1. 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, Taiwan 1also at Inst. Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan

2. Traveling-wave – Standing-wave
Normal modes ||
Traveling-wave – Standing-wave
Equivalence
sin(wt + kx) + sin (wt – kx)
= 2 sinwt * coskx

3. A typical seismogram

4. nulm , nωlm Eigenfunction , Eigenfrequency degree overtone number
(3-D) (discrete)
Eigenfunction , Eigenfrequency
nulm , nωlm
degree
overtone number
order
n=0: Fundamental modes ~ Surface waves
n>0: Overtone modes ~ Body waves

5. Earthquake Displacement Field
• Equation of motion
• Solve by expanding displacement field
Normal mode eigenfunctions for SNREI Earth
Expansion coefficients (note the static limit)
(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. Product power spectrum (logarithm)V
~60 stations H
~80 stations

8. Product power spectrum (logarithm)V
~60 stations H
~80 stations

9. Product power spectrum (logarithm)V
~60 stations H
~80 stations

10. Product power spectrum (logarithm)V
~60 stations H
~80 stations

11. Product power spectrum (logarithm)V
~60 stations H
~80 stations

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

13. GSI’s GNSS stations 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 (

14. (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
|Y(f)|2
0T2
0S9
2T1
0T15
2T2
2T7
0T20
1T11
1T12
0T3
0S10
0T17
1T9
0T11
0T13
0T19
0T4
0T22
0T10
0T12
0T14
0T18
0T21
- - - fundamental toroidal modes

17. Spectral Stack – GSI, JapanX
0S3
0S4
0T2
0S0
0S7
0S8
0S9
0S12
0S6
0S18
0S21
1S4
－: Fundamental spheroidal modes

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. 0S2 0S3 0S6 x 1S4 0S0 0S9 0S5 0T8 0S10 0S8

20. International GNSS Service IGS Network # GPS Station used : 337

21. Spectral Stack of horizontal Components

22. DART of NOAA Deep-ocean Assessment and Reporting of Tsunamis network

23. 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.

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

25. Spectrum of a single DART (BPR21413) record
for 2010 Chile earthquake
Blue: pre-earthquake Red: during earthquake
Pink line: spheroidal 0Sn modes Green line: toroidal 0Tn modes

26. Spectral Stack of 24 DART records for 4 earthquakes
Blue: pre-earthquake Red: during earthquake
Pink line: spheroidal 0Sn modes Green line: toroidal 0Tn modes

27. 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.