Purdue University

EAS 557

Introduction to Seismology

Robert L. Nowack

Lecture 17

Seismic Locations and Focal Mechanisms

 

 

Earthquake Locations

 

            The systematic location of seismic events in a region can be used to identify causative seismic faults.  On world maps, seismicity tends to locate along linear belts which define more active deformation compared to more stable interiors.  These belts can be used to separate the surface of the Earth into plates.  The seismicity maps below show world seismicity from 1965-1997 for magnitudes greater than 5.  The top map is for all depths and the bottom map is for events with focal depths greater than 100 km for all magnitude events.

 

 

 

 

(from Stein and Wysession, 2003)

 

Although most seismicity is shallow, less than 100 km in depth, in some regions of the Earth, seismicity can reach depths of greater than 600 km.  These regions are called subduction zones and are thought to represent places where oceanic crust descends or sinks into the mantle.  Earthquakes result because of the colder temperatures of the subducting plate.  An example of locations of hypocenters for the subduction zone beneath Japan is shown below.  Accurate earthquake locations show a double seismic zone.

 

 

 

 

(from Stein and Wysession, 2003)

 

            In California, most seismicity is shallow related to the plate boundary between the Pacific and North American plates.  Major faults in California and associated large earthquakes are shown in the figure below.

 

 

 

 

(from Stein and Wysession, 2003)

 

A seismicity map of small earthquakes from 1969-1978 less than magnitude 5 in central California are shown in the figure below.  This shows that even small magnitude earthquakes are often associated with known geological faults.

 

 

 

 

            After a large earthquake happens, many small aftershocks occur in the hypocentral area resulting from readjustments of stress along the fault.  These occur within days to weeks or months after the main shock has occurred.  An aftershock distribution for the 1989 Loma Prieta earthquake in California is shown below.  The aftershock zone is thought to map out the zone of rupture along the fault from the main shock.  The hypocenter is the point of initial rupture along the fault and has a depth of about 18 km for the Loma Prieta earthquake.  This event is also called the “World Series” earthquake since it occurred during a game of the World Series in 1989.

 

 

 

 

            Tectonic earthquakes are due to faulting, although volcanic earthquakes can have different mechanisms.  Rupture on a fault is a sudden catastrophic slip which occurs across roughly planar surfaces and corresponds to an abrupt release of elastic energy stored in the rocks around the fault zone.

 

            The 1906 earthquake offers an example.  Consider a fence originally oriented perpendicular to the San Andreas Fault.

 

 

 

 

The rebounding of the fault after rupture was described by Reid. 

 

 

 

Principle Stress Axes

 

            The stress tensor at a point is symmetric and has six independent numbers.  The stress tensor can be diagonalized to give three principle stresses (and three rotation angles).  The axis in which the compressive stress is greatest is called the maximum compressive axis (or the P-axis).  The axis along which the extensional stress is greatest is called the T axis.

 

            The simplest theory of faulting is that faulting occurs along the plane along which the shear stress is a maximum at approximately 45o from the maximum compressive stress direction.  For real faults with friction, this angle can be different.  But, to first order, 45o is used for focal mechanism studies.

 

            The figure below shows a vertical fault with the P and T axes also shown.

 

 

 

 

The P and T axes can be inferred if the orientation of the fault is known.  The fault orientations, therefore, gives clues to the origin of stresses which result in earthquakes.

 

 

 

Radiation Patterns of Seismic Waves

 

            P waves, S waves, and surface waves are all affected by the orientation of the fault plane.  The figure below shows the lobes of the radiation patterns for P-waves and S-waves for an earthquake source resulting from slip on a fault.

 

 

 

 

The figure below shows the radiation patterns for P and S waves for an explosive source.  Theoretically, for the explosion case, there would be no S-waves, but real explosions do generate some S-waves.

 

 

 

 

 

Fault Plane Solutions

 

            Consider the azimuthal variation of P-wave “first motions” recorded at different station from earthquake faulting.  It turns out the polarity of the first arrivals vary in a systematic fashion with direction from the earthquake fault; even for stations at teleseismic distances.  Below is a map view of a right lateral strike slip fault.  In the upper right and lower left quadrants, the ground is being pushed by the motion on the fault resulting in the P-waves showing initial up motions or compressions.  For the other two quadrants, the ground is being pulled resulting in P-waves showing initial dilations or down motions of the ground.

 

 

 

 

So, if we had enough seismometers at different azimuths and distances from the earthquake source, we could determine the orientation of the fault plane and the perpendicular “auxiliary plane”.

 

But, can we determine which nodal plane is the actual fault plane?  It turns out we would need extra geological constraints to tell which is the fault plane and which is the auxiliary plane.

 

            In the Earth, fault planes aren’t always vertical.  Plotting polarities on a map would then be messy as shown in the figure below.

 

 

 

 

In order to simplify the analysis, the concept of the “focal sphere” is introduced.  The focal sphere is an imaginary sphere drawn around the source region enclosing the fault.  If we know the earthquake location and local Earth structure, we can trace rays from the source region to the stations and find the ray take-off angle at the source to a given station.  At a given source-receiver, the distance can be determined and from this T and  can be found from the travel time tables.  For example, the Jeffreys-Bullen travel time tables can be used to obtain  and from this .  These can then be used to find the take-off angle i.

