focal mechanism usgs

8/20/2019 Focal Mechanism USGS

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U.S. Department of the Interior

U.S. Geological Survey

Earthquake Focal Mechanisms


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Focal Mechanism Solutions

Also called “ beachball diagrams” “ fault planesolutions”

Tell us the geometry and mechanism of thefault in a simple diagram

Generally reconstructed from waveform data

derived from the moment tensor (which ismore general), but originally calculated using

first motions – done here to illustrate the

concepts


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Examples

USGS


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1) The stereographic projection

2) The geometry of first motions and how this is

used to define fault motion.

Two steps to understanding

http://www.uwsp.edu/geo/projects/geoweb/participants/dutch/STRUCTGE/sphproj.htm


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Stereographic projection

A method of projectinghalf a sphere onto a circle.

e.g. planes cuttingvertically through the

sphere plot as straight

lines

Images from http://www.learninggeoscience.net/free/00071/index.html


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Stereonets

A template

called a

stereonet

is used to

plot data.

Example –

plottingplanes

(e.g. faults)

USGS


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Stereonets

Example –

plottinglines (e.g.

ray paths)

USGS


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Stereonets

Example –pitch (or

rake) of a line

on a plane(e.g. the slip

direction on a

fault)

USGS


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Refresher on terminology

USGS

Slip angle is measured from horizontal

(positive for thrusts)


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Energy and Polarity of “ First Motions”

Cox and Hart. Plate Tectonics – How it works.


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Earthquake on a vertical plane

Edited from Cox and Hart. Plate Tectonics – How it works.


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Determination of nodal planes



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Spreading of the seismic wave



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Data on thesurface,

interpreted in3D



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Take-off angle

The angle (from vertical) that the ray leavesthe earthquake = take-off angle

Stein and Wysession, An Introduction to seismology, earthquakes and Earth structure


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Azimuth ( ) andtake-off angle

USGS



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With a lot of recordings we can

reconstruct faults with any orientations



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Fault types and “ Beach Ball” plots

USGS


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Example Focal

mechanismdiagrams on mid-

ocean ridges



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Same N-S fault,

different slip direction



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Great review on the web at:

http://www.learninggeoscience.net/free/00071/


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By constructing

synthetic seismograms

and comparing them tothe recorded data we

use more of the

information in the

seismogram, not just

the arrival time and firstmotion data

Waveform modeling

Stein and Wysession, “An Introduction to

seismology, earthquakes and Earth structure”


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Waveform modeling

u(t) = x(t) * e(t) * q(t) * i(t)

seismogram

source timefunction instrument

responsereflections &

conversionsat interfaces

attenuation

U( ω )= X( ω ) E( ω ) Q( ω ) I( ω )

Construction

of the

syntheticseismogram

Stein and Wysession, “An Introduction to seismology,

earthquakes and Earth structure”


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At one point on the fault slip takes a finitetime (called “ rise time” ):

The slip travels along the fault at rupture

velocity vr, so there is also a finite “ rupture

time”

Source-time function

Time

S l i p

TDTime

S l i p r a t e

TD

Time

S l i p

r a t e

TR

Fault= rupture

Map view


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Source time function

The source time function is the combinationof the rise time and the rupture time:

Directionality affects the rupture time

Time S l i p

r a t e

TDTime

S l i p

r a t e

TR

S l i p

r a t e

TR TD* =

TR TD

TR TD

TR TD

TR TDRupture direction


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phase reflections

e(t) representsreflections due to

the Earth

structure

If modeling only

the P arrival, it’sonly needed for

shallow events

Stein and Wysession, “An Introduction to seismology, earthquakes and Earth structure”


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Attenuation

The loss of energy with time

Q controls the

amount of loss

A(t) = A 0

e - ω 0 t/2Q

Sipkin and Jordan 1979, copywrite

Seismological Society of America


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Instrument response function

The response of the seismometer is different

for different frequencies so it also filters thedata.

Stein and Wysession, “An Introduction to seismology,

earthquakes and Earth structure”


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Moment Tensor Inversion

The Moment tensor describes the fault as setof equivalent forces

Calculated from the amplitude of surfacewaves Love Rayleigh

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