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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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From S. Stein and M. Wysession
-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.
From S. Stein and M. Wysession
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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
From S. Stein and M. Wysession
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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