The Richter magnitude scale assigns a magnitude number to quantify the energy released by
an earthquake. The Richter scale is a base-10 logarithmic scale, which defines magnitude
as the logarithm of the ratio of the amplitude of the seismic waves to an arbitrary, minor
amplitude. As measured with a seismometer, an earthquake
that registers 5.0 on the Richter scale has a shaking amplitude 10 times that of an earthquake
that registered 4.0, and thus corresponds to a release of energy 31.6 times that released
by the lesser earthquake.
Development
In 1935, the seismologists Charles Francis Richter and Beno Gutenberg, of the California
Institute of Technology, developed the Richter magnitude scale, specifically for measuring
earthquakes in a given area of study in California, as recorded and measured with the Wood-Anderson
torsion seismograph. Originally, Richter reported mathematical values to the nearest quarter
of a unit, but the values later were reported with one decimal place; the local magnitude
scale compared the magnitudes of different earthquakes. Richter derived his earthquake-magnitude
scale from the apparent magnitude scale used to measure the brightness of stars.
Richter established a magnitude 0 event to be an earthquake that would show a maximum,
combined horizontal displacement of 1.0 µm on a seismogram recorded with a Wood-Anderson
torsion seismograph 100 km from the earthquake epicenter. That fixed measure was to prevent
negative magnitudes from being assigned. The slightest earthquakes that could be recorded,
and located in that time, were around magnitude 3.0, however, the Richter magnitude scale
has no lower limit, and contemporary seismometers can register, record, and measure earthquakes
of a negative magnitude. was not designed to be applied to data with
distances to the hypocenter of the earthquake greater than 600 km. For national and local
seismological observatories the standard magnitude scale is today still . Unfortunately this
scale saturates at around = 7, because the high frequency waves recorded locally have
wavelengths shorter than the rupture lengths of large earthquakes.
Later, to express the size of earthquakes around the planet, Gutenberg and Richter developed
a surface wave magnitude scale and a body wave magnitude scale. These are types of waves
that are recorded at teleseismic distances. The two scales were adjusted such that they
were consistent with the scale. That adjustment succeeded better with the scale than with
the scale. Each scale saturates when the earthquake is greater than magnitude 8.0, and, therefore,
the moment magnitude scale was invented. The older magnitude-scales were superseded,
by methods for calculating the seismic moment, from which derived the moment magnitude scale.
About the origins of the Richter magnitude scale, C.F. Richter said:
I found a [1928] paper by Professor K. Wadati of Japan in which he compared large earthquakes
by plotting the maximum ground motion against [the] distance to the epicenter. I tried a
similar procedure for our stations, but the range between the largest and smallest magnitudes
seemed unmanageably large. Dr. Beno Gutenberg then made the natural suggestion to plot the
amplitudes logarithmically. I was lucky, because logarithmic plots are a device of the devil.
Details The Richter scale was defined in 1935 for
particular circumstances and instruments; the instrument used would became saturated
by strong earthquakes and unable to record high values. The scale was replaced by the
moment magnitude scale; for earthquakes adequately measured by the Richter scale, numerical values
are approximately the same. Although values measured for earthquakes now are actually
, they are frequently reported as Richter values, even for earthquakes of magnitude
over 8, where the Richter scale becomes meaningless. Anything above 5 is classified as a risk by
the USGS. The Richter and MMS scales measure the energy
released by an earthquake; another scale, the Mercalli intensity scale, classifies earthquakes
by their effects, from detectable by instruments but not noticeable to catastrophic. The energy
and effects are not necessarily strongly correlated; a shallow earthquake in a populated area with
soil of certain types can be far more intense than a much more energetic deep earthquake
in an isolated area. There are several scales which have historically
been described as the "Richter scale", especially the local magnitude and the surface wave scale.
In addition, the body wave magnitude, , and the moment magnitude, , abbreviated MMS, have
been widely used for decades, and a couple of new techniques to measure magnitude are
in the development stage. All magnitude scales have been designed to
give numerically similar results. This goal has been achieved well for , , and . The scale
gives somewhat different values than the other scales. The reason for so many different ways
to measure the same thing is that at different distances, for different hypocentral depths,
and for different earthquake sizes, the amplitudes of different types of elastic waves must be
measured. is the scale used for the majority of earthquakes
reported by local and regional seismological observatories. For large earthquakes worldwide,
the moment magnitude scale is most common, although is also reported frequently.
The seismic moment, , is proportional to the area of the rupture times the average slip
that took place in the earthquake, thus it measures the physical size of the event. is
derived from it empirically as a quantity without units, just a number designed to conform
to the scale. A spectral analysis is required to obtain , whereas the other magnitudes are
derived from a simple measurement of the amplitude of a specifically defined wave.
