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

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

A typical seismogram

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

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 )

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

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

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

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

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

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

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

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

(Mitsui et al., 2012)

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

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

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

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

Stack – PBO, Western U.S. 0S2 0S3 0S6 x 1S4 0S0 0S9 0S5 0T8 0S10 0S8

International GNSS Service IGS Network # GPS Station used : 337

Spectral Stack of horizontal Components

DART of NOAA Deep-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 earthquake Pink line: spheroidal 0Sn modes Green line: toroidal 0Tn modes

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

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.