Geoscience Reference
In-Depth Information
mic instruments are sensitive to the velocity of ground motion rather than to its displacement
or acceleration, in practice a double integration is required. Generally, seismic instrumentation
becomes increasingly insensitive at very low frequencies when the earth's noise is increasing
and integral estimates of displacement are, perforce, inaccurate.
This is the basis of the so-called
M
wp
algorithm
4
by which initial estimates of the seismic
moment of a large earthquake can be inferred from the earliest-arriving seismic signals
recorded in the far ield.
M
wp
has been implemented and currently constitutes the procedure
in use at both the Paciic Tsunami Warning Center (PTWC) and the West Coast/Alaska Tsunami
Warning Center (WC/ATWC) for the purpose of estimating earthquake sources for tsunami-
genic potential.
SHORTCOMINGS OF THE
M
wP
ALGORITHM
As compelling as the
M
wp
concept may be, it suffers from having never been subjected to
the necessary and independent exercise of being tested on synthetic seismograms (i.e., com-
putational renditions of the wavetrains expected to be recorded on a given seismic instrument
for a particular scenario of earthquake size, rupture parameters [including for example the
case of “tsunami earthquakes”], and receiver geometry). Obviously, the number of great and
mega-earthquakes is also highly limited, thereby reducing the opportunities for applications
of statistics. The theoretical understanding of seismic sources has reached the point where a
number of methods are available to produce these synthetic seismograms. To the best of the
committee's knowledge, vetting of the
M
wp
algorithm for tsunami inference was not done prior
to its use at the TWCs.
Indeed, it would be expected that the use of
M
wp
will encounter signiicant and systematic
problems both for very large events and for the tsunami earthquakes that demonstrably do
not follow scaling laws; that is, precisely those earthquakes carrying enhanced tsunami po-
tential given their size. Tsuboi et al.
4
compared
M
wp
to
M
w
, but only to sources that had magni-
tudes less than 8.0 (neither
great
nor
mega
-earthquakes). An
M
wp
algorithm is described in the
open source (source forge) website (http://seismic-toolkit.sourceforge.net/) with a comparison
of
M
wp
to
M
w
. For events larger than
M
w
= 8.25, the
M
wp
magnitude signiicantly underestimates
the magnitude and the moment-based
M
w
measure. As is the case for all other magnitude
measures,
M
wp
also saturates as earthquake moment increases. In addition, the development of
an eficient algorithm providing automated routine measurements of
M
wp
requires extending a
number of its parameters in ways that lead to further problems for larger earthquakes.
There are two categories of problems with the
M
wp
method: systematic problems inherent
in the theory underlying the method, and shortcomings of the particular modalities of imple-
mentation used at the TWCs. Among the former:
(1) The domain of applicability of the theory, known as geometrical optics, requires in prin-
ciple the use of wavelengths much shorter than the characteristic dimensions of the structures
involved. This principle is violated for large sources such as the Sumatra earthquake whose
