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W Phase source inversion results
3/11/2011 (Mw 9.0), Tohoku-oki, Japan

Fast and reliable moment tensor estimation


Zacharie Duputel (a), Luis Rivera (a), Hiroo Kanamori (b), Gavin Hayes (c), Stuart Weinstein (d) and Barry Hirshorn (d).

(a) IPGS-EOST, CNRS/UdS, UMR 7516, Strasbourg, France.
(b) Seismological Laboratory, Caltech, Pasadena, USA.
(c) U.S. Geological Survey, National Earthquake Information Center, USA.
(d) NOAA, NWS, Pacific Tsunami Warning Center, Hawaii, USA.




The Mw 9.0 2011 Tohoku-oki earthquake happened at 05:46 UTC (14:46 JST) on Friday 11 March 2011 near the northeast coast of Japan. The event mechanism and the shallow centroid depth clearly indicate a megathrust event occurring at the boundary between the Pacific plate and the North American plate.

We have recently developed a source inversion algorithm using W phase at teleseismic distances. W phase is a very long period phase (mainly 100s-1000s) arriving at the same time as the P wave. When the displacement seismograms are filtered between 100s and 1000s, it is conspicuous between the P wave and the surface waves. Because of its long period nature and because it precedes the large amplitude surface-wave arrivals, the W phase can provide rapid and reliable estimates of the overall source parameters of large events. This contrasts with other source inversion methods which usually take several hours to determine the first order attributes of a great earthquake (i.e. Mw>8.5) even in a well instrumented region.

The W phase source inversion algorithm is now running online at U.S. Geological Survey (USGS), at the Pacific Tsunami Warning Center (NOAA/NWS/PTWC) and at the Institut de Physique du Globe de Strasbourg (IPGS-EOST, CNRS/UdS). The W phase solution calculated at PTWC is issued internaly within 30 minutes after origin time (O.T.) in order to have a quick preliminary robust estimate of the event magnitude and focal mechanism of large earthquakes. The W phase solution computed at USGS is made available on line for each significant event. (e.g. Tohoku-oki 2011 earthquake).

The figure below shows the updated W phase solution computed with a selection of "low noise" stations showing the best signal to noise ratios. This solution yields a moment magnitude Mw=9.0 with a quasi pure double-couple mechanism showing a small dip toward the west. The optimum W phase centroid location is 37.92°N, 143.11°E at a depth of 19.5 km and the best double couple is [Strike=196°, Dip=12°, Rake=85°] which is in very good agreement with the subduction interface geometry given by SLAB1.0 (G. Hayes, USGS).


W phase CMT solution obtained for the 2011 Tohoku-oki earthquake. The green circles correspond to USGS location of events occurring between 2011-03-11 and 2011-03-20.


Preliminary results

The first preliminary magnitudes provided by the different agencies within 15 min after the event origin time (O.T.) are clearly underestimating the actual event size as it is generally the case for large events. The PTWC first Mwp estimate gave an Mw=7.5, the USGS announce an M=7.9 in its preliminary earthquake report and the European-Mediterranean Seismological Center (EMSC) rapid determination of source parameters yield to Mw=8.0. The table below show the results delivered by real-time implementations of the W phase algorithm at the Pacific Tsunami Warning Center (NOAA/NWS/PTWC), the U.S. Geological Survey (USGS) and at the IPG Strasbourg (IPGS-EOST, CNRS/UdS). The PTWC and IPGS W phase solutions are implemented for internal use only while the USGS W phase solution is routinely disseminated to the public.

The automatic trigger of the W phase algorithm at USGS and PTWC quickly yielded an Mw>=8.8 (20, 22min and 30min after O.T.) which is significantly larger than the initial magnitudes provided by PTWC, USGS and EMSC. The magnitude Mw=8.8 obtained at PTWC is still lower than the final moment magnitude because of the large depth assumed initially in the automatic process (depth=83.5km). A manual trigger at PTWC 40 min after the origin time using a centroid depth at 24km yielded a more reasonable magnitude Mw=9.0 with a dip=12°. The first USGS W phase solution which was publicly disseminated 1 hour after O.T. gave Mw=8.9 with a larger dip=16°. The two last real-time W phase solutions provided by IPGS and USGS show very similar magnitudes and dips (i.e. Mw=9.0, dip=14°).



