LECTURE 8 NOTES - MEASURING EARTHQUAKES (updated 11/10/97)
Instructor: Professor Barbara Romanowicz
Director of Seismological Laboratory
Office Hours: Thursday 2-4 pm , upon appointment only
475 Mc Cone Hall
MEASURING EARTHQUAKES
How to locate an earthquake
1) Intensity maps
We have seen how this was done before the advent of precise seismic
instrumentation that could identify seismic waves and enable seismologists
to measure their travel times precisely (clocks...).
Until that, use intensity of shaking from reports of human reactions and
from damage: from these, position and extent of the source of the wave
radiation could be ROUGHLY determined, by drawing isoseismal contours.
-show New Madrid again
-show intensity map of SF 1906 indicating the length of rupture.
Still a very valuable technique for historical earthquakes before the beginning
of this century, for which there are no other documents.
Also useful to guide geologists; where to look for surface rupture (although
there are other more modern means too).
Drawbacks:
-not very precise epicentral location
-no information about the depth of the earthquakes
-information only in areas where population is dense enough:
vast areas of the world are not covered, in particular the oceans
(2/3 of the earth's surface) --> could not get a picture of the
correlation of seismicity with plate boundaries, or any other
observation is support for plate tectonics theory (e.g. Benioff
zones).
Nowadays, location is determined in general from the time taken by P waves
to travel from the focus to the seismograph, with , sometimes the help of S
waves.
S waves are more complicated to measure, because they:
1) have longer periods --> require broader band instrumentation, more
difficult to define the onset of the wave,
2) require 3 component recording, the most standard methods rely primarily or
exclusively on measurements of P arrival times, and for this purpose,
arrays of stations have been installed at many scales:
-dams and power plants: dense arrays around them to detect earthquakes
that may threaten the safety of the facility
-at the scale of a region, e.g. California ---> NCSN, SCSN, UC Berkeley
-at the global scale, for larger earthquakes :
reports to ISC, bulletins, time: UT
observatory practice.
Usefulness of telemetry to provide rapid and precise estimates of location,
and reduce confusion of the press and public.
For locating smaller earthquakes: want to be closer by.
Need good distribution of stations (good azimuthal coverage) to obtain
precise estimates, with at least a few stations within 300 km of the actual
epicenter. If regional network available, and epicenters fall within the
network, can usually locate to within 5-10 km.
Teleseismic locations: precision to within 20 km.
Methods for locating earthquakes differ in details, but all rely on the same
principle: the travel time of a seismic wave , such as P wave, from the source to a given point on the Earth's surface is a direct measure of the distance between the two points.
Over many years of observation, seismologists have been able to determine,
by trial and error, the average travel times of P and S waves, for any specified distance. The times have been printed in tables and graphs as a function of distance. Then the appropriate distance between the observatory and the focus can be read from the tables by comparing them with those that have been actually measured from an ensemble of earthquake sources to seismic observatories.
Uncertainties due to imperfect knowledge of the structure and thus the
velocities of the waves (variations in the structure). Depth much less
precisely determined (need more than just P waves to get it right - reflections from surface....).
One observatory, on P wave reading: only distance from earthquake source
can be determined reasonably well.
If arrival times of P waves at 3 observatories: then triangulation can be used to determine the epicentral location and origin time of the earthquake.
Common practice: use readings from many observatories, sometimes several
hundreds, often over 50.
Demonstration using differential time between P and S waves at 3 stations.
From past experience, we know the average distance between an epicenter
and a seismograph corresponding to each S minus P interval
S-P times: distance:
Berkeley 21 seconds 190 km
JAS 20.4 sec 188 km
MIN 12.9 sec 105 km
Caution: distinguish distance to focus from distance to epicenter: circles drawn are intersection of spheres with the surface: one point (epicenter).
In 3D intersection forms a chord, on which focus should lie
applying a distance scale, one can use a compass to draw three arcs of circle, with the 3 observatories at the centers. The arcs will intersect (approximately) at one point, which is the estimated location of the earthquake source.
If all fall short of intersection: could be due to deep focus (or too late an origin time).
If all arcs appear to overshoot: too early an origin time, or from badly recorded shock where manys stations missed the first motion.
In fact, the tables or charts allow to also provide an estimate of origin time of the earthquake, which follows directly from reading the transit time from earthquake to the station:
An origin time is derived from the data of each station. Of course, the OT
should be consistent. Sometimes there is a gross discrepancy at one station:
could be a time error (station clock) or misidentified phases: go back and clear up the problem. Origin time determined with some uncertainty attached to it.
Depth determination requires more data:
4th measurement needed: tP or tS at one other station, or T-time of some
other stations at the same 3 stations (if we have tP immediately above, this
would give us the depth of the earthquake: methodology used in teleseismic
cases using the phase pP).
(P-O times multiplied by best estimate for mean velocity of P in California to give "straight line distances" between hypocenters and stations :D)
compare D's to surface distances from epicenter to stations: D
hypocentral depth:
h2 = D2 - D2
In practice:
-plot S-P times as a function of P arrival time:
should plot on straight line which interesects the absissa axis at the
origin time O.
-multiply P-O times by best estimate of P velocities in the region to obtain
distance from focus D.
-find epicenter by drawing circles of radii D from each station and determine
their "average" intersection point (the actual intersection point is
somewhere at depth
-determine epicentral distance, then h.
Not very precise.
But if there is a 4th station, can get depth:
-epicentral distance known
-travel time to P gives D, hence h
-use knowledge about arrival times and wave velocities in iterative manner,
or put everything into least squares problem.
