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New Observations in Earth’s Normal Modes of Free Oscillation. 趙丰 Benjamin F. Chao, 雷湘鄂 Xiang’E Lei 1 朱澄音 Amelie C. Chu, Institute of Earth Sciences, Academia Sinica , Taiwan 1 also at Inst. Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan. Normal modes ||. - PowerPoint PPT Presentation
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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)
22
)ρ( = t
ursfgf
u(r,t) = ak (t) uk* (r)
k
1] )[exp()(:ˆ = )( 2 tioMta kkk
k srM (Gilbert, 1970 )
6
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
7
V~60 stations
H~80 stations
Product power spectrum (logarithm)
8
V~60 stations
H~80 stations
Product power spectrum (logarithm)
9
V~60 stations
H~80 stations
Product power spectrum (logarithm)
10
V~60 stations
H~80 stations
Product power spectrum (logarithm)
11
V~60 stations
H~80 stations
Product power spectrum (logarithm)
12
Radial “breathing” modes nS0 (n = 0 ~ 11) Observation vs. model
13
• 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)
15
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
16
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
18
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
19
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
20
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.