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 horizontally-oriented 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.

General representation of seismic source using 9 force couples 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.