of aP z on the earthquake magnitude. We show in
Fig. 3 the synthetic signals for a realistic Tohoku-type earthquake, down-scaled to Mw = 8.5. Keeping the assumption of a triangular moment rate
function m; (12), scaling relationships (18, 19)
predict such an earthquake to have m; growing
half as fast as and with half the duration of
the Tohoku earthquake. As expected from the
respective moment time evolutions, the signal
amplitudes of the simulated Mw = 8.5 earthquake are about half the ones of the Tohoku
earthquake at early times [INU and Matsushiro,
Japan (MAJO) stations] and become increasingly smaller at late times, approaching the moment ratio value of 1/8. Even in this simulation,
where the Mw = 8.5 earthquake lasts 70 s (which
is short for such a magnitude) (19, 20), jaP z j never
exceeds 0.5 nm/s2. This simple test therefore
shows that detection of pre-P acceleration amplitudes reaching 1 nm/s2 is a direct evidence
of an earthquake with a seismic moment at least
twice as large (Mw > 8.7), hundreds to thousands
of kilometers away.
This estimate can be refined when a large
earthquake has been detected and its epicenter
has been located with local data (which can be
done in the tens of seconds after the origin time).
In this case, based on the theoretical or empirical
(with classical triggering techniques) P-wave
arrival time at regional stations, it is straight-
forward to extract the pre–P-wave arrival time
window. Compared with the usual post–P-wave
time window recording the complex regional
elastic wavefield, the former window provides
both an earlier and a simpler way to evaluate
how large the earthquake was. In this respect,
Fig. 3 can be directly used to get a reliable lower
bound of a megathrust earthquake magnitude.
As the Tohoku earthquake has a short duration
compared with its magnitude (12, 19, 20), it is
unlikely that a smaller magnitude earthquake
generates larger aP z values at a given distance.
Observing values of ≃1:5 nm=s2 about 1300 km
from the earthquake (as in the case of MDJ, FUK,
or INCN stations), just before the P-wave arrival
time, is therefore evidence of the occurrence of
a Mw > 9 earthquake. If such an approach were
followed for the Tohoku earthquake, using these
stations where the P arrival times are less than
180 s, a lower bound of its huge magnitude
would have been reliably detected 3 min after
the origin time. Using additional elastogravity
signals recorded at further distances (like ULN
or XAN stations) delays the time at which a first
magnitude can be provided but offers the po-
tential to provide an exact magnitude determi-
nation. Such data can indeed better detect that
the earthquake has stopped growing (7), a nec-
essary condition to move from a lower bound
estimation to an exact determination.
The possibility of detecting, 3 min after the
origin time, that the Tohoku earthquake had a
magnitude larger than 9 has to be compared with
our current ability to quantify large earthquakes’
magnitudes. The determination of the moment
magnitude in the minutes after an earthquake
is possible with local data [e.g., (21, 22)], but for
large-magnitude events, this is complicated by
finite-source effects. Currently, moment magnitudes are more efficiently determined at distances
far from the source (23–25), with a fundamental
limitation imposed by the time needed for elastic
wave propagation. Even the fastest available
methods (24) are unlikely to provide a reliable
magnitude estimate within the first 20 min after
Synthetic signals of the Mw = 8.5 earthquake
show that maximum amplitudes are lower than
0.5 nm/s2 everywhere, making individual detection difficult, even with excellent broadband seismometers located in quiet sites. We therefore
emphasize the strong benefit of installing and
maintaining high-quality sensors at regional distances from potential large earthquakes, such that
stacking or coherence techniques can be applied
to detect early gravity signals from earthquakes in
the 8 to 9 magnitude range. At lower magnitudes,
the potential detection of such signals depends on
our ability to separate the gravity signal from the
background seismic noise. This can be done in
principle by measuring the gradient of the gravity
perturbation between two or more seismically
isolated test masses. Relevant technologies are
being developed in the context of low-frequency
gravitational-wave detectors, with concepts such
as torsion bars antennas (26, 27), superconducting gravity gradiometers (28, 29), and atom interferometers (30, 31). In the first two concepts,
the test masses are linked to the ground by a
common frame; the displacements driven by the
seismic noise and affecting the gravity measurement can be made very similar for the two masses,
and they are hence rejected by the differential
measurement. In an atom interferometer, the
phase of a laser beam is sensed by its interaction
with two or more atomic clouds, giving an intrinsic partial immunity to the background seismic noise. The gravity gradient is, however, much
weaker than the gravity itself, and making its
measurement feasible should motivate further
research to overcome additional challenges besides the suppression of seismic noise.
REFERENCES AND NOTES
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−100 0 100 200 300
Time relative to Tohoku earthquake origin time (s)
Fig. 3. Agreement between observed and modeled aP z signals and influence of the earthquake
magnitude. Red (observed) and black (simulated) curves are in good agreement at all distances
and azimuths from the Tohoku earthquake. The simulation for a fictitious Mw = 8.5 earthquake
(dashed blue curve) shows large amplitude differences, directly illustrating the magnitude
determination potential existing in these prompt elastogravity signals.