Download 6: Moment tensors (largely from Stein and Wysession 4.4)

LECTURE 6: SEISMIC MOMENT TENSORS
Represent other types of seismic sources as well as slip on a fault
Give additional insight into the rupture process
Simplify inverting (rather than forward modeling ) seismograms to
estimate source parameters
Used to produce global data set of great value for tectonics
EQUIVALENT BODY FORCES REPRESENTING
SEISMIC SOURCES
SINGLE FORCE Landslide (Grand
Banks slump) or
Explosion (Mt. St.
Helens)
SINGLE COUPLE add 3 for isotropic
explosion
DOUBLE COUPLE slip on fault
Stein & Wysession, 2003
MT SAINT HELENS 1980 ERUPTION
Seismic source modeled by southward-pointing single force, opposite
direction of the north-directed explosion and northward-flowing landslide.
Modeling gives estimates of the force involved in the landslide and
explosion, which devastated more than 250 square miles (640 km 2) on the
north side of the mountain.
This explosion is equivalent to an Ms 5.2 earthquake, significantly bigger
than the smaller earthquakes often associated with magma movements
within volcanoes.
USGS
Ms 7.2 earthquake,
one of the largest in
a minor zone of
seismicity along the
Atlantic continental
margin of Canada
Large underwater slump (landslide in which mass of rock moves as a coherent body)
generated powerful sediment flows, known as turbidity currents, which ruptured telephone
cables and hence provided important evidence on the speed and force of such currents.
S waves are reasonably well modeled by synthetic seismograms for a horizontallyoriented single force, implying that the slump itself was the seismic source. However,
another study found that the seismograms were well modeled by a double-couple
earthquake at about 20 km depth, which triggered the slump.
Whether earthquakes are needed to generate such slumps is interesting because such
mass movements, which might occur on many heavily sedimented continental margins,
can also generate significant tsunamis. The tsunami for this earthquake caused 27 deaths
along the Canadian coast, and a slump following an Ms 7 earthquake is thought to have
caused the devastating 1998 New Guinea tsunami which caused over 2,000 deaths.
SEISMIC MOMENT
TENSOR
General
representation of
seismic source
using 9 force
couples
Stein & Wysession, 2003
REPRESENTING EARTHQUAKE
WITH MOMENT TENSOR
Simple representation yields
seismic waves produced by a
complex rupture involving
displacements varying in space
and time on irregular fault
First, approximate rupture with a
constant average displacement D
over a rectangular fault
Approximate further as a set of
force couples.
Approximations are surprisingly
successful at matching observed
seismograms.
Stein & Wysession, 2003
FOR FAULT ORIENTED NORMAL TO
COORDINATE AXIS, MOMENT TENSOR IS
Mo is scalar moment
EARTHQUAKE
(DOUBLE
COUPLE)
MOMENT
TENSOR
Interchangeability of n and d makes the tensor symmetric (Mij = Mji).
Physically, this shows that slip on either the fault plane or the
auxiliary plane yield the same seismic radiation patterns.
TENSOR PROPERTIES OF Mij
COMPARE TO STRESS TENSOR
The moment tensor for a double couple transforms this way, because it
is a physical entity relating the normal and slip vectors in a way similar
to the way the stress tensor relates the normal and traction vectors.
FIND FAULT GEOMETRY FROM MOMENT TENSOR
EXPLOSION
IMPLOSION
EARTHQUAKES
(DOUBLE
COUPLE)
OTHER
SOURCES
(CLVD)
Dahlen and Tromp, 1998
EXPLOSION
IMPLOSION
EARTHQUAKES
(DOUBLE
COUPLE)
OTHER
SOURCES
(CLVD)
Dahlen and Tromp, 1998
Nettles and Ekstrom, 1998
MOMENT TENSOR ADVANTAGES
FOR SOURCE STUDIES:
Analyze seismograms without assuming that they result from slip on a
fault. In some applications, such as deep earthquakes or volcanic
earthquakes, we would like to identify possible isotropic or CLVD
components.
Makes it easier to invert seismograms to find source parameters,
because seismograms are linear functions of components of the
moment tensor, but are complicated products of trigonometric functions
of the fault strike, dip, and slip angles. This is not a problem in forward
modeling, but makes it hard to invert the seismograms to find the fault
angles.
MOMENT TENSOR INVERSION
MOMENT TENSOR DATA FOR TECTONIC STUDIES
Globally-distributed broadband digital seismometers permit reliable focal
mechanisms to be generated within minutes after most earthquakes with Ms >
5.5 and made available through the Internet.
Several organizations carry out this service, including the Harvard CMT (centroid
moment tensor) project.
CMT inversion yields both a moment tensor and a centroid time and location.
This location often differs from that in earthquake bulletins, such as that of the
International Seismological Centre (ISC), because the two locations tell different
things. Bulletins based upon arrival times of body wave phases like P and S give
the hypocenter: the point in space and time where rupture began. CMT solutions,
using full waveforms, give the centroid or average location in space and time of
the seismic energy release.
The availability of large numbers of high-quality mechanisms (Harvard project has
produced over 17,000 solutions since 1976) is of great value in many
applications, especially tectonic studies.