Plate motions

To trace the geological history of the earth, it is necessary to know how the tectonic plates have moved around upon its surface. Using geological evidence, scientists can determine their relative locations at various times in the past. Such information can help in understanding the distribution of geological provinces and also in locating economically important formations.

Relative Velocity

A central tenet of the plate tectonics theory is that plates are moving across the surface of the earth. Though all motion is relative in the context of plate tectonics, motion must be defined with respect to a given frame of reference. There is also the difficulty of treating an enormous period of time over which the plate motion has taken place. Some of the geological methods available to earth scientists can be utilized to find the position of a plate millions of years ago, while other methods can yield its present velocity. It is difficult, however, to resolve these two pieces of information into a consistent pattern describing the history of the plate's motion.

To measure a plate's motion, the first step is to find its velocity with respect to an adjoining plate. This is known as relative velocity. Such a relative velocity is actually a linear velocity and, like any velocity, is a vector, which means that it is described not only by the speed of the plate (the magnitude of the vector) but also by the direction in which the plate moves. Some of the methods that geologists employ to find plate velocities give both magnitude and direction; others provide only one of these quantities.

Euler Poles

Plates do not move in straight lines, as they are constrained to be on the surface of a globe. In fact, the plates are moving along curved paths, so their velocities should be described as angular velocities, strictly speaking. If one is considering only a very small area on the earth's surface, then linear velocities are an acceptable approximation. While linear velocities are quoted in units of millimeters per year, angular velocities are quoted as degrees per year, or radians per year. Furthermore, angular velocities are described as a change in angle per unit time around a pivot point (or axis). An everyday analogy might be a door: When a door opens, it pivots at the hinge, and the entire door moves at a particular angular velocity around this pivot. Note that the linear velocity of various parts of the door varies. Near the hinge, the distance moved in the time taken to open the door is small, so the linear velocity here is small, too. The door handle moves a much greater distance in the same time, so its linear velocity is greater. Note also that as the door opens the linear velocity of any point on the door changes continually, as any point on the door is constantly changing direction. Considering the door handle, at every instant during the opening its direction of motion is changing (even though the speed may be constant); hence, the velocity is also changing.

Now consider a plate on the surface of the earth. The linear velocity of the plate has a small magnitude near the pivot point around which it moves. This pivot point is called an Euler pole (named after the Swiss mathematician, Leonhard Euler, who developed this concept). Farther away from the Euler pole, the magnitude of the linear velocity increases. Suppose that two plates are spreading apart and that the pivot point is the north geographic pole. The mid-ocean ridge between the plates would lie on a line of longitude. The linear velocity of one plate with respect to the other (at any instant) would be zero at the Euler pole and increase to a maximum at the equator. On the other side of the equator, the linear velocity would decrease until it reached zero again at the South Pole, where another Euler pole would be located. In fact, the two Euler poles are just the points where the axis around which the rotation is taking place penetrates the earth's surface.

Reconstructing Ancient Landmasses

Knowledge of relative velocities and Euler poles enabled the reconstruction of the position of the continental landmasses in the past. Approximately 200 million years ago, the continents were grouped in a single supercontinent called Pangaea. Pangaea then split into a northern fragment (Laurasia) and a southern part (Gondwanaland) separated by the Tethys Sea. Since then, the fragmentation has continued, and the plates have shifted such that the continents have drifted to the positions they occupy in the modern age. Some of the continental fragments have drifted quite rapidly, such as the Indian subcontinent, which broke from Africa and Antarctica and drifted north until colliding with Asia to form the Himalayan Mountains.

Deposits of oil or coal in the earth may have originally formed before the breakup of Pangaea. Therefore, if the location of one such deposit is known it may be possible to determine the full paleogeographic extent of the environment that gave rise to the deposit in the past by reconstructing the ancient landmasses. By using this method, geologists can predict where further economically valuable sites of oil and coal may lie, even if these sites are currently thousands of miles from the known deposit on a separate continent.

Predicting Future Plate Movement

Future plate movement can be predicted using their known present relative velocities. For example, the Atlantic Ocean will continue to open, mostly at the expense of the shrinking Pacific Ocean. Australia and Africa will continue to move north, as will Baja California and parts of southern California as the San Andreas fault lengthens. In roughly 10 million years, Los Angeles and San Francisco will become neighbors.

Although plate motions are very slow, the consequences of those motions can often be very abrupt and dramatic. The study of plate tectonics has led to an understanding of why certain regions of the earth are prone to earthquakes and volcanic eruptions. It would beneficial to everyone to be able to predict when these events will take place, and some of the methods that are used to determine plate motions can give direct information concerning these phenomena. In a region such as Southern California, measurements of relative velocities along the San Andreas fault can be applied to the forecasting of earthquakes, and are, therefore, of direct interest to the local population.

