feb 19, 2008 1john anderson - cee/ge 479/679 earthquake engineering ge / cee - 479/679 topic 9....

Feb 19, 2008 1 John Anderson - CEE/GE 479/679

Earthquake EngineeringGE / CEE - 479/679

Topic 9. Seismometry, Magnitude Scales, and Seismicity

John G. Anderson

Professor of Geophysics


Key Points

• Seismometers are single-degree-of-freedom oscillators.• Different instruments for different applications• Different magnitude scales go with different instruments

– ML – Wood-Anderson, local– mb – short-period, teleseismic P-waves– MS – long-period, teleseismic surface waves– Mcoda – local, when calibration is a problem

• Magnitude scales are calibrated to be similar, but are not identical– MW is now accepted as best– All other scales saturate


Wood-Anderson Seismograph

• Important because:– Principles of operation are widely used.– Basis for the magnitude scales of earthquakes

that are still used today.– Provide data for early southern California

earthquake catalog that is still used today.


Optical magnification of the motion of the mass:Record shows d(t)=M x(t)

Richter (1958): M=2800Recent reanalysis: M=2080


Sample seismogram from a WAOriginal

vnta9201


Magnitude ML

• C. F. Richter was the first person to define the magnitude of an earthquake.

• The magnitude was defined from measurements taken using a Wood-Anderson seismogram.

• All subsequent magnitude scales are defined using the same principle.


Magnitude ML

• The magnitude was defined from measurements taken using a Wood-Anderson seismogram.

• For these examples, I use the DuHamel Integral to calculate a synthetic Wood-Anderson seismogram from digital strong motion records.


• ML = Local Magnitude

• Defined by Richter in 1940’s

⎥⎦

⎤⎢⎣

⎡=

earthquake reference of Amplitude

earthquake thisof AmplitudelogLM

Both amplitudes are measured peak amplitudes in mm from a standard Wood-Anderson seismogram.The amplitude of the reference earthquake is taken at the same distance.The reference earthquake: ML=3.0, A= 1.0 mm at R= 100 km.

( ) ( )RAARA

AM L 0

0

logloglog −=⎥⎦

⎤⎢⎣

⎡=


To find magnitude,need to find distance.This can be done from a single record.

vnta9201

Time (seconds)


How to estimate the distance?Use the relative speed of the P- and the S-waves.

This shows the simple math behind the process.

This is the origin of the rule of thumb used by seismologists for local earthquakes: multiply the s-p time (in sec) by 8 km/s, to get the approximate distance from the station to the epicenter.


Sample distance calculation

vnta9201

P-wave - t~1.0 s


Sample magnitude calculation

vnta9201

P-wave t~1.0 s

S-wave - t~6.0 s



vnta9201

P-wave tp~1.0 s

S-wave - ts~6.0 s ts-tp = (6-1) s = 5 sR~(ts-tp) * 8 km/s ~ 40 km


• ML = Local Magnitude

• Defined by Richter in 1940’s

⎥⎦

⎤⎢⎣

⎡=

earthquake reference of Amplitude

earthquake thisof AmplitudelogLM

Both amplitudes are measured peak amplitudes in mm from a standard Wood-Anderson seismogram.The amplitude of the reference earthquake is taken at the same distance.The reference earthquake: ML=3.0, A= 1.0 mm at R= 100 km.

( ) ( )RAARA

AM L 0

0

logloglog −=⎥⎦

⎤⎢⎣

⎡=


This table, from the textbook Elementary Seismology by Richter (1958), gives the distance correction for the local magnitude.

This shows that you need the amplitude and the distance to the earthquake to determine the magnitude.


Sample seismogram from a WAOriginal

vnta9201



vnta9201

R~40 km

Peak response = 828 mm

ML=log A - log A0

log A0(40 km) = -2.4ML=log(828)+2.4ML=2.9+2.4 = 5.3


Magnitude: General Comment

• Most magnitude scales, like ML, are tied to a certain kind of seismic instrument.

• Important issue: convenience of determining the magnitude from the seismograms.


SMA-1 Strong Motion Accelerograph

• Important because:– Strong motion data is the basis for all

quantitative earthquake resistant design.– Most of the early strong motion data is

recorded on instruments of this type or with a similar design.

– Principles of operation similar to Wood Anderson


Digital Accelerograph


Is there a magnitude scale associated with the strong motion

accelerograph? • Traditionally, NO. You cannot determine the

magnitude of an earthquake by reading the peak acceleration and knowing the distance.

• YES, in the sense that you can calculate the synthetic Wood-Anderson response easily from a digital accelerogram. ML is thus the scale most conveniently used with the accelerograph. (Above examples are done this way.)


More Sensitive Seismometers

• Uses– Teleseismic earthquake observations– Global picture of earthquake activity– Basis for Ms and mb magnitude scales– Observe microearthquakes on a regional basis


Some Definitions (not standard)

• Teleseismic - “distant seismic” - >30o

– Some might use a smaller distance, as little as 15o or 20o.

• Regional - 500 km (5o) to 30o

• Local - Closer than 500 km. – Some might say closer than 100 km.


Short Period Long Period


Rayleigh Wave


At large distances, seismologists use travel time tables or curves, such as these. The scale goes all the way from zero distance to half way around the world on this chart (200 intervals). The time goes from zero to 50 minutes, in 5 minute intervals.

Because the Earth is layered, there are more waves than just the P- and S- waves on this chart.


Role of the global networks

• Large-scale picture of the global seismicity.


Regional Networks


6


Microwave network operated by the Seismological Laboratory to transmit seismic data to Reno.


Coda Duration Magnitude

• Used by local networks because amplitude is unreliable, and also often clipped.

• Each network develops its own scale.

• UNR equations:

€

mC = −1.2 + 2.65log DS + 0.0013R


Seismic Moment

• Definition of Seismic Moment

• M0=μAD

– μ is the shear modulus of the rock– A is the area of the fault on which slip takes

place– D is the average slip on the fault


Moment Magnitude

• MW=(2/3) (log M0-16.05) (exact)

• MW=(2/3) log M0-10.73 (as applied)

• This is the preferred magnitude scale in the seismological community.


Relate ML with MW

• Note, moment of zero magnitude earthquake is M0(0)=1016.05 dyne-cm

• Compare with

( )

( )⎟⎟⎠

⎞⎜⎜⎝

⎛=

−=

0log

3

2

05.16log3

2

0

0

0

M

M

MMW

( )⎥⎦⎤

⎢⎣

⎡=

RA

AM L

0

log

feb 19, 2008 1john anderson - cee/ge 479/679 earthquake engineering ge / cee - 479/679 topic 9....

Documents

magnitude mlthe magnitude

subsequent magnitude

reference earthquake

sample seismogram

distance correction

approximate distance

problemmagnitude scales

local magnitudedefined