## Mantle at a Glance

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:

- 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. - 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.
- 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*by 5.3 x 10_{2}^{-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. - 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.
- 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*, 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_{2}*J*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._{22}*J*)._{3}, J_{4}, J_{5} - 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)