Measuring the Size of an Earthquake
Seismic waves are the vibrations from earthquakes that travel through the Earth; they are recorded on instruments called seismographs. Seismographs record a zig-zag trace that shows the varying amplitude of ground oscillations beneath the instrument. Sensitive seismographs, which greatly magnify these ground motions, can detect strong earthquakes from sources anywhere in the world. The time, locations, and magnitude of an earthquake can be determined from the data recorded by seismograph stations.
The Richter Scale
The Richter magnitude scale was developed in 1935 by Charles F. Richter of the California Institute of Technology as a mathematical device to compare the size of earthquakes. The magnitude of an earthquake is determined from the logarithm of the amplitude of waves recorded by seismographs. Adjustments are included for the variation in the distance between the various seismographs and the epicenter of the earthquakes. On the Richter Scale, magnitude is expressed in whole numbers and decimal fractions. For example, a magnitude 5.3 might be computed for a moderate earthquake, and a strong earthquake might be rated as magnitude 6.3. Because of the logarithmic basis of the scale, each whole number increase in magnitude represents a tenfold increase in measured amplitude; as an estimate of energy, each whole number step in the magnitude scale corresponds to the release of about 31 times more energy than the amount associated with the preceding whole number value.
At first, the Richter Scale could be applied only to the records from instruments of identical manufacture. Now, instruments are carefully calibrated with respect to each other. Thus, magnitude can be computed from the record of any calibrated seismograph.
Earthquakes with magnitude of about 2.0 or less are usually called microearthquakes; they are not commonly felt by people and are generally recorded only on local seismographs. Events with magnitudes of about 4.5 or greater - there are several thousand such shocks annually - are strong enough to be recorded by sensitive seismographs all over the world. Great earthquakes, such as the 1964 Good Friday earthquake in Alaska, have magnitudes of 8.0 or higher. On the average, one earthquake of such size occurs somewhere in the world each year.
The Richter Scale is not commonly used anymore, as it has been replaced by another scale called the moment magnitude scale which is a more accurate measure of the earthquake size.
Magnitude
Modern seismographic systems precisely amplifyand record ground motion (typically at periods ofbetween 0.1 and 100 seconds) as a function of time.This amplification and recording as a function of timeis the source of instrumental amplitude and arrival-timedata on near and distant earthquakes. Althoughsimilar seismographs have existed since the 1890's,it was only in the 1930's that Charles F. Richter,a California seismologist, introduced the concept ofearthquake magnitude. His original definition heldonly for California earthquakes occurring within600 km of a particular type of seismograph(the Woods-Anderson torsion instrument). His basic idea was quite simple:by knowing the distance from a seismographto an earthquake and observing the maximum signalamplitude recorded on the seismograph, an empiricalquantitative ranking of the earthquake's inherent sizeor strength could be made. Most California earthquakesoccur within the top 16 km of the crust;to a first approximation, corrections for variations inearthquake focal depth were, therefore, unnecessary.
Richter's original magnitude scale (ML) was then extendedto observations of earthquakes of any distanceand of focal depths ranging between 0 and 700 km.Because earthquakes excite both body waves, whichtravel into and through the Earth, and surface waves,which are constrained to follow the natural wave guideof the Earth's uppermost layers, two magnitude scalesevolved - the mb and MS scales.
The standard body-wave magnitude formula is
mb = log10(A/T) + Q(D,h) ,
whereA is the amplitude of ground motion (in microns);T is the corresponding period (in seconds);and Q(D,h) is a correction factor that is a function ofdistance,D (degrees), between epicenter and stationand focal depth,h (in kilometers), of the earthquake.The standard surface-wave formula is
MS = log10 (A/T) + 1.66 log10 (D) + 3.30 .
There are many variations of these formulas thattake into account effects of specific geographic regions,so that the final computed magnitude isreasonably consistent with Richter's original definitionof ML. Negative magnitude values are permissible.
