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EXERCISE

EARTHQUAKE MAGNITUDE AI§N II§TENSITY Supplies Needed . calculato¡ . metric ruier

PI]RPOSE Exercise

I introduced many of the fundamentalconcepts of earthquakes, and this

add two more importantconcepts: earthquakemagnitude and intensity. Eotlt magnitude and intensity are eipressions of the amount of energyreleas-ed when a fault exercise

will

rupiures. Scientists are interásted in measuring seismic engrgY in order to categoiun eaithquakes and to better understand tectonic processes. Society is interested in the strength of past and future earthquakes in order to assess and predict damag-e and loss of kfe. The foiiowing exercisewiil use data from the 1994 No*hridge earthquake.to illustrate the method for calculating Richter magnitude and for mapping seismic-shaking intensity.

MAGNITUDE

* garthquake.. The first !I by Charles" F. Richter, a

Magnitude is a measurement of the energy reieased earthquake--rnagnitude scale was the Richter scale, devised

seisrnologist atlhe Caiifornia Insti*¡te of Technology. The Richter scale is based on the ampiitudé of seismic waves - the stronger the earthquqe, the stronge¡ the seismic vibiations it causes. The Richtermagnitude of an earthquake is expressed as a decimaX number, such as 5.7. The most importantthing tc remember about Richter magnitude is thatit is a iogarithmic scale, meaningthat an increaseof one inmagnitude eorresponds toa factor of rcrlinerease in the amplitude of ground motion. For exanrple, a magnitude 6.7 earthquake causes shaking trO times greatgr in a:nplitude than a rnagnitude 5.7 earthquake and 100 times grcater than a magnitude 4.7 earthquake.

in seisrnic waves with Mathematicaily, an earthquake -The of magnitude x results actual seismic-wave amplitude at.a particular site ampiitudes proportional to i0*. defends on ttre distance of the site from the_earthquake epicenter, the depth of the earthquake, and iocal near-surface conditions. E_xampie 2.1" shows you how to compare the shaking that results from earthquakes with different magnitudes. 19

-

Magnitude and Intensity , Ex.zuRple

2.i.

.,,i i ,.,-,:

:,,.

Compiué the seismic shaking produced by,,a ¡¡¿gritüá;.8., é*thqü.k; *tiU..if," rnur.i"g

.' , ,,,;§[f.rén.rrwOrSá;,,:',thát,:tha::,,:ámplirude of seismiC *áves,,{#),,:fi0m'ififi,.emhquake magnitude x are proportional to 10x, that is equivalent to saying:

a

:):.l

a:

:il:' l:::::li::

iffi;

101.s

earthquake had a magnitude of about 8.3. The 1989 Loma Prieta earthquake that struck San Francisco had a magnitude of 7. 1. How much greater was the shaking in 1906 earthquake compared with the

1) The 1906 San Francisco shaking in 1989?

2) How much greater was the shaking

during the i906 §an Francisco earthquake than the shaking during a magnitude 4"0 trernor?

of

Exercise 2 The methodfor determiningthe magnitudeof an earthquakeis illustratedin Figure the amplitude of thelargest wave on a seismogram and the distance from the recording station to the epicenter (measured either directly in kilometers or indirectly as the S-P iag time; see Exercise 1). On Figure 2.1, the magnitude is determinedby connecting the maiimumwave amplitude (85 mm with proper scaling of the seismogram) with the epicentral distance (300 km, or 34 sec S-P iag). The magnitude of the earthquake shown is the intersection of thatiine with the magnitude axis of the diagram at M=6.0. 211

below, Richterrnagnitude (M) is a functionof

100 mm

5000

o

2000 ar

1000

\. \-

0g s00

s00 204

50

i00

400 40

50

300 30

2A

fn 2A 5

100

10

2

60 6 4A

i

n

0.5 4.2 /.1]

0.1 5

Amplitude Magnitude

Distance (km)

(mmi

S-P lag time (sec)

Figure 2.i. Method for determining the Richter magnitude of an earthquake f'rom a seismograrn. The maximum wave ampiitude on the seismogram is connected with the epicentral distance. The intersection of that iine with the magnitude axis gives the earthquake magnitucie. (After Bolt, 1978)

- 2t

-

Magnitude and Iniensity 3) Using Figure 2.1, determine the Richtermagnitudes for the 'given

.

in the table below. Ampiitude

(md

Distance

I

100

10

100

100

100

10

5

i0

50

10

500

(km)

earthquake data

Richter Mag.

4) Looking

at the first three earthquakes in the tabie abcve, what is the effect on magnitude of a ten-fold increase in maximum seismic-wave amplirude? §!9hte¡ Why does this occur?

5) Looking at the last three

earthquakes in the table above. u'hat is the effect on Richter rnagnrtucie of a ten-foid increase in the distance between the recordins station and the epicenter? Wh,v does this occur?

It-'* important to note that Richter magnitude is not the oniy system for measuring garthquakg energy. You may have noted that the iist of earthquakás at the end of Exercisé 1 included magnitudes with a variety of subscripts; M, M;,- M*, and All of these magnitude scales are logarithmic scales, but different systems have advantages in different situations. For example, whereas Richter maguitudá is based on the arñphtude of the largest wa\re associatedwith a giveq earthquake, magnitude aiso can be detérrnined using the largestbody wave Mu) or the iargestiurface wave Stt.i. If surface waves cause a

.

l

M¡.

particularseismograph-to go "off_scale" (the ampiitudeis greater than the seismograpir's

range of motion), then the smaller body waves may still be used to calculate rnagnitude.

27"

(

\-,

Exercise

2

._ - 9r" particularly useful alternative to Richtermagnitude is the Moment magnirude scale Qvl*). Moment magnitude is based on the seismic moment of an earthquake, which is a ürect measurement or estimate of the energy reieased by the earthquake. Seismic moment (Mr) can be calcuiated as foilows:

trA=p*Dur*A

(.2.1)

of rigidity of the crust (about 3.3 *

where p is the modulus 101 1 dynes lcm2; Brune, 1968), is the average dispiacement on the fault during the earthquake, and A is the total area of 4, rupture on the fault. Seismoiogists often favor using seismic moment because it is the most physically-based estimate of earthquake energy. Seismic moment can be converted into a magnitude scale using the following equation (Hanks and Kanomori, L979):

I\fu = 213 * IogIvIo

-

() 1\

10.7.

Find the séi§mic moment (Mo) of a Mrn=J.§ earthquake. Íh..ans*"rtolüis.question,isa.straightforwardsoiütonoiEquation2.2:,,

,:::3l2x(7.5+10:,7)=16g1¡1o,, ,:.. ..,..

,,,

,

:r,'l ,

.

.

Thá inversé of the loganthm tun.ilon

i tú;iúñi

n r.iion

(td¡

The waylto simptifu

ii,..ttá,..i r*=t;S,,,.;á;iii4üár