m … S : n : no direct relationship with nodes with depth l : # nodal planes in latitude m : # nodal planes in longitude ! Max nodal planes = l 0S020S02 T : n : nodal planes with depth l : # nodal planes in latitude m : # nodal planes in longitude ! Max nodal planes = l - 1 0T030T03

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0 S 0 : « balloon » or « breathing » : radial only (20.5 minutes) 0 S 2 : « football » mode (Fundamental, 53.9 minutes) 0 S 3 : (25.7 minutes) Spheroidal normal modes: examples: Animation 0 S 2 from Hein Haak Animation 0 S 0/3 from Lucien Saviot 0 S 29 from: 0 S 29 : (4.5 minutes)... Rem: 0 S 1 = translation...

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Toroidal normal modes: examples: 1 T 2 (12.6 minutes) 0 T 2 : «twisting» mode (44.2 minutes, observed in 1989 with an extensometer) 0 T 3 (28.4 minutes) Animation from Hein Haak Animation from Lucien Saviot Rem: 0 T 1 = rotation 0 T 0 = not existing

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Solid inner core (1936) Fluid outer core (1906) Solid mantle Shadow zone Geophysics and normal modes Solidity demonstrated by normal modes (1971) Differential rotation of the inner core ? Anisotropy (e.g. crystal of iron aligned with rotation)?

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Eigenfunctions Ruedi Widmer’s home page: shear energy density compressional energy density One of the modes used in 1971 to infer the solidity of the inner core: Part of the shear and compressional energy in the inner core Today, also confirmed by more modes and by measuring the elusive PKJKP phases

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Eigenfunctions : 0 S l shear energy density compressional energy density l > 20: outer mantle l < 20: whole mantle Ruedi Widmer’s home page: Equivalent to surface Rayleigh waves

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Eigenfunctions : S vs. T n = 10 nodal lines shear energy density compressional energy density T in the mantle only ! S can affect the whole Earth (esp. overtones) Ruedi Widmer’s home page: Deep earthquakes excite modes whose eigen functions are large at that depth

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Eigenfunctions : 0 S l and 0 T l 0 S equivalent to interfering surface Rayleigh waves 0 T equivalent to interfering surface Love waves pics/SAWRAiGH.gif

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Music and seismic normal modes «balloon» mode: T = 20.5 min. Frequency ~ Hertz Do 256 Hertz T= s 18 X

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The great Sumatra-Andaman Earthquake ?

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300 km The great Sumatra-Andaman Earthquake 1300 km

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Sumatra Earthquake: spectrum 0S30S3 0S20S2 2S12S1 0T40T4 0T30T3 0T20T2 0S40S4 1S21S2 0S00S0 Membach, SG C021, h h00

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Sumatra Earthquake: time domain Membach, SG C021, Q factor 5327 Q factor 500 M. Van Camp

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Splitting No more degeneracy if no more spherical symmetry : Coriolis Ellipticity 3D Different frequencies and eigenfunctions for each l, m If SNREI (Solid Not Rotating Earth Isotropic) Earth : Degeneracy: for n and l, same frequency for –l < m < l For each m = one singlet. The 2m+1 group of singlets = multiplet

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Splitting Rotation (Coriolis) Ellipticity 3D Waves in the direction of rotation travel faster Waves from pole to pole run a shorter path (67 km) than along the equator Waves slowed down (or accelerated) by heterogeneities

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Splitting Coriolis Ellipticity 3D Animation 0 S 2 from Hein Haak

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Splitting: Sumatra M. Van Camp Membach SG-C021 0 S 2 Multiplets m=-2, -1, 0, 1, 2 “Zeeman effect”

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Coupling: Balleny 1998 In an elliptic rotating heterogeneous Earth: Mode splitting and coupling : the modes no more orthogonal An eigenfunction can contain perturbation from the eigengfunctions of neighbouring modes e.g. T can present a vertical component or Different modes at the same frequency Coriolis force Displacement in SNREI

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Modes and Magnitude Time after beginning of the rupture: 00: (M W ) P-waves 7 stations 00: (M W )P-waves 25 stations 01: (M W )Surface waves 157 stations 04: (M W ) Surface waves (automatic) 19: (M W ) Surface waves (revised) Jan (M W )Free oscillations April (M W ) GPS displacements s surface waves

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Modes and Magnitude Seth Stein and Emile Okal Calculated vs. observed Rupture zone as determined using surface waves From aftershocks, free oscillations, GPS, …

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nm/s² Modes and Magnitude SG C021 Membach, same duration: Sumatra 2004: M w = Peru 2001: Mw = 8.1

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Undertones Seismic modes : restoring force (Elasticity, molecular cohesion) proportional with: Shear modulus Incompressibility Density Sub-seismic modes (or « undertones »): << restoring force proportional to: Archimedean force : gravity waves Coriolis force : inertial waves Lorenz force : hydro magnetic or Alvèn waves Magnetic Archimedean Coriolis : MAC waves Oscillations Restoring force If rigidity restoring force period

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Slichter mode (triplet) (pointed out in 1961) : 1 S 1 Translation of the solid inner core in the liquid outer core ( 1 S 1, period ~ 4-8 h) Controlled by the density jump between the inner and outer core, and the Archimedean force of the fluid core

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Core modes Oscillations in the fluid outer core (periods in the tidal band (?) Information on the stratification of the outer core

