When an earthquake occurs, seismologists create graphics of focal mechanisms, informally referred
to as beach balls, to show the faulting motions that produce the earthquake.
The focal mechanisms are based on the direction of the first arriving P wave.
Lets investigate the patterns of P-wave arrivals that result from different faulting mechanisms
by first considering a strike-slip earthquake.
When an earthquake occurs, seismic waves radiate away from the epicenter in all directions.
The parallel green lines in the northwest and southeast quadrants have been compressed
during the earthquake and the Northeast and southwest quads were stretched. This applies
also to vertical faults. Let’s look at the Pwaves moving away from the epicenter.
We will inset slinkies to demonstrate and exaggerate the compression/dilatation features.
Northwest and Southeast of the epicenter the rock is compressed
and the first arriving P waves at those stations are pushes away from the epicenter.
Northeast and Southwest of the epicenter the rock is stretched
and the first P waves are pulls toward the epicenter
The dilatational and compressional arrivals are often shown as plus and minus signs respectively.
With observations from many stations, we see 2 quadrants of compressional arrivals and
2 quadrants of dilatational arrivals separated by perpendicular nodal planes. To simplify
the illustration, compressional quadrants can be shaded, and dilatational quadrants
are left un shaded producing a P-wave first-motion pattern that looks like a beach ball.
Notice that this pattern of dilatations and compressions can be produced either by right
lateral strike-slip faulting on a North-south fault plane, or left lateral strike-slip faulting
on an east-west fault plane. Therefore you must use geological knowledge of the region
to decide which nodal plane is the fault plane. For example, if an earthquake with an epicenter
on the San Andreas fault had a focal mechanism that looked like this, the most likely choice
would be that the fault plane is oriented Northwest-Southeast, parallel to the strike
of the fault we observe at the surface. Let’s now consider a right-lateral strike-slip
earthquake on the Kane Fracture Zone in the Atlantic. This earthquake will produce compression
in the Northeast and Southwest quadrants, and dilatation in the Northwest and Southeast
quadrants. Since there are no nearby seismometers, the P-wave first arrival patterns are observed
at distant stations. Seismic energy travels away from the earthquake in all directions,
so we need to consider the three-dimensional geometry of the ray paths.
To do this, it is convenient to imagine a sphere, called the focal sphere, surrounding
the earthquake hypocenter. Rays that travel to distant stations will radiate from the
earthquake through the lower hemisphere of the focal sphere. To keep things simple, let’s
look at 2 cross sections at more-or-less right angles.
First, make a vertical cut into the Earth through the hypocenter in a northeast-southwest
orientation. P waves leaving the earthquake and travelling to Lima Peru in the southwest
quadrant or to Madrid, Spain in the northeast quadrant will have compressional first-arriving
P waves that push up, away from the earthquake, and are observed as an initial upward vertical
motion on those seismograms. The second cross section will show P waves travelling to Detroit
and Seattle in the northwest quadrant and to Cape Town, South Africa in the southeast
quadrant. These will have dilatational first-arriving P waves that are a pull toward the earthquake,
observed as a downward vertical motion on their seismograms. By examining first-arriving
P waves at many stations over a range of azimuths and distances from the earthquake, we can
determine the pattern of compressions and dilatations on the lower hemisphere of the
focal sphere. As we have seen, a strike-slip earthquake produces a crossing pattern of
approximately vertical faults, or nodal planes that separate 2 compressional and 2 dilatational
quadrants. Let’s now look at the pattern of compressions
and dilatations that result from an earthquake on a normal fault like on the east side of
Steen’s Mountain in the Basin and Range Province. The block on the east side of this
fault has dropped down with respect to the block on the west. Viewed in cross section,
we see that compressional first-arriving P waves will radiate to the east and west from
the hypocenter at shallow and intermediate downward angles. Dilatational first-arriving
P waves leave the hypocenter at a steep downward angle. The resulting focal mechanism has perpendicular
nodal planes that cut the lower hemisphere of the focal sphere in an “orange-slice”
appearance with compressions on the outside and dilatations in the center. This is the
focal mechanism signature of an earthquake on a normal fault produced by extensional
forces. Because of the way the fault plane intersects the bottom of the focal sphere,
the boundary between the regions on the focal mechanism is curved.
Finally, let’s consider a thrust fault like that beneath Sierra Pie de Palo within Sierras
Pampeanas of NW Argentina. This is a is a west-vergent thrust fault, wherein the block
on the east moves up & over the block on the west. Viewed in cross section, we will see
that dilatational first-arriving P waves radiate to the east and west from the hypocenter at
shallow and intermediate downward angles, whereas the compressional first-arriving P
waves leave the hypocenter at steep downward angles. The resulting focal mechanism has
perpendicular nodal planes with the same “orange-slice” appearance observed for a normal fault. However,
for a thrust fault earthquake, dilatations are on the outside and compressions are in
the center. This “cat’s eye” focal mechanism is the signature of an earthquake on a thrust
fault produced by compressional tectonic forces.