20min after O.T: USGS Internal W phase solution (6 channels)
Centroid loc.: Lat= 36.82N; Lon= 142.87E; Dep= 24.4 km
Time delay = Half duration = 68.7 sec
Best Double Couple: M0=3.941E+29
NP1: Strike=222.7 ; Dip=16.8 ; Slip=134.6
NP2: Strike=356.8 ; Dip=78.1 ; Slip=78.0



22min after O.T: PTWC Automatic W phase solution (29 channels)
Centroid loc.: Lat= 39.00N; Lon= 142.80E; Dep= 83.5 km
Time delay = Half duration = 56.0 sec
Best Double Couple: M0=1.934E+29
NP1: Strike=165.4 ; Dip=10.3 ; Slip=55.3
NP2: Strike=20.5; Dip=81.6 ; Slip=95.9



30min after O.T.: PTWC Automatic W phase solution (74 channels)
Centroid loc.: Lat= 38.30N; Lon= 143.50E; Dep= 83.5 km
Time delay = Half duration = 68.0 sec
Best Double Couple: M0=1.775E+29
NP1: Strike=194.3 ; Dip=22.8 ; Slip=81.3
NP2: Strike=23.7 ; Dip=67.5 ; Slip=93.6



40min after O.T.: PTWC Manual W phase solution (105 channels)
Centroid loc.: Lat= 38.40N; Lon= 142.90E; Dep= 24.4 km
Time delay = Half duration = 69.0 sec
Best Double Couple: M0=4.325E+29
NP1: Strike=190.6 ; Dip=11.1 ; Slip=76.7
NP2: Strike=24.2 ; Dip=79.1 ; Slip=92.6



48min after O.T: USGS Internal W phase solution (74 channels)
Centroid loc.: Lat= 37.82N; Lon= 142.87E; Dep= 24.4 km
Time delay = Half duration = 72.2 sec
Best Double Couple: M0=3.225E+29
NP1: Strike=204.4 ; Dip=14.8 ; Slip=104.3
NP2: Strike=9.7 ; Dip=75.7 ; Slip=86.3



1hour after O.T.: USGS Published W phase solution (89 channels)
Centroid loc.: Lat= 38.32N; Lon= 141.77E; Dep= 24.4 km
Time delay = Half duration = 48.0 sec
Best Double Couple: M0=2.836E+29
NP1: Strike=162.0 ; Dip=16.9 ; Slip=45.1
NP2: Strike=28.2 ; Dip=78.1 ; Slip=102.1



1hour 30min after O.T.: IPGS W phase solution (146 channels)
Centroid loc.: Lat= 38.12N; Lon= 142.97E; Dep= 24.4 km
Time delay = Half duration = 72.0 sec
Best Double Couple: M0=3.507E+29
NP1: Strike=196.3 ; Dip=14.4 ; Slip=85.1
NP2: Strike=21.4 ; Dip=75.7 ; Slip=91.3


Real-Time W phase CMT solutions obtained for the 2011 Tohoku-oki earthquake. The blue mechanisms indicate the solutions obtained at PTWC, the yellow mechanisms correspond to USGS solutions and the green mechanism indicate the IPGS automatic solution.


Updated results

We retrieved the LHZ, LHN and LHE waveforms belonging to FDSN, GSN and STS1 global virtual networks using the IRIS DMC facilities. Most of the channels used belong to BK, CI, CN, G, GE, IC, II, IU, MN and US networks.

Before trying a formal inversion for the moment tensor we perform a first-order fit of the W phase amplitude as a function of distance and azimuth. The idea here is to capture the information carried by the overall vertical amplitude of W phase and to translate it into magnitude. After reduction to a common distance, the peak-to-peak amplitudes are matched to a simple two lobed azimuthal pattern which accounts for variation due to the mechanism.

The figure on the right shows the amplitude-azimuth fit once the distance correction has been applied. The continuous line presents the result of the regression while the colored bars indicate the corrected peak-to-peak values which are measured at different epicentral distances. The average amplitude is estimated here to be 5 mm and the corresponding preliminary magnitude is Mw=9.1. We also note that the orientation of the lobes agrees well with the fault strike.


W phase preliminary amplitude fit for the 2011 Tohoku-oki earthquake. A polar representation is used: the angle and radius correspond respectively to the station azimuth and amplitude value. The continuous line represent the result of the regression determined from W phase amplitudes. The updated W phase centroid moment tensor (WCMT) solution is displayed for comparison.

Since this event is characterized by a shallow centroid depth (i.e. shallower than 30km), the W phase solution can be potentially affected by the trade-off between the dip and the scalar moment. To cope with this situation, one possibility is to carefully select low noise stations to constrain best the moment tensor elements controlling the fault dip.

