Geol 333
Seismology Fundamentals

Contributions of Seismology to Plate Tectonics

Describing Earthquakes

elastic rebound sketch
(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 term elastic imply about the mathematical relation between stress and strain?
Question: does the length of the rebound curvature tell you anything about the fault above?
M0 = mu A d
The sudden release of stored elastic potential energy during an earthquake releases both heat energy and seismic waves. The total energy is called the moment M0.

Mw = 2/3(log M0 -16)
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?

Seismic Waves

P and S wave sketch (J. Louie) The part of the elastic energy radiated from an earthquake as seismic waves takes two forms, compressional and shear.

seismograph sketch (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:
Vp = ((k + 4/3 mu)/rho)^1/2 Vs = (mu / rho)^1/2
where k is the incompressibility property of the rock, mu is the rigidity (or resistance to shear), and rho 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?

Locating Earthquakes

Most terrestrial rocks are nearly Poisson solids, for which the ratio Vs/Vp is close to the square root of three. In subtracting the arrival time at a seismograph of the P wave from the arrival time of the S wave (to find the S-P time delta t), this fact means that you can multiply the S-P time by a factor a 8 km/s to get a generally reliable estimate of the distance of the earthquake from the seismograph.
M = log A + 3 log (8 delta t) - 2.92
Given the fairly constant relation between delta t and distance, you can use the above empirical equation with a calibrated seismograph to estimate an earthquake's magnitude.

delta distance sketch (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.

earthquake location circles (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?

global seismicity map
(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?

Earthquake Mechanisms

fault types sketch (J. Louie) Knowing where the seismically-active zones are tells us what regions are currently deforming tectonically, but it does not tell us anything about the nature of the deformation. There are these three fundamental types of deformation; we can create any type of faulting by mixing them in different proportions. All of these faults are shear or sliding dislocations that produce no net volume change or net rotation. Only two opposing force couples can produce such motion. Very few earthquakes have been shown to result from volume changes, or from single forces.
Question: what are the directions of the maximum and minimum principal strains for each mechanism?
earthquake wave motions sketch
(from Kearey & Vine, copyright Blackwell Sci. Publ.) From the focus of an earthquake, the two types of body waves (P and S), and two types of surface waves (Love and Rayleigh, which are S-waves trapped near the surface) radiate in all directions.

P radiation pattern S radiation pattern
(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.

radiation quadrants
(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.

radiation node sketch
(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.

Question: why is it most convenient to use the lower-hemisphere projection?
strike-slip mechanism (from Kearey & Vine, copyright Blackwell Sci. Publ.) At left is the result of the fitting process for some strike-slip earthquake. All the compressional picks should land in the dark compressional quadrants, and all the dilatational picks should land in the light quadrants. Note the double-couple, and the fact that we cannot tell whether this was a north-striking left-lateral fault, or an east-striking right-lateral fault.

thrust mechanism (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.
thrust W sketch thrust E sketch

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

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

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