A rough idea of frequency of occurrence of largeearthquakes is given by the following table:
MS Earthquakes per year ---------- ----------- 8.5 - 8.9 0.3 8.0 - 8.4 1.1 7.5 - 7.9 3.1 7.0 - 7.4 15 6.5 - 6.9 56 6.0 - 6.4 210
This table is based on data for a recent 47 yearperiod. Perhaps the rates of earthquake occurrence arehighly variable and some other 47 year period could give quitedifferent results.
The original mb scale utilized compressional bodyP-wave amplitudes with periods of 4-5 s, but recentobservations are generally of 1 s-period P waves.The MS scale has consistently used Rayleigh surfacewaves in the period range from 18 to 22 s.
When initially developed, these magnitude scaleswere considered to be equivalent; in other words,earthquakes of all sizes were thought to radiate fixedproportions of energy at different periods. But it turnsout that larger earthquakes, which have larger rupturesurfaces, systematically radiate more long-periodenergy. Thus, for very large earthquakes, body-wavemagnitudes badly underestimate true earthquake size;the maximum body-wave magnitudes are about6.5 - 6.8. In fact, the surface-wave magnitudes underestimatethe size of very large earthquakes;the maximum observed values are about 8.3 - 8.7. Someinvestigators have suggested that the 100 s mantle Love waves(a type of surface wave) should be used toestimate magnitude of great earthquakes. However,even this approach ignores the fact that damage to structure is oftencaused by energy at shorter periods.Thus, modern seismologists are increasingly turning totwo separate parameters to describethe physical effects of an earthquake:seismic moment and radiated energy.
Fault Geometry and Seismic Moment, MO
The orientation of the fault, direction of fault movement,and size of an earthquake can be described bythe fault geometry and seismic moment. These parametersare determined from waveform analysis of theseismograms produced by an earthquake. The differingshapes and directions of motion of the waveformsrecorded at different distances and azimuths from theearthquake are used to determine the fault geometry,and the wave amplitudes are used to compute moment.The seismic moment is related to fundamentalparameters of the faulting process.
MO = µS‹d› ,
where µis the shear strength of the faulted rock, S isthe area of the fault, and <d> is the average displacementon the fault. Because fault geometry and observerazimuth are a part of the computation, momentis a more consistent measure of earthquake size thanis magnitude, and more importantly, moment does nothave an intrinsic upper bound. These factors have ledto the definition of a new magnitude scale MW, based onseismic moment, where
MW = 2/3 log10(MO) - 10.7 .
The two largest reported moments are 2.5 X 1030dyn·cm (dyne·centimeters) for the 1960 Chile earthquake(MS 8.5; MW 9.6) and 7.5 X 1029 dyn·cm for the1964 Alaska earthquake (MS 8.3; MW 9.2).MS approaches it maximum value at a moment between1028 and 1029 dyn·cm.
Energy,E
The amount of energy radiated by an earthquake is a measureof the potential for damage to man-made structures.Theoretically, its computation requires summingthe energy flux over a broad suite of frequencies generatedby an earthquake as it ruptures a fault. Because of instrumental limitations, most estimates of energy have historically relied on the empirical relationship developed by Beno Gutenberg and Charles Richter:
log10E = 11.8 + 1.5MS
where energy,E, is expressed in ergs.Thedrawback of this method is that MSis computed from anbandwidth between approximately 18 to 22 s.It is now known that the energy radiated by an earthquakeis concentrated over a different bandwidth and at higher frequencies. With the worldwide deployment of modern digitally recording seismograph with broad bandwidth response, computerizedmethods are now able to make accurate and explicit estimatesof energy on a routine basis for all major earthquakes.A magnitude based on energy radiated by an earthquake, Me, cannow be defined,
Me = 2/3 log10E - 2.9.
For every increase in magnitude by 1 unit, the associated seismic energyincreases by about 32 times.
