Seismology Fundamentals

- Earthquakes will characterize the present-day motions of the lithosphere,
while geology and paleomagnetics describe motions in the past.
**Question:**what principle says that plate tectonics should operate now as it has in the past? Could there be exceptions? - Simply locating earthquakes on the globe shows a rough outline of plates and their boundaries.
- We can analyze earthquakes to describe the type or mechanism of plate-tectonic deformations.
- Finding a mechanism for plate-tectonic motions requires knowledge of the earth's interior. Seismology gives the most detailed characterizations of structure and composition.

(J. Louie) Relative motions cause rocks to strain out of shape, generating elastic stress. When the stress exceeds the strength of the fault zone, the accumulated strain will suddenly release in an earthquake.

Question:what does the termelasticimply about the mathematical relation between stress and strain?

Question:does the length of thereboundcurvature tell you anything about the fault above?

The sudden release of stored elastic potential energy during an earthquake releases both heat energy and seismic waves. The total energy is called the

By essentially taking the logarithm of the moment, we can create a
*magnitude* rating. Every earthquake has a unique total energy,
and therefore a unique magnitude.

Question:what is the magnitude of the largest earthquake ever? The largest possible? The smallest?

(J. Louie)
Sensitive seismographs record the passing ground motions of the seismic
waves with respect to time, noting the motions of an inertial mass against
the moving ground.

On seismograms it is easy to separate P-waves from S-waves because
they travel at different speeds, Vp and Vs:

where k is the incompressibility property of the rock,
is the rigidity (or resistance to shear), and is the
density.

Question:why will P-waves arrive first at a seismograph, and S-waves later?

Question:as rocks age and become more deeply buried, Vp and Vs generally increase. Why?

Given the fairly constant relation between and distance, you can use the above empirical equation with a calibrated seismograph to estimate an earthquake's magnitude.

(from *Kearey & Vine*, copyright Blackwell Sci. Publ.)
Of course the distance we get from the S-P time is the distance along the
travel path of the seismic waves, so we have to adjust for the earth's
spherical shape.

(J. Louie) Given the S-P times and distances of an earthquake from three stations, we can triangulate to find its location.

Question:why do we need at least three stations to get a location?

Question:how would location errors appear? What earthquakes are likely to have the greatest location errors?

(from USGS)
Simply locating earthquakes around the world over the past 100 years
(black dots above) produces a striking pattern.
Earthquakes are not evenly spread around the earth, but occur in continuous
but thin belts or zones surrounding areas of far lower seismicity.
Thus on the earth tectonic deformation is largely confined to zones of
interaction between apparently rigid regions.
Note that the pattern is more diffuse on the continents than it is in the oceans.

Question:are there any cultural or technological factors affecting the earthquake distributions on this map?

Question:what are the directions of the maximum and minimum principal strains for each mechanism?

(from

(from *Kearey & Vine*, copyright Blackwell Sci. Publ.)
The body waves do not radiate in all directions with the same strength,
however. Above are radial plots of relative wave amplitude in all directions
in a plane through a shear dislocation, or *double couple*.
The P-wave radiation pattern at left shows that the strongest compressions
(C) and dilatations (D) radiate at 45 degree angles from the fault plane.
The S-wave radiation pattern at right shows that the strongest shear
waves radiate at directions parallel and perpendicular to the fault plane.

(from *Kearey & Vine*, copyright Blackwell Sci. Publ.)
The double-couple origin of earthquake motions divides the area around the
focus into quadrants revealing different directions of motion.
For the P-wave recordings above, initial motions will be up if the wave
originated in a compressive quadrant, and down if from a dilatational
quadrant. Note that two planes separate the quadrants: the real fault plane;
and an indistinguishable *auxiliary* plane. The object of finding an
earthquake focal mechanism is to describe the orientations of these planes.

(from *Kearey & Vine*, copyright Blackwell Sci. Publ.)
What seismographs record radiation from which quadrant depends on the
location and depth of the focus, the orientation of the fault plane, and the
paths the waves take to the seismographs.

(from *Kearey & Vine*, copyright Blackwell Sci. Publ.)
To estimate a focal mechanism we pick the direction of P-wave motion
(up and compressional, or down and dilatational) at each seismograph,
find the azimuth of each ray from the locations of the event and the
seismograph, and estimate the *takeoff angle* of each ray from the
locations and ray projections through earth structure models.
Each C or D pick is plotted in lower-hemisphere projection on an equal-area
stereonet. With that data we try to find a unique strike and dip for the
mutually-perpendicular fault and auxiliary planes on the stereonet.

(fromQuestion:why is it most convenient to use the lower-hemisphere projection?

(from *Kearey & Vine*, copyright Blackwell Sci. Publ.)
At left is the focal mechanism of a thrust earthquake, and below are
cross sections showing the two possibilities for fault motion allowed
by this mechanism. From the mechanism alone, the strike and dip
of the actual fault break is ambiguous.

Note that the centers of the compressional wave quadrants are at a
direction perpendicular to the axis of the maximum compressional strain.
So the compressional *axes* appear in the dilatational wave *quadrants*.

(from *Kearey & Vine*, copyright Blackwell Sci. Publ.)
At left is the mechanism of an extensional normal fault earthquake,
with the two faulting possibilities below.

Question:what other data could we use to resolve the ambiguity between the fault and auxiliary planes?

The map above shows hundreds of mechanisms determined by a group at Harvard for the Tibet and Himalaya region. Each mechanism is a lower-hemisphere projection with the compressional quadrant darkened. The dots locate the compressional axis directions. (Click for G. Ekstrom's original 1.5 Mbyte PostScript file at Harvard, or here for a 0.73 Mbyte viewable PDF file. Used here by permission)

Question:identify a strike-slip, a normal-fault, and a thrust-fault mechanism on the map above, and describe at least three different mixed-mode mechanisms.