earthquake seismology - purdue...

Earthquakeseismology

The San Andreas fault in theCarrizo plain, California

Offset drainage along the SanAndreas fault, Wallace Creek,

California

Fence offset by the 1906 SanFrancisco earthquake

Elastic strainaccumulation

• (Most) faults are lockedbetween earthquakes

• The area around faultsaccumulates elastic strain

GPS-derived velocities in Southern California (1992-2000). Velocities are shown with respect to NorthAmerica. The active faults of California are shown inorange.

The seismiccycle

• Between earthquakes:– Faults are locked– Area around faults accumulate deformation

• During an earthquake:– A fault slips suddenly– The deformation accumulated around the fault is

released• After an earthquake:

– Stresses around the fault are modified– Readjustments on the fault plane = aftershocks

The seismic cycle

During an earthquake:– A fault slips suddenly– The deformation accumulated around the

fault is released– Stresses around the fault are modified

Between earthquakes:– Faults are locked– Area around faults accumulate deformation

Animation: R. Stein, USGS

Click for earthquake cycle animation

Earthquake seismology

• Location of the earthquake (hypocenter)?• Frequency of similar earthquakes?• Focal mechanism?• Rupture mechanism?• Size?

– Intensity– Magnitude– Moment– Energy release

• Earthquake triggering?

Locating earthquakes

Difference in travel timefor P and S wavesincreases with increasingepicentral distance:

!

tS

=D

VS

tP

=D

VP

" tS# t

P= D

1

VS

#1

VP

$

% &

'

( )

VP

= 5.85 km /s VS

= 3.38 km /s

" D = tS# t

P( ) * 8.0

Locating earthquakes• Errors:

– Picking arrivals– Actual travel times are slightly

different from theoretical ⇒ locationis dependent on the Earth model used(global or local).

• With at least 3 stations:– Calculate S-P time difference– Convert to distance– Draw circles centered on stations– Location = intersection of circles

Earthquake focalmechanisms

• Earthquake = release ofaccumulated elastic energy bydisplacement on a fault

• Problem: what type of fault motion?• Case of a strike-slip fault: particle

motion due to fault slip:– Blue quadrants: particles pushed

away from the focus ⇒compressional first motion = UP

– Red quadrants: particles pulledtowards the focus ⇒ dilatationalfirst motion = DOWN

• As a result, we obtain 4 quadrants:– 2 compressional quadrants: first

motion down– 2 extensional quadrants: first

motion up

dilatationalfirst motion

compressionalfirst motion

fault plane

auxiliary plane

compressionalquadrant

compressionalquadrant

extensionalquadrant

extensionalquadrant

tensionaxis

compressionaxis


• Earthquake = release of accumulatedelastic energy by displacement on afault

• Problem: what type of fault motion?• Let’s assume an earthquake on a

reverse fault:– Compressional / tensional quadrants– Compressional quadrant: surface is

pulled down ⇒ first motion DOWN– Tensional quadrant: surface is pushed

up ⇒ first motion UP• If we map first motion, we can find:

– 2 focal planes– P- and T-axis

Earthquake focal mechanisms• Seismic rays travel away from the focus• Each ray “samples” a dilatational or compressional quadrant around the

focus• Seismic stations at different distances record up or down first motions• Rays along nodal planes?

in cross-sectionfocal mechanism(stereonet proj.)

Earthquake focal mechanisms

• The “focal sphere”:– Center = earthquake hypocenter– In each quadrant: first motion identical

• Seismic stations are at the surface,(usually) not underground

– Rays bend upward and eventuallyreaches a seismic station at the surface

– The important parameter is the initialtake-off angle

– Take-off angle can be calculatedknowing the earth’s structure =>accuracy of focal mechanisms dependon our knowledge of the Earth structure(local, regional, global)


• Strike-slip faulting:– Vertical focal planes– Horizontal P-axis and T-axis

• Other types of faulting:– Focal planes will have a dip– P-axis and T-axis will have a

dip• For representation: focal sphere

+ stereographic projection offocal planes and P-T-axis ⇒“Beach balls”

In the horizontal plane:

The focal sphere:


• Focal mechanisms definethe type of faulting thatoccurred during theearthquake.

• The actual fault plane isambiguous

• Focal mechanisms cancombine these types offaulting.

