rose 2013 w1d3l1 focal mechanisms

8/11/2019 ROSE 2013 W1D3L1 Focal Mechanisms

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FUNDAMENTALS ofENGINEERING SEISMOLOGY

EARTHQUAKE FOCAL

MECHANISMS (FAULT

PLANE SOLUTIONS)


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Credits:

-Some slides provided by Dino Bindi (INGV) and A. Kelly (USGS)

-Cox and Hart. Plate Tectonics How it works.-Stein and Wysession, An Introduction to seismology, earthquakes and

Earth structure

- Focal mechanisms: body wave radiation pattern

- Focal mechanisms: stereographic fault plane representations


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Elastic rebound model of earthquakes assumes that between earthquakes, materialon the two sides of a fault undergoes relative motion. Because the fault is locked,

features across it that were linear at time (a), such as a fence, are slowly deformed

with time (b). Finally the strain becomes so great that the fault breaks in a earthquake,

offsetting the features (time c). (Courtesy of S. Wesnousky)

From S. Stein and M. Wysession


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A minority of

faults break

the surface;

how is the

orientation of

the fault plane

and the

direction of

slip

determined ifthe fault does

not break to

the surface?


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To describe the geometry of a fault, we assume that the fault is a planar surface across

which relative motion occurred during an earthquake.

The fault is characterized by the normal vector n, while the slip in the fault plane is

along the vector d. Several coordinate systems can be considered; one is aligned such

that the x1 axis is along the fault strike direction (intersection of the fault plane with the

Earth surface); x3 axis points upward; x2 axis is perpendicular to the other two. The

direction of x1 is selected such that the dip of the plane with respect to -x2 is less than

90 degrees. The direction of the motion is represented by the slip angle, l, measured

counterclockwise in the fault plane from the x1 direction.From S. Stein and M. Wysession


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A very important figure describing

sign conventions for focal

mechanisms From S. Stein and M. Wysession


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Seismograms recorded at different distances and azimuth are used to study the

geometry of faulting during an earthquake, known as focal mechanism. This operation

uses the fact that the pattern of radiated seismic waves depends of the fault geometry.

There are several methods to infer the focal mechanism, such as the analysis of the

polarity of the first arrivals or the inversion of waveforms. We discuss only the former

approach (e.g., see Introduction to Seismology by Stein and Wysession for details)

The first P-wave arrival varies between stations at different directions from an

earthquake. The first motion is either compression (motion toward the station) or

dilatation (motion away from station). The first motion defines 4 quadrants, divided

by the fault and the auxiliary planes (nodal planes).From S. Stein and M. Wysession


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Focal Mechanism (Fault

Plane Solution)


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The seismic source

is modelled as a

point, but in realityit is rupture over a

plane and

relaxation over a

volume but, can

use radiation

pattern of first P-

waves to determine

the focal

mechanism at the

hypocenter


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The Centroid Moment Tensor is the most

complete description of the forces acting onthe fault rupture.

If it is assumed that the fault rupture is

PURE SHEAR (ie., that it involves no

volume change) then the model of the forces

acting on an equivalent point source isreduced to a much simpler system known as

a DOUBLE COUPLE.


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Radiation from a shear dislocation with slip S over

area A in material with rigidity is identical to that

from a double couple.


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P-wave radiation

pattern

Faulting & Compressional Waves


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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

Cox and Hart. Plate Tectonics How it works.


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N.B. The first motions from a slip on the actual fault plane and froma slip on the plane perpendicular to it (auxiliary plane) would be the

same, so the first motions alone cannot resolve which plane is the

actual fault plane. Additional information can often settle the

question. Sometimes geologic or geodetic information indicates the

fault. Often smaller aftershocks following the earthquake occur on,

and thus delineate the fault plane.In other cases, for earthquakes large enough, source effects can

be used to determine the fault plane (e.g. directivity effects can

destroy the symmetry of the radiation pattern)


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Data on thesurface, interpreted

in 3D

Cox and Hart. Plate Tectonics How it works.Courtesy of A. Kelly


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To determine the fault plane solution using the first motions, the observations at

stations (Earth surface) have to be converted to observations over a sphere (of

infinitesimal radius) around the source. The position on the sphere is determined by

the take-off angle (computed from the slope of the travel-time curve).

S. Stein and M. Wysession

D. Boore

A. Kelly, USGS

azimuth


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Determining the focal mechanism

from P-wave first motions

Use azimuth and take off angle to determine where the P-

wave intersects a sphere around the source Plot those points of intersection on a stereographic

projection, using a filled circle (or +) for compressions and

an open circle for dilatations

Determine the two possible fault planes


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P-wave first motions from 1989 Loma Prieta earthquake.