Absolute Plate Motions

Although relative velocities are useful, the absolute motions of plates can be defined from a frame of reference that is geologically determinable. What is needed is a frame of reference fixed with respect to the interior of the planet, beneath the lithosphere. This region of the interior is termed the mesosphere. It appears that there are locations on the earth's surface that are in some way tied to the mesosphere: hot spots. Hot spots are places where there is volcanic activity that is unrelated to plate boundary activity. These regions are often typified by lavas that are geochemically dissimilar to those formed at either mid-ocean ridges or island arcs, and it has been theorized that the dissimilarity results from the fact that their magma source is much deeper.

Perhaps the best example of a hot spot trace is the Hawaii-Emperor chain of seamounts, which is basically a chain of extinct volcanoes except for the island of Hawaii itself. As one moves away from Hawaii along this seamount and island chain, the lava flows become progressively older. In the hot spot hypothesis, this is explained by the postulation that each island (or seamount) formed over the hot spot, but that the motion of the Pacific plate over the hot spot continually moved the islands away from the magma source—rather like a conveyer belt moving over a static Bunsen burner, leaving a progressively lengthening scorch mark. The Hawaii-Emperor chain has a bend in it, at about the location of Midway Island, which is interpreted as meaning that the Pacific plate motion changed direction at the time that that island formed (some 37 million years ago). Because it is possible to date the lava flows on these islands, the velocity of the Pacific plate relative to this particular hot spot can be calculated (its direction being obtained from the bearing of the seamount chain). The same can be done for other hot spots, so that geologists can ultimately find the velocities of the hot spots relative to one another. The result of this procedure is the discovery that the hot spots move with respect to one another but at rates much slower than do the plates. Assuming that these relative motions are insignificant and that the hot spots are in reality fixed with respect to their proposed source, the mesosphere, then the mean hot spot frame of reference can be defined and all plate motions calculated with respect to that. In fact, this method essentially determines the velocities of the plates with respect to a mantle velocity that best simulates all the known hot spot traces. Absolute plate velocities determined by this method are commonly given in contemporary global plate motion analyses. Studies in 2006 reviewed evidence for a westward motion of the continents due to the tidal action of the moon.

Theoretical Implications

The analysis of absolute plate motions has a bearing on theories concerning why the plates move. One group of plates is apparently moving quite slowly, with velocities of between 5 and 25 millimeters per year. This group includes the Eurasian plate, the North and South American plates, and the African and Antarctic plates. In contrast, the Indian, Philippine, Nazca, and Pacific plates move much more rapidly, and the Cocos plate has a velocity of roughly 85 millimeters per year. This observation has led to the realization that it is the plates with actively subducting margins that move the fastest. None of the slower group has a significant percentage of its margin being subducted, whereas all in the faster group do. The implication may be that the subduction process itself plays an important role in driving plate motions. This idea is in contradiction to the earlier hypothesis that the lithospheric plates rode on the back of giant convection cells within the mantle. If this latter view were correct, one might expect the larger plates to move faster (although that is debatable, depending on the geometry of the convecting cells). At the least, a passive plate theory such as that would not produce the correlation noted earlier. It seems that the plates are not passive players in the plate tectonic cycle but rather an active part of convection.

Determining Euler Pole Locations

Geologists have a variety of ways to determine how plates have moved in the past and how they may move in the future. Crucial to this endeavor is determining the location of Euler poles, but finding the location of an Euler pole for the relative motion between two plates can be difficult. As indicated in the previous section, however, if one follows a line of longitude along which a ridge lays, one must eventually arrive at the Euler pole. Unfortunately, ridges do not always lay on the geographic longitude lines of the earth. The ridge system separating two plates describes its own set of longitude lines, which may not correspond with geographic longitude lines. To distinguish them, these longitude lines can be referred to as great circles. In fact, any circle that is drawn around the earth is a great circle. All great circles would be identical in length on a perfectly spherical earth. Latitude lines, in contrast, are not great circles, with the exception of the equator, and vary considerably in length. They are referred to as small circles.

Mid-ocean ridge segments are offset by transform faults. Therefore, a set of great circles can be drawn through the various segments of the ridge system, revealing the Euler pole. The transform faults can be used. Small circles drawn through these define the position of the Euler pole as well. This latter case has the added advantage that the fracture zones on either side of the transform fault effectively extend their length and make the geometric construction easier, as it is advantageous to have as long a feature as is possible to which to fit the circle in order to cut down on the errors inevitably involved with any line-fitting method.