• Focal mechanisms in anactively deforming areacontain information aboutthe strain regime

reverse

normal

strike-slip


• Eastern Mediterranean• Earthquake focal

mechanism illustrate:– Strike-slip faulting– Reverse faulting– Extensional faulting

• Compare with GPSvelocities

(McClusky et al., JGR, 2000)

Earthquake rupture• An earthquake usually breaks a segment of a fault• The rupture does not always reach the surface• The earthquake is followed by aftershocks:

– Readjustments on the rupture plane– Help define the rupture plane

Animation http://www.scecdc.scec.org/northreq.html

Northridge earthquake, January 1994, M=7.2

Earthquake rupture• Time and space history of a rupture, example of the Northridge earthquake• Slip on the rupture plane is not homogeneous• Asperities and barriers

Animation D. Wald, http://www.scecdc.scec.org/northrup.html

Earthquake size

• Shear forces on a faults ⇒moment

• Hooke’s law relates stressand strain for elasticsolids: for shear,proportionality factor isrigidity µ

!

MO

= 2bF

"shear

= µ #$shear

with $shear

=d

2band "

shear=F

A=

F

L #W

% MO

= µAd

Moment = rigidity x displacement x rupture area

F

-F

b

Rupture area: A = L x W

Earthquake magnitude• 1935: Richter worked on ranking

earthquakes as a function of theirsize

• First definition:– “Maximum amplitude recorded

at 100 km from the epicenter”:

– For local earthquakes: S-waveshave the largest amplitude

– Correction for distance: Δ (=angular epicentral distance indegrees)

• Richter magnitude scale:• Open scale• Largest magnitude recorded =

Chile, 1960, MW=9.6 (MS=8.3)• Negative magnitudes are

possible…

ML=log10(Amax) + 3 log10Δ - 2.92

nomogram used to compute magnitude quickly by eye

Earthquake magnitude

• ML = local magnitudes (~ 600 km from earthquake)• At larger distances:

– Using surface waves (they have the largest amplitude)

A=max. amplitude of vertical component in microns, T = period inseconds, D = angular distance in degrees.

– Using body-waves (P-waves)

– Ms – mb relationship:

MS = log10(Amax/T)+1.66 log10Δ + 3.3

mb = log10(Amax/T)+0.01 Δ + 5.9

mb = 0.56 MS + 2.9


2/TR 2/TD

• Spectrum of seismogram gives spectralamplitude at all frequencies

• Static moment = amplitude at lowfrequencies

• Corner frequency depends on durationof rupture time TD and and rise time TR

• Above corner frequency– there is destructive interference– Shaking cannot get higher amplitude but

continues in time longer• As a result:

– Ms saturates at 8.3– mb saturates at 6.2

• Use of moment magnitude:

MW = (2/3) log10MO – 10.7


• Less than 3.5: Generally not felt, but recorded.• 3.5-5.4: Often felt, but rarely causes damage.• Under 6.0: At most slight damage to well-designed

buildings. Can cause major damage to poorlyconstructed buildings over small regions.

• 6.1-6.9: Can be destructive in areas up to about 100kilometers across where people live.

• 7.0-7.9: Major earthquake. Can cause serious damageover larger areas.

• 8 or greater: Great earthquake. Can cause seriousdamage in areas several hundred kilometers across.

Earthquake size• Logarithmic relationship between magnitude and:

– Coseismic displacement: M5=1 cm, M8=10m– Rupture length: M5=1 km, M8=400 km

• Large earthquakes have a MUCH LARGER rupture displacement andlength than smaller ones

Energy release

• Energy release:

• Increase of one level ofmagnitude corresponds to:⇒Amplitude increase: 101 = 10⇒Energy increase: 101.5 ≈ 30

• Energy release increases veryrapidly with magnitude

!

log10 E = 4.4 +1.5MS

Largest Earthquakes in the World Since 1900

1. Chile - 1960 05 22 - 9.5 (Ms = 8.5)2. Prince William Sound, Alaska - 1964 03 28 - 9.2 (Ms = 8.3)3. Off the West Coast of Northern Sumatra - 2004 12 26 - 9.04. Kamchatka - 1952 11 04 - 9.05. Off the Coast of Ecuador - 1906 01 31 - 8.86. Northern Sumatra, Indonesia - 2005 03 28 - 8.77. Rat Islands, Alaska - 1965 02 04 - 8.78. Andreanof Islands, Alaska - 1957 03 09 - 8.69. Assam - Tibet - 1950 08 15 - 8.610. Kuril Islands - 1963 10 13 - 8.511. Banda Sea, Indonesia - 1938 02 01 - 8.512. Chile-Argentina Border - 1922 11 11 - 8.5

