Early Tectonic Ideas. Herodotus of Halicarnassos(484 BC-ca. 425 BC), now part of Turkey, observed seashells in the hills of Egypt and concluded that they had lain beneath the sea. Predecessors Anaximander and Xenophanes are quoted as making similar statements.
Wegener, in 1924, proposed a reconstruction of Pangaea, based primarily on geometric fit.
From USGS “This Dynamic Earth, Kious and Tilling,1996
Smith and Hallam, 1970, generated fits which were consistent with structural and paleontological data.
The signs left on continental cratons by plate tectonic activity are not as clear as we see when we have todays maps of the ocean basins before us.The remains of unsubducted fragments of oceanic lithosphere are stuck onto the edges of continents and represent many cycles of basin openings and closing (Wilson cycles). These were not so easy to interpret.
Earthquakes give us information about their sources through the waves they radiate.Surface waves (L,R) are bound to the surface, while body waves travel through the interior.Body waves can be polarized.
Many faults are not as simple as the strike-slip example in the previous slide. The geometric variables which define fault plane geometry and relative motion are defined below.Figure from Stein and Wysession, 2003
Up motion occurs in the compression quadrantDown motion occurs in the dilation quadrantThe little doughnuts show where the rays whose seismograms are shown exit from the box.
The following several slides are from Stein and Wysession, 2003
The amplitude depends on the angle of the vector to the receiver as seen from the fault.For P waves this radiation pattern can be represented as a beach ball, which represents a FOCAL SPHERE around the source.For S waves it is more complicated because of the polarization.The lower panel shows the direction of first motion for S waves on a sphere.
This slide shows the radiation pattern from a source which is called a double couple, since it is composed of two vector pairs instead of one.It conserves angular momentum, which is usually a good thing.Here the right panels show the direction of first motion for both P and S waves.
In the real earth, we make observations on the surface, which we can map back to the focal sphere by ray tracing, since we know the earth's velocity structure (of which more later).This means that the fault and auxiliary planes will map onto the earth's surface in a diagnostic pattern, as these rays are mapped.
Projections are ways of displaying all or part of the surface of the spherical (or more complicated) earth on a flat surface, such as a piece of paper.Useful properties of projections are that they be(1) conformal, that is, that for small areas, angles are preserved. So a right angle on the earth's surface is represented as a right angle on the map.(2) equal-area. So areas are conserved.Unfortunately, we cannot have both simultaneously.
Six Books of Optics, useful for philosophers and mathematicians alike
François d'Aiguillon, 1613
Figure by Peter Paul Rubens
To visualize the fault and auxiliary planes onto a flat piece of paper, we use a stereographic net.The azimuth coordinate is used to plot strike and, naturally, dip is for the dip.
To plot a plane normal (perpendicular) to plane A, rotate the net until A is on a meridian.The pole for plane A will be 90 degrees from its “equator”. All planes through this pole will be normal to plane A.Then any meridian in a rotated net, if it passes through the pole of A, will be normal to A.
Plotting PointsThe direction a ray leaves the focus is defined by its azimuth from north, and its dip (measured from horizontal) or its takeoff angle, measured from vertical.To plot a ray on the focal sphere, use its dip to plot it on the equator of the net. This would be correct if the azimuth were east (090), then rotate the point as shown here. This not the same as following the meridian.
The compressional area of the P radiation pattern is, by convention, shown as black.The direction of motion on the fault depends on which plane is the fault plane.Choose a fault plane, then imagine standing in the white area. Then follow the directions of Darth Vader and “come to the dark side”*. You will then be following the motion of the earth on that side of the fault.
* Noted by Vince Cronin
The fault geometry also controls the radiation of surface waves, since they are composed of interference patterns of body waves.Here are radiation patterns of Love waves (made of SH body waves) and Rayleigh waves (made of P and SV waves).
The classical method for finding focal mechanisms is to assemble seismograms which observe a quake and trace their rays back to the focal sphere, plotting the points as filled circles if the first motion is dilational (down) and solid if up (compressional). By examination, two planes are fit dividing the compressional and dilational quadrants. Needless to say, the results of this process are do not always define planes uniquely.Now mechanisms are usually derived using moment tensor inversion, about which more later.
We have looked at focal mechanisms from the point of view of earth motions. These motions have clear interpretations in the case of the strike-slip fault.These motions are, however, not immediately indicative of the forces which produce them.So we introduce the pressure and tension axes.