Although Mw and Me are both magnitudes, they describe different physical properites of the earthquake. Mw, computed from low-frequency seismic data, is a measure of the area ruptured by an earthquake. Me, computed from high frequency seismic data, is a measure of seismic potential for damage. Consequently,Mw and Me often do not have the same numerical value.
Intensity
The increase in the degree of surface shaking (intensity)for each unit increase of magnitude of a shallowcrustal earthquake is unknown. Intensity is based onan earthquake's local accelerations and how long thesepersist. Intensity and magnitude thus both depend onmany variables that include exactly how rock breaksand how energy travels from an earthquake to areceiver. These factors make it difficult for engineersand others who use earthquake intensity and magnitudedata to evaluate the error bounds that may existfor their particular applications.
An example of how local soil conditions can greatlyinfluence local intensity is given by catastrophic damagein Mexico City from the 1985, MS 8.1 Mexicoearthquake centered some 300 km away. Resonances ofthe soil-filled basin under parts of Mexico City amplifiedground motions for periods of 2 seconds by a factorof 75 times. This shaking led to selective damageto buildings 15 - 25 stories high (same resonant period),resulting in losses to buildings of about $4.0 billionand at least 8,000 fatalities.
The occurrence of an earthquake is a complexphysical process. When an earthquake occurs, much ofthe available local stress is used to power the earthquakefracture growth to produce heat rather that togenerate seismic waves. Of an earthquake system'stotal energy, perhaps 10 percent to less that 1 percentis ultimately radiated as seismic energy. So the degreeto which an earthquake lowers the Earth's availablepotential energy is only fractionally observed asradiated seismic energy.
Determining the Depth of an Earthquake
Earthquakes can occur anywhere between theEarth's surface and about 700 kilometers below thesurface. For scientific purposes, this earthquake depthrange of 0 - 700 km is divided into three zones: shallow,intermediate, and deep.
Shallow earthquakes are between 0 and 70 km deep;intermediate earthquakes, 70 - 300 km deep; and deepearthquakes, 300 - 700 km deep. In general, the term "deep-focusearthquakes" is applied to earthquakesdeeper than 70 km. All earthquakes deeper than 70 kmare localized within great slabs of shallow lithospherethat are sinking into the Earth's mantle.
The evidence for deep-focus earthquakes wasdiscovered in 1922 by H.H. Turner of Oxford,England. Previously, all earthquakes were consideredto have shallow focal depths. The existence of deep-focusearthquakes was confirmed in 1931 from studiesof the seismograms of several earthquakes, which inturn led to the construction of travel-time curves forintermediate and deep earthquakes.
The most obvious indication on a seismogram that alarge earthquake has a deep focus is the small amplitude,or height, of the recorded surface waves and the uncomplicatedcharacter of the P and S waves. Althoughthe surface-wave pattern does generally indicatethat an earthquake is either shallow or may havesome depth, the most accurate method of determiningthe focal depth of an earthquake is to read a depthphase recorded on the seismogram. The most characteristic depth phase is pP. This is the P wave that is reflected fromthe surface of the Earth at a point relatively near theepicenter. At distant seismograph stations, the pP follows the Pwave by a time interval that changes slowly withdistance but rapidly with depth. This time interval,pP-P (pP minus P), is used to compute depth-of-focustables. Using the time difference of pP-P as read from the seismogram and the distance between theepicenter and the seismograph station, the depth ofthe earthquake can be determined from publishedtravel-time curves or depth tables.
Another seismic wave used to determine focal depthis the sP phase - an S wave reflected as a P wave fromthe Earth's surface at a point near the epicenter. Thiswave is recorded after the pP by about one-half of thepP-P time interval. The depth of an earthquake can bedetermined from the sP phase in the same manner asthe pP phase by using the appropriate travel-timecurves or depth tables for sP.
If the pP and sP waves can be identified on theseismogram, an accurate focal depth can be determined.
by William Spence, Stuart A. Sipkin, and George L. Choy
Earthquakes and Volcanoes
Volume 21, Number 1, 1989