Visit: http://neic.usgs.gov/

Earthquakefrequency

• There are far more small earthquakesthan large ones

• Many small earthquakes are notdetected

• Gutenberg-Richter law:– Linear relationship between

log[number of earthquakes] andmagnitude:LogN = a – b x M

– Slope = ‘b-value’• Worldwide average is 1.0• May vary regionally• Lab. experiments show:

– High stress ⇒ low b (less small eqs)– Low stress ⇒ high b (more small eqs)

• Empirical tool for seismic hazardstudies

Earthquakefrequency

The USGS estimates that severalmillion earthquakes occur in theworld each year. Many goundetected because they hitremote areas or have very smallmagnitudes. The NEIC nowlocates about 50 earthquakeseach day, or about 20,000 a year.

Earthquake information:http://neic.usgs.gov/

Descriptor Magnitude Average Annually

Great 8 and higher 1

Major 7 - 7.9 18

Strong 6 - 6.9 120

Moderate 5 - 5.9 800

Light 4 - 4.9 6,200 (estimated)

Minor 3 - 3.9 49,000 (estimated)

Very Minor < 3.0 Magnitude 2 - 3: about 1,000 per dayMagnitude 1 - 2: about 8,000 per day

Frequency of occurrence of earthquakes based on observations since 1900

Intensity• Qualitative description of earthquake size• Based on damage assessment ⇒ Mercalli scale• Can be severely biased

– Area with local amplification of seismic waves or secondary effects such as liquefaction– Subjective reports from people– Depends on vulnerability

• Often the only information available for historical earthquakes

Seismic hazard• Earthquake damage:

– Ground acceleration, in g (up to 2 g)– Secondary effects: liquefaction, landslides, fires, etc

• Seismic risk = seismic hazard ⊗ vulnerability• Seismic hazard = seismic potential (When? Where? What

size?) ⊗ propagation of seismic waves– Seismic potential = probability for an earthquake of a given size

to occur– Propagation = attenuation of seismic waves, site response

• Seismic hazard = probability to exceed a givenacceleration for a given time period

Seismic potential

• Derived from Gutemberg-Richter law, tailored forthe are under study

• Requires earthquakecatalog ⇒ b value

• Can be complemented byinformation on activefault: geometry, slip rate

• Can be complemented bygeodetic information:strain rate

Attenuation

• Amplitude of seismic wavesis attenuated:– Geometric attenuation– Intrinsic attenuation– Attenuation relationship:

determined empirically• Many different attenuation

relationships are available:– Quantity of available data– Geological nature of the

terrain: amplification ordamping

Site response

• Ground acceleration decreaseswith distance, but can vary by afactor of 10 for 2 sites at thesame distance to an earthquake⇒ site response

• Site response depends ongeological factors:– Softness of soil or rocks near

the surface: ground motionamplified by soft rocks

– Sediment thickness abovebedrock: ground motionamplified by thick sediments

Snapshots of simulated wave propagation in the LA area for thehypothetical SAF earthquake (K. Olsen, UCSB)

Final result: seismic hazard maps• Peak acceleration that has a 2% probability to be exceeded in 50 years• Compare New Madrid and California!

What have we learned?• Active faults are (usually) locked between earthquakes, while the area

around them is accumulating elastic strain.• An earthquake is the sudden release of the elastic strain accumulated

over decades.• The earthquake results in:

– A rupture, that may sometimes reach the surface– Seismic waves, that propagate away from the rupture area

• Using seismic wave, one can figure out:– The location of the earthquake– The type of fault motion (focal mechanism)– The magnitude of the event (energy released)– The slip distribution on the rupture plane

• Magnitude scale:– Is not linear but power law– Gutemberg-Richter law: N = a –b M

• Earthquake hazard depends on source, attenuation, and site response

What have we learned?• One can use seismic waves generated artificially to image

deep structures:– Seismic reflection:

• Receiver and source close• Arrivals describe hyperbolas

– Seismic refraction:• Receiver and source far apart• Arrivals describe straight lines

• Data collection, processing (increase SNR and removeartefacts), interpretation

• Applications: oil exploration, sequence stratigraphy, etc.

earthquake seismology - purdue...

Documents