All scales, except , saturate for large earthquakes, meaning they are based on the amplitudes of
waves which have a wavelength shorter than the rupture length of the earthquakes. These
short waves are too short a yardstick to measure the extent of the event. The resulting effective
upper limit of measurement for is about 7 and about 8.5 for .
New techniques to avoid the saturation problem and to measure magnitudes rapidly for very
large earthquakes are being developed. One of these is based on the long period P-wave,
the other is based on a recently discovered channel wave.
The energy release of an earthquake, which closely correlates to its destructive power,
scales with the 3⁄2 power of the shaking amplitude. Thus, a difference in magnitude
of 1.0 is equivalent to a factor of 31.6 in the energy released; a difference in magnitude
of 2.0 is equivalent to a factor of 1000 in the energy released. The elastic energy radiated
is best derived from an integration of the radiated spectrum, but one can base an estimate
on because most energy is carried by the high frequency waves.
Richter magnitudes The Richter magnitude of an earthquake is
determined from the logarithm of the amplitude of waves recorded by seismographs. The original
formula is:
where A is the maximum excursion of the Wood-Anderson seismograph, the empirical function A0 depends
only on the epicentral distance of the station, . In practice, readings from all observing
stations are averaged after adjustment with station-specific corrections to obtain the
value. Because of the logarithmic basis of the scale,
each whole number increase in magnitude represents a tenfold increase in measured amplitude;
in terms of energy, each whole number increase corresponds to an increase of about 31.6 times
the amount of energy released, and each increase of 0.2 corresponds to a doubling of the energy
released. Events with magnitudes greater than 4.5 are
strong enough to be recorded by a seismograph anywhere in the world, so long as its sensors
are not located in the earthquake's shadow. The following describes the typical effects
of earthquakes of various magnitudes near the epicenter. The values are typical only
and should be taken with extreme caution, since intensity and thus ground effects depend
not only on the magnitude, but also on the distance to the epicenter, the depth of the
earthquake's focus beneath the epicenter, the location of the epicenter and geological
conditions. (Based on U.S. Geological Survey documents.)
The intensity and death toll depend on several factors and can vary widely.
Minor earthquakes occur every day and hour. On the other hand, great earthquakes occur
once a year, on average. The largest recorded earthquake was the Great Chilean Earthquake
of May 22, 1960, which had a magnitude of 9.5 on the moment magnitude scale. The larger
the magnitude, the less frequent the earthquake happens.
Examples The following table lists the approximate
energy equivalents in terms of TNT explosive force – though note that the earthquake
energy is released underground rather than overground. Most energy from an earthquake
is not transmitted to and through the surface; instead, it dissipates into the crust and
other subsurface structures. In contrast, a small atomic bomb blast will not, it will
simply cause light shaking of indoor items, since its energy is released above ground.
31.6227 to the power of 0 equals 1, 31.6227 to the power of 1 equals 31.6227 and 31.6227
to the power of 2 equals 1000. Therefore, an 8.0 on the Richter scale releases 31.6227
times more energy than a 7.0 and a 9.0 on the Richter scale releases 1000 times more
energy than a 7.0. Thus, Quakes using the more modern magnitude scales
will denote their abbreviations: and . Those that have no denoted prefix are . Please be
advised that the magnitude "number" displayed for those quakes on this table may represent
a significantly greater or lesser release in energy than by the correctly given magnitude.
Magnitude empirical formulae These formulae are an alternative method to
calculate Richter magnitude instead of using Richter correlation tables based on Richter
standard seismic event. The Lillie empirical formula:
Where: A is the amplitude of the P-wave, in micrometers,
measured at 0.8 Hz. is the epicentral distance, in km.
For distance less than 200 km:
For distance between 200 km and 600 km:
where A is seismograph signal amplitude in mm, D distance in km.
The Bisztricsany empirical formula for epicentral distances between 4˚ to 160˚:
Where: is magnitude
is the duration of the surface wave in seconds is the epicentral distance in degrees.
The Tsumura empirical formula:
Where: is the magnitude.
is the total duration of oscillation in seconds. is the epicentral distance in kilometers.
The Tsuboi, University of Tokio, empirical formula:
Where: is the magnitude.
is the amplitude in um. is the epicentral distance in kilometers.
See also
References
External links IRIS Real-time Seismic Monitor of the Earth
USGS: magnitude and intensity comparison USGS: Earthquake Magnitude Policy
USGS: 2000–2006 Earthquakes worldwide USGS: 1990–1999 Earthquakes worldwide
Alaska Railroad Earthquake with a table of yield-to-magnitude relations.
Earthquake Energy Calculator with seismic energy approximated in everyday equivalent
measures.