Vector Addition

When a plate does not have a mid-oceanic ridge system separating it from a neighboring plate, other methods must be employed. Such is the case with the Philippine plate, which is surrounded entirely with subduction zones. In this instance, finding its velocity with respect to its neighboring plates and the Euler pole around which the rotation occurs is much more difficult. The motion of the Philippine plate is usually found by adding the velocities of all the other plates on the earth's surface and finding the resultant. The velocity that exactly cancels this resultant is taken to be the velocity of the Philippine plate.

Locations where three plates meet at a single point (triple junctions) can be analyzed by vector addition as well; if the velocities of two of the plates are known, then the velocity of the third can be determined. Significantly, the relative velocity of the triple junction itself can be determined; from that number it can be determined whether any of the plate boundaries is lengthening or shortening. In this fashion geologists were able to determine that the San Andreas fault is lengthening. At its southern end, the triple junction (a convergence of all three types of plate boundaries) migrates south, and at its northern end, the triple junction (two transform faults meet a subduction zone) moves north. This deduction led to the realization that part of the ancient Pacific sea floor, the Farallon plate and part of the East Pacific Rise, had been subducted down a trench that used to lie offshore of western North America. The two remnants of this older plate are the Cocos plate to the south and the Gorda (or Juan de Fuca) plate to the north.

Instantaneous Velocities

The relative motions of two plates can also be measured by more direct approaches. One technique is to try to measure directly the changes in positions occurring over a few years, which, from a geological point of view, is instantaneous. These are referred to as instantaneous velocities. One example of how that may be done is using geodetic measurements—essentially surveying the region across a plate boundary at regular intervals and, therefore, observing the motion. This technique does not lend itself to the examination of mid-ocean ridges but has been extensively used in studying the San Andreas fault in California. The results of these measurements give the magnitude of the relative linear velocity between the Pacific plate and the North American plate to be between 50 and 75 millimeters per year, the direction of this relative velocity being known from the bearing of the fault line. These numbers agree quite well with other estimates based upon geological evidence, such as the separation of once-continuous geological features that has taken place over much longer time periods.

Another example is the use of satellite laser ranging (SLR). This technique employs a laser beam bounced off a satellite, which affords a method to calculate the distance between two points on the surface of the earth with great accuracy. The distance between two points on separate plates is regularly found, and hence the velocity between the points is calculated. By this method, the relative velocity between North America and Europe has been found to have a magnitude of approximately 15 ± 5 millimeters per year. Once again, that is in agreement with geological data for much longer time periods. In some cases, however, the agreement between the results of SLR and geological evidence is not as good. In the Zagros Mountains of Iran, the two methods do not agree, implying that the instantaneous velocity indicates a change in the relative motion of the two plates on either side of this plate boundary.

Finite Velocities

The velocities calculated by geological means over much longer time spans are referred to as finite velocities. One major technique used to determine finite velocities depends upon the Vine and Matthews theory of seafloor spreading. The geomagnetic polarity record is now well established and the dates of the geomagnetic reversals known (although this information is still undergoing refinement and short polarity episodes are sometimes added to the known record). This time scale can be used to identify marine magnetic anomalies caused by the magnetization of the sea floor and affords a method by which to date a point on the sea floor. If one measures the distance between two locations of the same age, located on either side of a mid-ocean ridge, then it is quite simple to calculate the relative velocity between the two plates (the direction of the motion being, in most cases, perpendicular to the ridge or parallel to the transform faults). If the separation of two points on the ocean floor, on the same plate but of different ages, is measured, then geologists can still find the “half spreading rate” of the ridge (the amount of new crustal material added per year at the ridge), but this is not a relative velocity.

Remanent Magnetization

Because the oceanic crust is relatively young, with the oldest crust being approximately 160 million years old (as compared to 4.6 billion years of earth history), the techniques described above are not applicable to the majority of the history of the earth. To work out plate motions for older periods, other methods must be employed. The most prevalent of these methods is the use of the remanent magnetization of rocks. Remanent magnetization is acquired when rocks form, and it is oriented parallel to the geomagnetic field at the time and place at which they are forming. This magnetization is retained in much the same way that a bar magnet retains its magnetization. If the rock is subsequently moved, by being carried along with a moving plate, the rock may end up at a location where the direction of the geomagnetic field is substantially different from that of its own magnetization. It is this difference between the field and magnetization directions that was critical in proving that continents do indeed drift across the earth's surface and that was a contributing factor in the acceptance of this theory by geologists.

