A seismic event, apart from the "shaking" that is the earthquake, leaves behind permanent, step-function-like dislocations in the Earth. This redistribution of mass changes the Earth's inertia tensor; and the Earth's rotation will change according to the conservation of angular momentum. Such is the co-seismic excitation of Earth rotation changes. Similarly this mass redistribution causes the Earth's gravitational field to undergo slight changes expressible in terms of changes in its harmonic Stokes coefficients. The question is whether such excitations are large enough to be of any significance or consequence. The answer is mixed, as highlighted below:
(1) The 1960 Chilean event, which is by-far the largest earthquake ever recorded, should have left a co-seismic kink in the polar path which is worth 23 milliarcseconds in terms of polar motion excitation, barely discernible in records back in 1960 but certainly very noticeable if happened today.
(2) The length-of-day (LOD) is more resistant to change. The Chilean event would only have produced 8 microseconds of co-seismic decrease in LOD, an effect hardly detectable even in today's best measurements.
(3) The second largest earthquake recorded, the Alaskan event of 1964 (only 1/4 as large as the Chilean event in terms of its seismic moment or energy), should have produced a co-seismic increase in J_{2} by 5.3 x 10^{-11}, which would take the post-glacial rebound two years to "iron out", but still an order of magnitude smaller than the observed short-term fluctuations mostly due to atmospheric mass transport.
(4) All earthquakes that occurred after the Alaska event were much smaller (the largest was only 1/20 as energetic as the Alaskan event). None of their individual signatures were discernible either in Earth rotation or in gravitational field. These earthquake-induced signatures are in general two orders of magnitude smaller than, and completely buried in, natural fluctuations of Earth rotation and gravitational field, which are known to be caused by mass transports associated with other geophysical processes in other geophysical fluids.
(5) The collective effects of all earthquakes greater than magnitude 5 in the last two decades have an extremely strong statistical tendency with time. The parameters that show the strongest non-randomness are the dynamic oblateness J_{2}, the total moment of inertia (the trace of the inertia tensor), the length of day, the sum of the two equatorial principal moments of inertia, and the difference J_{22} between the two equatorial principal moments of inertia. Their time series all exhibit a strong decrease with time, indicating the tendency of earthquakes to make the Earth rounder and more compact. No such tendency is evident for higher harmonics of the gravitational field changes caused by earthquakes (e.g. J_{3}, J_{4}, J_{5} ).
(6) A similar strong tendency is seen in the polar motion excitation: earthquakes cumulatively are trying to "nudge" the Earth rotation pole towards ~140^{o} E, roughly opposite to that of the observed polar drift. However, the speed of this earthquake-induced polar drift in the last two decades is two orders of magnitude smaller than that observed.
The above findings (4-6) are summarized in these plots,
showing the cumulative, earthquake-induced changes in geodynamical parameters.
These changes are calculated based on formulation of Chao and Gross (1987;
see below), for the 21,600 major earthquakes listed in the
Harvard CMT catalog (magnitude > 5 since 1977).
The Earth's
polar motion has been observed for over a hundred years, initially by astrometric
and in modern times by space geodetic techniques. The polar motion excitation
function derived from these observations shows a generally broad-band structure,
but with certain prominent signals superimposed: a more-or-less secular
drift largely attributed to the present-day post-glacial rebound, a
30-year Markowitz wobble whose origin remains mysterious, and the very
notable annual wobble of obvious meteorological origin.
In addition,
the observed polar motion has a strong Chandler wobble component with a
time-varying amplitude comparable to that of the annual wobble. Although
the Chandler wobble is a natural free mode, it still needs continual excitation
to maintain its observed amplitude. Despite many studies, the Chandler
wobble's excitation sources have remained elusive to date, although atmospheric
angular momentum variations, perhaps together with oceanic variations,
may prove to be largely responsible for its excitation.
Historically,
another notable candidate excitation source for the Chandler wobble was
seismic dislocation; a first proposal was made as early as Milne (1907),
soon after the annual and Chandler wobbles were identified. Cecchini
(1928) later noted some correlation between the large polar motion and
the high seismicity during 1900-1908. Similar correlations have been alluded
to in subsequent reports, such as Runcorn (1970), Pines and Shaham (1973),
Press and Briggs (1975), Kanamori (1976).
However, to establish an unequivocal relationship between
seismic excitation and the observed polar motion, one needs to be able
to compute quantitatively how much an earthquake can excite polar motion
by altering the Earth's inertia tensor. In their milestone geophysical
monograph, Munk and MacDonald (1960) briefly treated the problem. They
used a simplistic local block-dislocation model for an earthquake, and
quickly dismissed the importance of earthquakes in polar motion excitation,
even for the largest earthquakes.
Then came the
great 1964 Alaskan earthquake, which provided new, fundamental insight
into the displacement field of an earthquake: Based on a strainmeter record
in Hawaii, Press (1965) announced that a static displacement was recorded
at teleseismic distances several thousand kilometers from the epicenter.
That prompted a series of investigations of seismic excitation of polar
motion: Mansinha and Smylie (1967), Smylie and Mansinha (1968; 1971), Mansinha
et al. (1970; 1979), Ben-Menahem and Israel (1970), Israel et al. (1973),
Israel and Ben-Menahem (1975), Rice and Chinnery (1972), Dahlen (1971;
1973), O'Connell and Dziewonski (1976), Smith (1977). Unfortunately the
search for signatures left by large earthquakes (e.g., the great 1960 Chilean
event and the 1964 Alaskan event) in polar motion was essentially inconclusive:
the quality of the polar motion data at the time was insufficient for that
purpose both in accuracy and temporal resolution.
A revival
of interest in the problem appeared during the latter half of the 1980s,
largely because of advances in polar motion measurement techniques, but
also owing to the availability of the Harvard centroid moment tensor (CMT)
catalog of all major earthquakes (see below). Using Dahlen's (1973) formula
on the thousands of earthquakes listed in the catalog, Souriau and Cazenave
(1985) and Gross (1986) computed time series of seismic excitation of polar
motion. They concluded that the earthquakes since 1977 were simply too
small to produce any appreciable signature in polar motion, with the cumulative
seismic excitation power being orders of magnitude smaller than that observed.
The next development
was by Chao and Gross (1987) who again computed the seismic excitation
of polar motion for all events listed in the CMT catalog, but using the
normal-mode summation scheme of Gilbert (1970). Their method has since
remained a most efficient way of computing the seismic excitation of not
only polar motion, but also of other important geodynamic parameters such
as gravitational field changes. Furthermore, Chao and Gross (1995) and
Chao et al. (1995) extended the formulation to compute earthquake-induced
changes in rotational energy and gravitational energy, respectively. These
papers and later Chao et al. (1996) have updated, and in fact strengthened,
the results of Chao and Gross (1987) who found many earthquake-induced
phenomena having intriguing geodynamical implications, listed as (4)-(6) above.
It should be stressed that all these studies only pertain to the coseismic effects, that is, to the effect due to the elastic dislocation that happens within, say, an hour following the initial rupture of the fault. The inelastic pre- or post-seismic movements that are often associated with large earthquakes on timescales of months to years have been studied based on rheological modeling (e.g., Dragoni et al., 1983; Sabadini et al.,1984; Soldati and Spada, 1999) . These effects typically augment the coseismic ones by a factor depending on the source mechanism and mantle rheology.