 

            An example of P-wave takeoff angles for a surface focus source is shown below.  The azimuth of the ray is taken as the direction of the source to the station from north.

 

 

 

 

(from Stein and Wysession, 2003)

 

            Each ray that intersects the focal sphere is then projected onto equatorial plane of the focal sphere using a sterographic projection as shown below.  Several different types of projections can be used, such as equal area and equal angle stereographic projections.

 

 

 

 

Usually, a stereographic projection of the lower hemisphere of the focal sphere is used.  Planes intersecting the focal sphere plot as arcs on stereographic projections.  Lines plot as points (for rays from the source for example).

 

 

 

 

The focal sphere around the source and the takeoff angle for a seismic ray leaving the source is shown below.

 

 

 

 

(from Lay and Wallace, 1995)

 

            For example, three planes striking N-S with different dips are shown below on a stereographic projection.

 

 

 

 

A plane with another strike direction, but a given dip from the horizontal can be plotted by rotating a piece of paper above the stereonet project to draw the arc and then rotating to the true aximuth of the fault strike as shown below.

 

 

 

 

(from Stein and Wysession, 2003)

 

            A point representing a line, such as a seismic ray intersecting the focal sphere, can be plotted on the stereonet by rotating the stereographic projection to the east-west line and plotting the point at the given takeoff angle from the vertical (or dip from the horizontal represented by the edge of the stereonet) and then rotating to the appropriate azimuth.

 

 

 

 

(from Stein and Wysession, 2003)

 

            Ex)  A fault plane dipping 40o east and striking N-S is shown below in map view, in cross section, and on a stereographic projection of the lower hemisphere of the focal sphere.

 

 

 

 

Several parameters are required to determine the orientation of slip on a fault.  The strike angle  is determined clockwise from north where, by convention, if you look along strike, the fault is dipping to your right.  The dip angle  is measured from the horizontal.

 

Finally, we need to know the orientation of the slip vector of the “hanging block” with respect to the “foot block”.  This slip or rake angle, , is measured counterclockwise from the horizontal direction in the fault plane.  For example, a slip angle of 0 degrees would result from a left lateral strike slip fault.  A slip angle of +90 degrees would result from a pure thrust fault where the hanging block is pushed up with respect to the foot block.  A slip angle of -90 degrees would result from a pure normal fault.  The fault orientation parameters are shown in the figure below showing the foot block.

 

 

 

 

(from Aki and Richards, 2002)

 

            On a stereonet, a double couple source can be represented by one curve representing the fault plane and another curve representing the “auxiliary plane”.  These curves separate regions of the stereonet into zones where compressional seismic P-wave motions and dilatational P-wave motions radiate from an earthquake fault.

 

The auxiliary plane is perpendicular to the fault plane.  Thus, the pole or normal of the auxiliary plane is a point on the stereonet which must be on the curve of the fault plane.  Also, the auxiliary plane must include the pole or normal of the fault plane.  The slip vector is a point along the fault plane curve and is also the pole of the auxiliary plane.

 

 

 

 

We can then plot fault planes and auxiliary planes on the stereographic projection and also plot points representing seismic P-wave polarities.

 

            By convention, P-wave compressions are plotted as small solid circles and P-wave dilatations are plotted as small open circles.  An example of a well constrained “focal mechanism” from P-wave polarity data for the orientation of the fault plane and the auxiliary plane is shown below.

 

 

 

 

(from Lay and Wallace, 1995)

 

Alternatively, the entire compressional quadrants is shaded in and the dilatational quadrants are unshaded as shown below.

 

 

 

 

(from Stein and Wysession, 2003)

 

Often, only the shaded quadrants are shown in small “beach balls” that can be plotted on maps at the location of the epicenters.  The centers of the stereonets are shaded for thrust faults and unshaded for normal faults.

 

 

 

 

(from Stein and Wysession, 2003)

 

After a little practice, you should see how any arbitrary fault with a given slip direction will plot on a stereonet.  An example of plotting focal solutions on a map is shown in the figure below for magnitude 4 and 5 earthquakes from 1969-79 in central California.

 

 

 

 

 

Seismology and Plate Tectonics

 

            Many people in the 1960’s were laying the foundations of plate tectonics, including Hess, Cox, Vine and Matthews, and J.T. Wilson.  Seismology also did much to demonstrate the postulates of plate tectonics and seafloor spreading.  A classic paper is Isacks, Oliver, and Sykes, Seismology and the New Global Tectonics, JGR, v. 73, p. 5855 (1968).  They realized the contributions that seismology could make and several of their observations led to the acceptance of plate tectonics by the late 1960’s.

 

A cartoon of different plate boundary motions is shown in the figure below.

 

 

 

 

(from Stein and Wysession, 2003)

 

 

 

Transform Faults

 

            In 1965, Wilson suggested that fracture zones that offset undersea ocean ridges were special kind of faults called transform faults.  These were formerly thought to be transcurrent faults.

 

 

 

 

In the figure above, if Wilson was right, there would be no seismic activity past the fault ridge junctions and also the fault plane solutions should look like the right hand figure and not the left figure.  When Wilson presented his ideas at a symposium, Sykes attended and had done fault plane solutions for a fracture zone in the Atlantic, but couldn’t remember what sense the motion was.  Returning to Columbia, he found the motion to be as in the right hand figure; a striking confirmation of the occurrence of transform faults in the theory of plate tectonics.