LECTURE 4 NOTES - FAULTS AND RUPTURE (updated 09/30/97)
Instructor: Professor Barbara Romanowicz
Director of Seismological Laboratory
Office Hours: Thursday 2-4 pm , upon appointment only
475 Mc Cone Hall
Notes by Prof. B. Romanowicz, instructor
FAULTS AND RUPTURE
After establishement of seismographic networks at the beginning of last
century, global surveillance made it clear that many large earthquakes occur
far away from volcanoes. Most earthquakes (90%)occur on tectonic plate
boundaries. ---> interplate earthquakes
A small fraction occur in the middle of plates : ³intraplate earthquakes²
Most earthquakes are crustal earthquakes (foci at depths less than 20-30 km)
but some occur much deeper, down to 700 km depth, along planar zones
called ³Benioff zones² in specific tectonic settings : convergent margins,
where they represent ruptures along the borders of the underthrusting plate.
This is in fact one more observation confirming the theory of plate tectonics.
Also, visiting sites of large earthquakes ---> evidence of large surface ruptures
mapped into linear systems of abrupt topographic changes.
---> earthquakes occur on ³faults²
San Francisco earthquake (1906) ---> elastic rebound theory (Reid)
plate tectonic theory ---> provides the ³tectonic forces² that drive the large
scale deformation that leads to instantaneous shifts of rocks during
earthquakes, or ³rupture²:
as time passed, deep-seated forces steadily deform the rocks in the form of
³elastic strain² (elastic: if forces are removed , the material springs back to
initial position), resisted along faults until failure point is reached.
Examining triangulation results from two campaign periods (1851-1865) and
(1874-1892) Reid noticed 3.2 m of movement over the 50 year period
preceding the San Francisco earthquake. The earthquake itself resulted in
about 6 m of displacement between the two sides of the San Andreas fault. He
concluded that the average recurrence time for an earthquake of this size
would be on the order of 100 years (it would take 2 x 50 years for tectonic
deformation to catch up with the displacement occasioned by the earthquake).
Rock failure
Rocks can be made to break or fail in a variety of ways when put under
pressure in the laboratory. Fractures form that divide the rock into sections.
The sides of the fracture slip abruptly past each other as the rock breaks into
pieces. The pieces can be fitted together again, indicating that they broke in
a ³clean² fashion, called ³brittle fracture². On the other hand, sometimes
there is no sudden, abrupt slip, but only slow slippage maintaining cohesion
of the rock sample: ³Creep²
In nature, this happens on a much larger scale, giving rise to geological faults
(than can be anywhere from a few meters long to thousands of km) that can
fail in two fasions:
sudden rupture ---> earthquake
gradual sliding --->creep
Some portions of the same long fault can be ³locked² (they only rupture in
large earthquakes) and others may be ³creeping² continuously at a rate of a
few mm/year. This is the case for the San Andreas fault, locked in the south
from Parkfield down over 400 km (rupture zone of the 1857 Fort Tejon
earthquake), and creeping north of Parkfield.
Parkfield location (population ~22) is notable because 1) transition from
creeping to locked zone
2) site of a long term earthquake prediction experiment (observations of
regular recurrence of magnitude 6 earthquakes since the end of 19th century)-
-> hope to catch one soon!
Also, Hayward Fault is creeping right in our backyard (e.g. field trip,
observations in Berkeley Stadium or in city of Hayward). Water tunnel across
the Berkeley Hills was emptied in 1966: crack several cm across the tunnel
were found just where the tunnel intersects the Hayward Fault. Creep 2-5
mm/yr.
The physical mechanism of the very deep earthquakes along Benioff zones is
much more difficult to explain, because these occur at very high temperatures
(~1900oC) and very high pressures ( xxx) at which it is thought that rocks
should flow and not be capable of brittle fracture.
Faults:
can be narrow, clean fractures
or diffuse shattered zones, ~100 m wide. Inside this ³fault zone² there is
much crushed material called ³fault gouge², which has little strength and is
thought to play a major role in how ruptures proceed in time and space (e.g.
velocity weakening/velocity strengthening).
Faults are classified according to their geometry and the direction of relative
slip.