Compressions are +. Lines divide stereonet into quadrants of

compression and dilation. Strike=130, dip=70. Note: Because

of symmetry, focal mechanism cannot distinguish fault plane

from auxiliary plane. The two planes must be perpendicular

to one another (how do you check this in the projection?).

Note some

inconsistencies;

this is to be

expected when

working with real

data.


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Seismic Beach Balls

Project the pattern of initial motions intersectingan imaginary sphere around the source (the focalsphere) onto a flat surface.

We use the radiation patterns of P-waves toconstruct a graphical representation of earthquakefaulting geometry (two planes intersecting oneanother at right angles)

The symbols are called Focal Mechanisms orBeach Balls, and they contain information onthe fault orientation and the direction of slip.


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Focal Mechanism

When mapping the focal sphere to a circle

(beachball) two things happen:

Lines (vectors) become points

Planes become curved lines


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Stereographic projection A method of projecting half

a sphere onto a circle.

e.g. planes cutting

vertically through the

sphere plot as straight lines

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

Courtesy of A. Kelly


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Focal mechanisms: Shown by stereographic projection.

Graphic shows stereographic projection of a fault plane

(2D projection of plane onto focal sphere)

This is a lower hemisphere projection


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-Azimuths are along the great circle

-Dip angles are along the equator-NS-striking Planes with different dip

are meridians

If th l i t iki i th i th th b di l d b t ti th


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If the plane is striking in other azimuths, they can be displayed by rotating the

stereonet

E.g : strike 45 , dip 60

First rotate the steronet such that the strike 45 is vertical. Then, select

the meridian corresponding to 60. Finally, rotate back the stereonet.



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Courtesy of A. Kelly


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To plot a point, the procedure is the same.

E.g. station with azimuth 40 and take-off 60

Rotate the stereonet of 40 clockwise (the equator is along azimuth 40). Select the

dip=30 (remember, take-off are measured with respect to vertical, dip with respect to

horizontaldip=90-take-off). Then, turn back the stereonet



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Focal Mechanisms

Beachballs always have two curved linesseparating the quadrants. That means that

beachballs show twoplanes.

But there is only onefault plane.

The other plane is called the auxiliaryplane. The planes are orthogonal.

Seismologists cannot tell which is which fromseismograms alone, so we always show both ofthe possible solutions.


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Azimuth of these fault planes all strike north, with

dips as shown. Rotate stereonet for other strike

azimuths.

Projection of the normal to the plane; the auxiliary plane must go

through this point. Does this define a unique auxiliary plane?


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Same N-S fault,

different slip direction

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


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+

+-

+

-

-

Normal dip-slip

fault

Reverse dip-slip

fault


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Fault types and Beach Ball

plots

USGS


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Stein and Wysession


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The Principal Mechanisms

which is the fault plane?


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Focal Mechanisms

It is often possible to make an educated

guess as to which of the two possible

planes is the actual fault plane:

Normal earthquakeswork with gravity so

are oftensteep Thrust eventswork against gravity so are

oftenshallow


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Focal Mechanisms For strike slip focal mechanisms we can often

determine the fault plane by its orientation with

respect to the fault.

Plate A

Plate B

(right or left lateral ??)

Ridge

Ridge


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Summary of focal mechanism concepts

Direction of first motions (up, down) can be usedto divide focal sphere into quadrants of

compression and dilation (stereographic

projection).

The planes separating these quadrants are the faultplane and its auxiliary plane (at 90 degrees to fault

plane). The planes are orthogonal.

Thus first motions can be used to determine fault

orientation (provided we can find some

information to distinguish fault plane from

auxiliary plane).


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Summary

The focal mechanism of an earthquake is agraphical description of the type of faulting

Although the fault type can be determined from

seismograms, the particular fault plane cannot bedetermined.

There are always 2 possibilties:

The real plane, known as thefault plane

The fake plane, known as the auxiliary plane


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Summary

The fault plane can be distinguished from theauxiliary plane by considering:

The steepness of the fault

Reverse = shallow

Normal = steep

Nearby morphological features The strike of the transform segment for instance

The distribution of aftershocks

Aftershocks tend to line up along the fault plane (but notalways of course)

Directivity effects on the waveforms

Faulting and Plate Tectonics


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Faulting and Plate Tectonics


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Stein and Wysession


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Stein and Wysession


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End

rose 2013 w1d3l1 focal mechanisms

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