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Undertones Normal modes of a rotating elliptic Earth Nearly Diurnal Free Wobble (NDFW) Chandler (~ 435 d)

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NDFWNearly Diurnal Free Wobble (432 days in the Celestial frame = Free Core Nutation) P1P1 K1K1 Fréquence (cycles par jour) Observing the NDFW / FCN is thus very useful to measure the CMB flattening and to obtain information about the dissipation effect at this interface. Fortunately, the eigenfrequency of the NDFW is located within the tidal band and induces a perturbation of diurnal tides (Unfortunately the amplitude of 1 is weak!). In the space frame, the FCN is measured by the Very Long Baseline Interferometry (VLBI). Non-Seismic proof of the fluidity of the outer core. NDFW

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Chandler wobble (« polar motion ») (1891) This motion, due to the dynamic flattening of the Earth, appears when the rotation axis does not coincide anymore with the polar main axe of inertia. Without any external torque, the total angular momentum remains constant in magnitude and direction, but the Earth twists so that related to its surface, the instantaneous rotation axis moves around the polar main inertia axis. Period : 435 days (~14 months)(Chandler 1891) – 305 days if the Earth was rigid (Euler) Most probably excited by atmospheric forcing

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Period quart-diurnal ter-diurnal diurnal Fortnightly monthly semi-diurnal Tidal band 10 s100 s1 h 0.1 nm/s² 1 nm/s² 0.01 nm/s² 10 nm/s² 100 nm/s² 1000 nm/s² 1 s 12 h1d1 month14 d 1 yr435 d Seismic normal modes Induced by the atmosphere (« humming ») Microseism Surface waves 6 h (?) Slichter triplet Polar motion, tectonics NDFW Liquid outer core modes Hydrology Spectrum of the ground acceleration (T > 1 s) Undertones

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Observing normal modes Extensometres (Isabella, 1960) Long period seismometers Spring and superconducting gravimeters !!! Not able to monitor toroidal modes (but…)

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How measuring an earthquake ? Seismogram Seismometer Seismograph inertial pendulum (same idea since 130 years 10 km: M = 3 2 µm M = 5 0.2 mm

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Different design of seismometers Garden gate Inverted pendulum Leaf spring LaCoste Bifilar (Zöllner) Spring

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g g mvc Spring gravimeter Superconducting gravimeter (magnetic levitation) Principle of the superconducting gravimeter

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Superconducting gravimeter Advantage: stable calibration factor (phase [<0.1 s] and amplitude [0.1 %]) Sumatra 2004: some seismometers suffer 5 to 10 % deviation (Park et al., Science, 2005) 10 % M W = 8.4 ( largest event between 1965 and 2001) !!!

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STS-1 Vertical

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Hinge Leaf spring Boom Seismic mass (m) g

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STS-1 Horizontal Allows us to measure Toroidal AND Spheroidal modes Garden gate suspension

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Atmospheric effects (also affecting Earth tide analysis) Newtonian effects : -4 nm/s²/hPa (+ buoyancy) Loading : +1 nm/s²/hPa + local deformations

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Spectra after correction of the barometric effect Balleny Islands 1998, M w =8.1

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“International Deployment of Accelerometers” (Cecil and IDA Green) Late ’60ies: First idea after a LaCoste gravimeter provided nice data The original network was a global network of digitally recorded La Coste gravimeters They could provide valuable constraints on earth structure and earthquake mechanisms, but a shortage of data limited further progress. During the same period, low-noise feedback seismometers were developed that allowed such data to be obtained from relatively small (and hence frequent) earthquakes. A complete description of the IDA network can be found in Eos (1986, 67 (16)) C. & I. Green

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Evolution of the acquisition systems used by the IDA network Presently: 1 accelerometer + BB seismometer (STS-1, Güralp)

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The Global Geodynamics Project GGP Network of ~ 20 superconducting gravimeters Goal: Extract global signal disturbed by local effects (« Stacking ») Study of undertones, tides, hydrology, …(Crossley et al., EOS, 1999) Study of seismic normal modes : recent investigations have showed they are the best < 1 mHz: important to constrain Earth’s density profile

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-No data on-line (“live”); delay of 6 months: seismologists do not use it -Format not used by seismologists -Transfer function not always known The Global Geodynamics Project GGP -Standardized format -Stability of data acquisition systems and calibration factors -Exchange of gravity data -Detailed logbooks

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A world première: the SG at the IRIS data base NASA/Goddard Space Flight Center Scientific Visualization Studio

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The IRIS data base

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Membach SG C021 on the IRIS data base Pressure

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The future of a geophysical station One instrument, 240 dB dynamics ( A/D 40 bits) Noise level: 0.1 nm/s² (frequency dependent) Frequency band : to 1000 Hz (1 yr to s) This is what we do in Membach…but with 3 instruments -1 broadband seismometer Güralp (> 1990):100 s to 0.02 s (50 Hz) -1 accelerometer Kinemetrics ETNA (>2003):10 s to 0.01 s (100 Hz) -1 superconducting gravimeter (>1995): 20 s to years -1 absolute gravimeter (>1996): 12 h to centuries (?) + 1 L4-3D “historic” (>1985): 0.2 to 50 Hz

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Elsewhere? Helioseismology and Astroseismology (or Asteroseismology): Spheroidal modes On the other planets: Mars, Venus? Modes could be excited by the atmosphere (« humming »)

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