Orientation is defined by two angles:
strike: angle in horizontal plane between a reference direction (north) and the
intersection of the fault plane with the surface
dip: angle with horizontal plane in the vertical plane perpendicular to fault
strike: dip =0o ---> the fault lies horizontally (never the case)
dip = 90o ----> vertical fault
faults are classified according to the orientation of the movement during slip ,
on the fault plane, along the dip and strike.
slip : 3rd angle describing the direction of movement between the 2 sides of
the fault during an earthquake
strike-slip fault: slip in predominantly horizontal direction. Often near
vertical fault plane.
right lateral
left lateral
dip-slip fault: movement is predominantly up or down on the fault plane,
measured on the ³hanging² wall of the fault:
if it is up: reverse fault ------> associated with ³compression²
if it is down: normal fault -----> associated with ³extension²
usually direction is oblique : oblique faults
In the context of plate tectonic theory, different types of faults are
predominant in different types of tectonic settings:
convergent margins : thrust faults
divergent margins : normal faults
transcurrent margins : strike-slip faults on near vertical planes
Not all faults reach all the way to the surface and produce ³surface rupture²
Many are only detected by seismicity or inferred from geological observation.
Notion of ³blind thrust² now popular since Coalinga 1983 and Northridge,
1994, especially in the L.A. Basin
Earthquake Geometry
Earthquake focus: point from which seismic waves first emanate.
Simplification: in reality source spread through a volume of rock, but when
observed at large distances, this looks like a point.
Focus is at some depth below the ground (except for artificial earthquakes,
very near the surface).
Point on the ground surface directly above the focus is called the epicenter.
The ³point² approximation is more valid for small earthquakes for which
rupture dimensions are much smaller than the distance at which they are
observed.
Taking a close-up view:
Earthquake rupture occurs on roughly planar surfaces: we can define the
rupture zone of an earthquake, roughly approximated by a rectangle:
rupture dimensions:
length of the rupture: L along the horizontal direction
width of the rupture: W ³Down-dip² along the fault dip
rupture surface is roughly S=L*W.
Length of Chile 1960 earthquake (M 9.6) about 900 km
length of San Francisco 1906 (~M 8): 400 km
length of Fort Tejon 1857 earthquake (L.A): ~450 km
width limited by the thickness of the zone within which deformation occurs
through brittle fracture. Below about 15-20 km, the temperature and pressure
in the crust become so high that rocks cannot fail by brittle fracture any more,
but rather are deformed in a plastic, ductile fashion: brittle/ductile transition.
This limits the effective width of faults.
In strike-slip environments, with vertical faults, width generally less than 20
km
In subduction zones, where earthquakes occur along shallow dipping planes,
width of fault can be in excess of 100 km.
In general, rupture length is larger than rupture width for large earthquakes.
For small earthquakes, a simple model is that of a circular fault (where the
rupture is roughly a circle of radius r around an initiation point, the focus).
This surface is generally ³illuminated² by aftershocks: mainshock rupture is
not perfect and small pieces of the surface remain unruptured and are
subsequently ruptured during aftershocks. The aftershock zone (determined
from location of aftershocks) thus gives a rough idea of the rupture extent of
the main shock. Sometimes aftershock will ³fill² a zone within the main
rupture that did not break during the main shock.
Rupture zone is not uniform: barriers and asperities
barriers are impediments to rupture: stronger spots on the fault surface, or
geometrical kinks which may actually stop the rupture.
asperities are rough spots in along the fault zone that rupture during an
earthquake.
There is currently much excitement in the study of microseismicity using
sensitive borehole instrumentation that can record very high frequency
seismic waves emitted by tiny earthquakes (earthquakes of magnitude less
than 3: down to negative magnitudes) because of evidence for repeatability of
rupture at the very small scale (rupture patches of dimensions up to several
tens of meters- compared to km for large earthquakes).
During an earthquake, rupture propagates along the rupture zone at speeds of
several km/s (limit is the speed of sound in rocks), resulting in a final
displacement of the two sides of the fault, or SLIP.
The direction of slip is measured by the slip angle (measured from the
horizontal direction, in the fault plane).
The extent of slip in significant earthquakes ranges from cm¹s to several
meters (e.g. for San Francisco 1906, maximum slip measured around 10m,
average around 5m).
The larger the rupture surface S, the larger the earthquake
The larger the slip d, the larger the earthquake:
earthquake size is in proportion to S and d. This leads to a measure of
earthquake size that can be directly related to measurements in the field (if
accessible):
Seismic moment (Mo)
When a rupture is produced during an earthquake, it affects a finite area
within the fault surface. The larger this area, the larger the earthquake.
