New Observations in Earth’s Normal Modes of Free Oscillation

趙丰 Benjamin F. Chao, 雷湘鄂 Xiang’E Lei1

朱澄音 Amelie C. Chu,

Institute of Earth Sciences, Academia Sinica, Taiwan1also at Inst. Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan

Traveling-wave – Standing-waveEquivalence

sin(wt + kx) + sin (wt – kx)= 2 sinwt * coskx

Normal modes||

A typical seismogram

nulm , nωlmovertone number order

degree

(3-D) (discrete)Eigenfunction , Eigenfrequency

n=0: Fundamental modes ~ Surface wavesn>0: Overtone modes ~ Body waves

Earthquake Displacement Field

• Equation of motion

• Solve by expanding displacement field

Normal mode eigenfunctions for SNREI Earth

Expansion coefficients (note the static limit)

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)ρ( = t

ursfgf

u(r,t) = ak (t) uk* (r)

k

1] )[exp()(:ˆ = )( 2 tioMta kkk

k srM (Gilbert, 1970 )

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Deep Earthquakes:

1970 Colombia, M 8.0, depth = 650 km

1994 Bolivia, M 8.2, depth = 630 km

2013 Okhotsk Sea, M 8.3, depth = 609 km

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V~60 stations

H~80 stations

Product power spectrum (logarithm)

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V~60 stations

H~80 stations

Product power spectrum (logarithm)

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V~60 stations

H~80 stations

Product power spectrum (logarithm)

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V~60 stations

H~80 stations

Product power spectrum (logarithm)

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V~60 stations

H~80 stations

Product power spectrum (logarithm)

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Radial “breathing” modes nS0 (n = 0 ~ 11) Observation vs. model

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• GSI (Geospatial Information Authority of Japan)

– GEONET (GNSS Earth Observation Network System)• Total 1230 stations at an average

interval of about 20km for crustal deformation monitoring and GNSS surveys.

• # Station used in this study: 1019

GSI’s GNSS stations

(http://dbx.cr.chiba-u.jp)

(Mitsui et al., 2012)

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GPS Data Processing:

–GIPSY/OASIS-II (Ver. 6.1)–Precise Point Positioning (PPP) technique– Sampling Rates: 30 sec.–Data Length:

21hrs (starts from 06:00 (UTC) 11th, March) 30hrs (starts from 18:00 (UTC) 11th, March)–We carry out simple spectral stacking,

reducing the variance of the noise level

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Spectral Stack – GSI, Japan

- - - fundamental toroidal modes

0T2

0T13

0T120T10

2T1

0T15

2T2

0T17

1T9

0T21

2T7

0T20

1T11 0T22

0T3

0T4

0T11

0T14 0T18

0T19

1T12

|Y(f)

|2

0S4

0S9

0S10

0S2

0S3

Spectral Stack – GSI, Japan

0T2

0S2

0S3 0S4

0S6

0S8

0S9 0S120S18 0S21

0S0

－ : Fundamental spheroidal modes

X

0S20

0S7

1S4

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PBO Network• The Plate Boundary Observatory (PBO) of EarthScope

measures Earth deformation through its arrays of GPS receivers, strainmeters, seismometers.

• Ref. Frame: IGS08• # GPS Records: 1548

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Stack – PBO, Western U.S.

0T6

0S0 1S4

0S10

0T10

0T8

0T12

0T18

2T1

0S8

0S9

0S4

0S6

1S8

1S10

x

0T11

0T23

2T2

0T13

x0S2 0S3

0S5

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International GNSS Service IGS Network# GPS Station used : 337

DART of NOAADeep-ocean Assessment and Reporting of Tsunamis network

24 BPR records used (15 for 2010 Chile, 5 for 2011 Japan, 3 for 2005 Sumatra/Nias, 1 for 2004 Sumatra): After arrival of seismic waves but before tsunami, typically several hours long, at “event mode” 15-sec sampling.

A typical BPR earthquake record(4 days long, after de-tide)

Spectrum of a single DART (BPR21413) record for 2010 Chile earthquake

Blue: pre-earthquake Red: during earthquakePink line: spheroidal 0Sn modes Green line: toroidal 0Tn modes

Spectral Stack of 24 DART records for 4 earthquakes

Blue: pre-earthquake Red: during earthquakePink line: spheroidal 0Sn modes Green line: toroidal 0Tn modes

What does ocean BPR record?

• Assuming hydrostatic (OK for <60 mHz)• Pressure changes because the “g” in P=ρgH changes,

from g to g±a (equivalence principle), where a is the vertical acceleration associated with the given mode, or dω2 => spheroidal modes only? (but we see toroidal modes too…)

• Additionally the dynamic drag produces an opposing pressure ½ CDρv2 which is tiny.