A first rough screening is preformed first in order to reject the worst stations (median screening, misfit screening). The noise level is then computed for all the remaining channels using the 3 hour-long signal preceding the 2011 Tohoku-oki event. We then select 96 low noise channels showing an average noise level within 30dB of the New Low Noise Model (NLNM) in the 1-5mHz passband. Using this optimum dataset, we estimate the moment tensor as well as the centroid latitude, longitude, depth and timing.

The figures below show the updated W phase CMT (WCMT) inversion results. The W phase waveform and later arrivals are very well fitted by the data predicted from the WCMT solution. The optimum centroid depth of 20km as well as the dip of about 12° agrees very well with the SLAB1.0 geometry in this region (Gavin Hayes, USGS). The difference between the W phase magnitude Mw=9.0 and the Global CMT Mw=9.1 can be fully explained by the dip difference beween the two source models (i.e. gCMT dip is 10° and the WCMT dip is 12°). If we fix the gCMT dip to 12°, the gCMT magnitude becomes similar to WCMT with Mw=9.0. However, since the fault ruptured over several hundred kilometers down-dip with significant variation of dip, a strict interpretation of dip of a point source is not meaningful.

Updated W phase solution

Mw: 9.0

latitude : 37.92°N
longitude: 143.11°E
depth : 19.5 km

Time delay : 68.0 sec
Half duration: 68.0 sec
96 channels (69 stations)

Moment tensor: scale= 1.0E+29
rr= 1.695 ; tt=-0.147 ; pp=-1.548
rt= 1.403 ; rp= 3.637 ; tp=-0.534

Principal Axes:
1.(T) Val= 4.242 ; Plg= 57 ; Azm=292
2.(N) 0.031 ; 1 ; 201
3.(P) -4.273 ; 33 ; 110

Best Double Couple: M0=4.26E+29
NP1: Strike=196 ; Dip=12 ; Slip= 85
NP2: Strike= 21 ; Dip=78 ; Slip= 91



W phase centroid position grid-search for the 2011 Tohoku-oki earthquake. The black cross indicates the USGS PDE location while the red star shows the optimum W phase centroid location.



Comparison of observed waveforms (black) and the corresponding synthetics (red) computed from the W phase updated CMT solution. The station azimuth (Φ) and epicentral distance (Δ) are indicated as well as the W phase time windows which are bouded by red dots. The W phase CMT inversion is based on the ground motion of stations within Δ<90° after applying a passband filter in the 1-5mHz passband. W phase and later arrivals are very well predicated by the W phase CMT solution. For some stations like INCN, PET, BJT, MA2, TATO, YAK and QIZ, the surface waves are affected by instrument problems while the W phase is not affected.


Links and References


Kanamori, H., 1972. Mechanism of tsunami earthquakes, Phys. Earth Planet Inter., 6, 356-359.

Kanamori, H. & Rivera, L., 2008. Source inversion of W phase: speeding tsunami warning, Geophys. J. Int., 175, 222-238.

Hayes, G., Rivera, L. & Kanamori, H., 2009. Source inversion of the W phase: real-time implementation and extension to low magnitudes, Seismol. Res. Let., 3, 800-805.

Duputel, Z., Rivera, L., Kanamori, H., Hayes, G.P., Hirsorn, B. & Weinstein, S., 2011. Real-time W Phase inversions during the 2011 Tohoku-oki earthquake, Earth, Planets and Space, 63, 535-539.

Z. Duputel, L. Rivera, H. Kanamori, G. Hayes, 2012. W-phase fast source inversion for moderate to large earhquakes (1990 - 2010), Geophys. J. Int., 189, p. 1125-1147.



W phase solutions

USGS W phase solution

ERI W phase solution


Data sources

IRIS Data Management System, and specifically the IRIS Data Management Center, were used for access to waveform and metadata required in this study (

Global Seismographic Network (GSN) is a cooperative scientific facility operated jointly by the Incorporated Research Institutions for Seismology (IRIS), the United States Geological Survey (USGS), and the National Science Foundation (NSF). (

Geoscope operated by the Institut de Physique du Globe de Paris (IPGP) and the Ecole et Observatoire des Sciences de la Terre (EOST) (

The GEOFON network funded and operated by GFZ Potsdam, Germany, in co-operation with almost 50 institutions worldwide. (

The Mediterrean Network (MedNet) mantained by INGV in cooperation with many geophysical institutes. (

Northern California Earthquake Data Center operated by Berkeley Seismological Laboratory and USGS (

Southern California Seismic Network operated by Caltech and USGS (

Canadian National Seismograph Network (CNSN) mantained by the Geological Survey of Canada (

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