The size of the earthquake also depends on the amount of slip that
accompanies it ( cm to several meters). Finally, the rock resistance to failure
also plays a role (intrinsic property of rock: rigidity). A rigorous way to
characterize the earthquake size is through the seismic moment Mo:
Mo = m d S in units of Newton-meters (energy) typically some fraction of
10^20 N-m
where:
m is rigidity of the rock (units:
u is average slip, or displacement during earthquake (units: meters)
S rupture surface ( units: m^2)
We will see later how we relate seismic moment to magnitude
Notion of moment corresponds to a mechanical model:
to rotate a table: effort is reduced when hands are more widely separated:
force-couple. Apply two equal and opposite forces..
The size of this couple is called the moment: value is the product of th value
of one of the two forces and the distance betweent hen.
Same idea to system of forces that produce slip on a geological fault. In this
case seismic moment is defined as product of three quantities:
elastic rigidity of the rocks
area over which force applied
fault offset that takes place, or fault slip.
Advantage of this measure, results are not distorted by any dissipation of
energy during wave propagation. When available, can measure moment
directly from length of surface rupture and depth of rupture inferred from the
depths of the aftershock foci.
Seismic moments may vary over many orders of magnitude from smallest to
largest earhtquake. M2 to M 8 : range over six orders of magnitudes.
Moment of 1906 SF earthquake (450 km length of fault) is more than 10 times
the moment of 1989 which ruptured over about 45 km length (also take into
account difference in slip).
Active, inactive faults
Finding which faults are presently active/inactive is detective work for
geologists. Over periods of thousands of years faults can present intermittent
slip. There are some geological markers, such as in the topography:
sag ponds, fresh fault scarps, offset stream channels, some of which become
apparent only over periods of several million years.
Geologists also dig trenches into the fault zones of known faults: they observe
offsets of sedimentary deposits corresponding to ancient earthquakes. The
timing intervals between fault offsets can be determined by fixing the ages of
various soil layers that have been displaced (actual dates from known ages of
buried organic materials through 14C dating).
Stick-slip behavior of faults
Typical slip during an earthquake lasts seconds to minutes. In the process
earthquake waves are generated and result in shaking.
Some earthquakes take longer to occur, up to hours : ³slow earthquakes²,
the slower the rupture, the less efficient it is at generating earthquake waves.
If slow enough, the earthquake can be ³silent².
Why do faults sometimes slip slowly and harmlessly (creep) and at other
times catastrophically?
Why are there large time intervals between earthquakes on a given fault?
A simple model was first proposed by G.K. Gilbert, 1884 (well in advance of
his time). The analogy is that of a simple spring-slider model:
heavy box (brick) dragged along the floor by means of a rope (or spring) and a
windlass.
At first, as the cranking starts, the box does not move, but tension in the rope
gradually increases until it suffices to overcome friction at the inteface
between the box and the floor.
Then the box starts to move, the tension in the rope is released just
sufficiently to overcome the sliding friction. The motion would continue
smoothly BUT the box has acquired momentum: it is carried too far and then
stops, until tension builds up again
This results in a jerky motion called stick-slip motion.
The three main elements in the earthquake machine are therefore:
1) A driving mechanism: the motion of tectonic plates (windlass in the
analogy)
2) An elastic element: the earth¹s crust (spring or rope in the analogy)
3) a frictional element: fault surface (box/floor interface).
In fact , this analogy is too simple, and as observed in the laboratory, the
passage from static friction to sliding friction is not instantaneous but gradual
and depends on the displacement and speed of displacement: how this
actually happens is a subject of intense research at the present time.
We can contrast two types of motion:
stick-slip motion, which corresponds to earthquakes
stable sliding, which corresponds to creep
The kind of motion depends on the interaction of frictional properties and
elastic loading of the system:
€stiff systems favor stable slip behavior(for example replace rope by steel rod
in analogy experiment)
compliant systems favor stick-slip behavior
€ stress perpendicular to the fault surface plays an important role (normal
stress) - weight of the box
High normal stress (heavy box) leads to unstable stick-slip
low normal stress leads to stable sliding.
Faults contain fluid saturated gouge (crushed rock) whose properties can
influence the fault stability, i.e. if high pressure fluids are present, the normal
stress decreases resulting in more stable slip.
There are therefore two competing hypotheses for stable creeping section of
the San Andreas fault:
1- low permeability rocks next to fault trap pore fluids at high pressure
2 - rocks on fault sides have intrinsically frictional properties.
An interesting paradox: because of heat generated by friction during slip, one
would expect to see higher heat flow above fault zones (high heat flow
anomaly). But none is observed. A successful physical model of earthquake
rupture should be able to account for that: possible role of fluids.