Assessing earthquake size
Subjective/objective assessment of size:
Felt earthquakes and damaging ones are generally equated with large
earthquakes, but in fact some of the largest earthquakes may go unnoticed
(eg. Bolivia, June 6, 1994 - because it was very deep, or many earthquakes in south-west pacific that are far from populated areas).
Bakersfield, Ca (1952; M 7.7) in the minds of local population was much less
important than a comparatively minor aftershock (5.8) a month later, which
occurred much closer to the city and occasioned more local damage,
representing higher local intensities.
The distance from the earthquake can be an important factor, and when
measuring intensities and drawing isoseismal maps it becomes clear that the
local intensity can be just as large, it is the maximum intensity that allows to compare event sizes (albeit qualitatively).
More objective measure of size : magnitude scale, developed in Japan by
Wadati and in California by Richter, in the 1930;s. Later extended worldwide.
FUndamental idea is to measure earthquake size according to the amplitudes
of the recorded seismic waves.
Because earthquake sizes vary by many orders of magnitude, it is convenient
to compress the measured wave amplitude by using a logarithmic scale.
Roughly speaking, it amounts to counting the power of 10 in the value of the
amplitude:
amplitude of 10 ----> 1
amplitude of 100 ----> 2
amplitude of 1000 ----> 3 etc...
The Richter magnitude ML is the logarithm to base 10 of the maximum
seismic wave amplitude, which is measured in thousands of a millimeter as
recorded on a special seismograph: the Wood-Anderson seismograph.
No particular wave type, just the maximum amplitude.
Since amplitude decreases with distance, Richter selected a distance of 100 km from the epicenter as a standard:
if peak amplitude is 1cm for an earthquake 100km away, then ML=4
(1cm=10000 thousandths of a mm).
Because earthquake sources are located at all distances from seismographic
stations, Richter developed a method to make allowance for this attenuation
with epicentral distance.
Definition involves a Zero level.
M = log A - log Ao
where Ao is "reference" earthquake: one thousandth of a millimeter at a
distance of 100 km.
-then determine the variations of Ao with distance (tabulated).
-add station corrections (each station will have a systematic bias when
compared to ensemble of measurements at many individual stations, due to
local ground conditions and instrument response)
Scale has no limits, although earthquake sizes do: magnitudes of -1, -2 all the way to magnitudes 8.5 , but only few exceed that value.
Alaska 1964: Richter Magnitude of 8.6.
Richter magnitude worked better than expected: originally, Richter wanted to
roughly put earthquakes into 3 categories: large, medium and small, but
found that obtained a fine grading that was very consistent from earthquake
to earthquake.
Richter magnitude is the most popular with the public and the press, but it is not used much in research now, because wave type not specified and WA had
limited recording capabilities (saturation in particular). Also, adapted only to local shocks (distances less than 200-400 km). Other magnitude scales have been developed for teleseismic events and to gain independence from
instrumentation.
Various magnitude scales (creates confusion with the public).
Amplitude of the P wave: "mb", not affected by the depth of the source.
For shallow earthquakes: "MS" based on 20 sec surface waves.
For a given earthquake: different types of magnitudes will have different values.
Alaska 1964: MS 8.6 but mb only 6.5
MS was better description of overall earthquake size. But Ms saturates for
large earthquakes (max amplitude of 20 sec waves remains the same even
though earthquakes can be of different sizes, because source dimensions play
a role in the band of periods they "excite" and for large sources, at 20 sec you do not see the entire source - corner frequency, roughly the inverse of radius of source).
Also differences between Mb and MS can be symptomatic of deep
earthquakes. (large Mb, small Ms because surface waves are not well excited).
Best current magnitude scale is the moment magnitude Mw:
Magnitude as measured by maximum amplitude of some wave type gives a
peak value which does not directly measure the overall mechanical power of
the source, just as the strongest wind gust is not a reliable measure of the
overall force of a windstorm.
We could measure the energy radiated by the earthquake as seismic waves.
There is a problem: energy is absorbed by fracture and friction in the rocks so that the recorded motion is always less than if the earthquake "machine" was a perfect one. Correction for such attenuation has to be made: numerous
attempts at developing consistent formulas to estimate energy from the wave
motion measured by instruments has not been completely successful so far.
We go back to a definition which involves the forces at play, thus the seismic moment, which give a consistent and reliable scale of earthquake size.
seismic moment = Mo.
Mw= 2/3 log Mo -10.7
A magnitude scale has been derived from moment, so as to coincide with
surface wave magnitude for shallow earthquakes in a large magnitude
range --> Mw. The advantage of Mw is that it gives a consistent measure of size of earthquakes from the very smallest ones to the greatest earthquakes ever recorded: the reason is that seismic moment gives a measure of the whole dimension of the slipped fault, whereas Ms uses waves that have
wavelengths of only about 100 km, which sample only a fraction of the
slipped fault area of the largest earthquakes.
(show pictures of moment versus length)
Use of magnitudes:
-size for public, press, scientists
-discrimination with nuclear bombs
to predict maximum ground accelerations for construction engineering.
Earthquake mechanisms
First motions:
-either compressions (push upward) or dilatations (downward)
-points towards which fault is moving: compressions
-points away from which fault is moving: dilatations
-alternating compressions and dilatations
-lines separating regions of compressions/dilatations: no motion occurs(no
first motion!): nodal lines
-lower hemisphere projections
-different "beachball patterns" according to type of earthquake: allow to
distinguish normal, reverse and strike slip motion on faults
-one of the great successes: remotely classify the type of faultings along
midoceanic ridges and trenches: definite pattern indicating a global
consistency of thrusting subduction, transform faults and normal faulting
(extension).