The angle that the geomagnetic field makes with the horizontal varies considerably, from vertically up at the south magnetic pole to horizontal at the equator to vertically down at the north magnetic pole. This angle is referred to as the inclination. By calculating the inclination of the magnetization of a rock, the latitude at which the rock formed, called the paleolatitude, can be ascertained. If a series shows paleolatitudes for successively older rocks, the latitudinal motion of the plate over time can be traced. Unfortunately, the same cannot be done for longitude, for the simple reason that while latitude is an inherent property of a spinning planet, longitude is not.

Plates not only shift in latitude but also rotate as they move with respect to one another. The angle between true north and a rock's magnetization is referred to as the declination, and it is this angle that allows such rotations to be determined. It is interesting that geologists have been able to delineate rotations of small blocks near the edges of the major plates, which means that a considerably more complex story unravels concerning the interactions at plate boundaries. In both Southern California and Southeast Asia, there are numerous microplates that may have rotated between larger plates.

Principal Terms

declination: the angle in the horizontal plane between true north and the direction that the magnetization of a rock points

Euler pole: the point on the surface of the earth where an axis, about which a rotation occurs, penetrates that surface

frame of reference: a part of the planet, with respect to which all velocities are quoted

hot spot: a point on the earth's surface, unrelated to plate boundaries, where volcanic activity occurs

inclination: the angle in the vertical plane between horizontal and the direction of magnetization of a rock

Pangaea: a supercontinent consisting of all the present continental fragments; it existed approximately 200 million years ago

relative velocity: the velocity of one object measured relative to another

triple junction: a point where three plate boundaries meet

vector: a quantity that is defined by both magnitude and direction

velocity: speed and direction of motion

Bibliography

Condie, Kent C. Plate Tectonics and Crustal Evolution. 4th ed. Oxford: Butterworth Heinemann, 1997. An excellent overview of modern plate tectonics theory that synthesizes data from geology, geochemistry, geophysics, and oceanography. A very helpful tectonic map of the world is enclosed. The book is nontechnical and suitable for a college-level reader. Useful “suggestions for further reading” follow each chapter.

Cox, Allan, and R. B. Hart. Plate Tectonics: How It Works. Palo Alto, Calif.: Blackwell Scientific, 1986. A well-illustrated and detailed account of the methodology of plate tectonics. Includes information on many different aspects of plate tectonics theory and supplies explanations of the mathematical techniques utilized in solving plate tectonic problems. Suitable for those with a good mathematical background.

Dewey, J. F. “Plate Tectonics.” In Continents Adrift and Continents Aground. San Francisco: W. H. Freeman, 1976. This article appears in a book of articles reprinted from Scientific American. The first part of the article gives a succinct explanation of plate rotations and includes several excellent diagrams. While not giving a full mathematical treatment, the article does approach some complex ideas in an understandable fashion. Suitable for high school readers who have some prior knowledge of the subject.

Frisch, Wolfgang, Martin Meschede, and Ronald C. Blakey. Plate Tectonics: Continental Drift and Mountain Building. New York: Springer, 2010. This textbook provides a basic overview of continental drift and plate tectonics focusing on the resulting changes in the earth's surface.

Grotzinger, John, et al. Understanding Earth. 5th ed. New York: W. H. Freeman, 2006. This comprehensive physical geology text covers the formation and development of the earth. Readable by high school students, as well as by general readers. Includes an index and a glossary of terms.

Kearey, Philip, Keith A. Klepeis, and Frederick J. Vine. Global Tectonics. 3rd ed. Cambridge, Mass.: Wiley-Blackwell, 2009. This college text gives the reader a solid understanding of the history of global tectonics, along with current processes and activities. The book is filled with colorful illustrations and maps.

Press, Frank, and Raymond Siever. Earth. 4th ed. New York: W. H. Freeman, 1986. A general geology text. The chapter on global plate tectonics is quite thorough and contains “boxes” that explain the motions of the plates. Hot spots are explained elsewhere in the text and not related to plate motions. The diagrams, although only two-tone, are quite detailed. The text is appropriate for advanced high school readers.

Prichard, H. M. Magmatic Processes and Plate Tectonics. London: Geological Society, 1993. Although fairly technical, this special publication has relevant information about plate motions and plate tectonics. The maps and graphics help to illustrate the ideas presented.

Uyeda, Seiya. The New View of the Earth. San Francisco: W. H. Freeman, 1978. A very readable account of the development of plate tectonics up to the early 1970's. Does not go into mathematical detail concerning plate motions but does give many examples. Suitable for high school readers.

Wyllie, Peter J. The Way the Earth Works. New York: John Wiley & Sons, 1976. A good introductory geology text written from the point of view of plate tectonics. The author does not go into detail concerning the mathematics involved with determining plate motions. Well illustrated and easy to read. Information concerning plate motions is disseminated throughout the text. Suitable for high school readers.