Geoscience Reference
In-Depth Information
Magnitudes from C. Richter to
M
wp
and the W phase
The process of assigning a magnitude to a seismic event is far from simple, all the more
so in the case of the large earthquakes that can generate tsunamis. Originally, Charles Richter
1
used the concept of measuring the maximum ground motion amplitude recorded from local
events on a standard Wood-Anderson seismograph. The determination is quite straightforward,
involving the measurement of the largest amplitude of the pen during the earthquake in
microns—for earthquakes this is generally the shear (or secondary [S]) wave. The amplitude is
empirically corrected for distance in southern California, and the observations from several sta-
tions are averaged to increase the statistical stability of the measurement. Richter thus deined
a regional magnitude scale for earthquakes, which is now referred to as a local magnitude
M
L
.
The deinition of
M
L
was very important because all the subsequent magnitude scales have
been tied to this initial algorithm. The concept was soon extended worldwide using a combina-
tion of measurements on body and surface waves at teleseismic distances, leading to the dei-
nition of two standardized algorithms, a body-wave magnitude
m
b
measured on short-period
P-waves at a target frequency of 1 Hz, and a surface wave magnitude
M
s
measured at a period
of 20 s. These early algorithms were a largely empirical endeavor because of the use of simple
models of seismic sources and wave propagation.
In the late 1950s and early 1960s, the work of Vvendeskaya in Russia and Aki in Japan
showed that earthquake sources could be described by a relatively complex system of forces,
expressed in physical units of dyne*cm or N*m as a “seismic moment”
M
0
, and directly related
to the total amount of slip occurring on the fault plane, integrated over the full surface area
of faulting. Unlike seismic magnitudes, seismic moments are directly related to the physical
properties of the source. In order to facilitate comparisons with existing catalogues (and also
in the process to facilitate communication with the general public), Kanamori
2
and Hanks
and Kanamori
3
proposed to recast seismic moment values into a “moment magnitude” scale,
M
w
, using
M
w
= 2/3 (log
10
M
0
- 9.1), where
M
0
is in N*m (or fault area times displacement times
material rigidity).
The problem of assessing earthquake size in the context of tsunami warning is several-fold:
(1) The most eficient algorithms for seismic moment inversion require the use of large
datasets (in practice, tens to hundreds) of long-period (low-frequency) surface waves, which
unfortunately travel slowly and thus delay the warning process.
(2) The conventional magnitude scales, which target relatively short periods (1 and 20 s),
are not representative of the low-frequency part of the source spectrum, which controls the
excitation of the tsunami. Because of the frequency dependence of the seismic source,
m
b
and
