jeffrey.park@yale.edu, 432-3172, 316 KGL
Office Hrs 4-5PM Monday
This lecture will address how the vibrational waves that are generated
by earthquakes around the world can be used to study plate tectonics and
the viscous flow of the Earth's mantle. The Earth is layered. The iron-nickel
core has a solid inner-core sphere (radius 1220 km) surrounded by a liquid
outer-core shell (3480-km radius). The core is surrounded by a solid-rock
mantle with average outer radius of 6355 km. The last layer is the Earth's
crust, also solid rock, with thickness that varies between 7 and 70 km.
Since the 1960s, geologists have recognised that the mantle will deform
and flow over "geologic" time scales in order to transport heat from the
liquid outer core to the Earth surface. The mantle is not molten, yet it
flows over millions of years like the water in a heated pot of soup. Thermal
expansion induces hotter rock to rise toward the surface and colder rock
to sink to the depths. In the outer 100km or so of the mantle, heat escapes
by thermal conduction and the outer layer, as it cools, stiffens to form
a semi-rigid "tectonic plate." You can refer to the
plate tectonics tutorial of the US Geological Survey for background
on this process.
At the boundaries of the plates, the relative motion of plates leads to earthquakes. Geoscientists use the locations of earthquakes to map the outlines of plates on a global scale. The characteristics of a particular earthquake (fault orientation, depth, slip direction) often reflect the type of relative motion at a plate boundary: are the plates converging, diverging, or just sliding past each other? Seismologists can determine the earthquake characteristics by a careful examination of the seismic waves radiated from the rupture and recorded at seismometers worldwide. Earthquakes generate both compressional (P) and shear (S) waves, and these types of waves are radiated by a fault slip in two "cloverleaf" patterns that are complementary in geometry.
To see the relationship between earthquakes and plate boundaries, refer to the homepage of the US Geological Survey's National Earthquake Information Center (NEIC). On this page, the "Near Real Time Earthquake List" offers geographical information about recent earthquakes, plotting their locations on local topographic maps. The fault orientations and slips are displayed in monthly summary maps, whose "beach ball" symbols are explained here. In any given year, he largest earthquakes are typically found along the edges of the Pacific Plate, whose edges are (mostly) sinking back into the mantle along the so-called "ring of fire" - a girdle of deep-sea trenches and above-water volcanoes that rings the Pacific Ocean. If one displays *all* recorded earthquakes in a year above, say, Richter magnitude 4, the full network of tectonic-plate boundaries becomes visible. The USGS NEIC maintains a useful FAQ on earthquakes, which describes Richter magnitudes, earthquake frequency-of-occurrence as a function of size, and has a glossary of seismological terms. The IRIS Consortium maintains a collection of "one-pager" information sheets on earthquakes (in downloadable PDF format) that are also useful.
The locations of earthquakes are not the only method for reconstructing plate tectonics. Seismic wavespeed within the earth's interior depends largely on temperature. Cold, descending material will have higher wavespeed, so that P and S waves will travel less time across it. At a seismic observatory, the P and S waves that travel through cold material will appear to arrive earlier than expected. Hot, ascending mantle rock will have lower wavespeed. P and S waves that traverse hot mantle will suffer travel-time delays. The changes in wavespeed can be several percent, and the travel-time advances and delays can be as large as several seconds. Using measured traveltime delays from thousands of seismic waves that criss-cross the Earth's mantle, seismic tomography, similar to medical imaging of brain tumors, can image localized regions of fast and slow wavespeed. The descending edges of old tectonic plates appear as fast "slabs" that sink into the mantle. Some of the hot upwelling regions can be imaged as slow wavespeed anomalies as well, but mantle upwelling is usually smaller in extent -- warmer mantle rock is less viscous, and appears to ascend in narrow "plumes," in contrast to the long stiff "slabs" that characterize the descending flow.
A second method for detecting the traces of plate motions is seismic anisotropy. Seismologists usually assume that P- and S-wavespeeds do not depend on the direction that a wave travels. This is an "isotropic" assumption -- "iso" means "same", and "isotropy" means "same" in all directions. However, many minerals offer stiffer resistance to applied forces in some directions than others, and are therefore "anisotropic." Shear in the mantle will tend to align the minerals within its rock, and lead to a directional dependence in the seismic wavespeeds. Since plate motions involve considerable shear at the bottom of plates and especially near plate boundaries, one expects mineral alignment and seismic anisotropy to be evident near them. The mineral olivine (magnesium-iron silicate) is the most abundant mineral in the upper 400 km of the mantle. In a rock of pure olivine, shear and compressional wavespeeds could vary by as much as 20% if all the olivine crystals in the rock were to align in the same direction. Laboratory measurements indicate that the fast propagation direction of olivine crystals tends to align with the direction of maximum rock extension (strains of less than 100%) and/or the direction of mantle flow (for larger strains). Therefore seismic anisotropy in the mantle could reveal the slow, gradual subterranean flow associated with plate tectonics. Upper-mantle rocks are typically 50-60% olivine, and the alignment of olivine is never perfect. The observed limit of anisotropy is 10% in natural mantle rocks, and is more typically 4% or less in typical hand-samples. This level of anisotropy, however, can lead to effects that are easy to measure in seismograms from earthquakes.
There are several ways to detect seismic anisotropy. One method tries to incorporate wavespeed directional dependence into a tomographic inversion. Another popular method uses shear-wave birefringence, or "splitting," to detect local variations in mantle strain and mantle flow. A third exploits the fact that, if a seismic wave enters or leaves a volume of rock that has significant anisotropy, it tends to generate scattered waves of a different type. P waves that convert partially to S waves are easiest to observe and quantify in earthquake data. The latter two methods for detecting seismic anisotropy in the mantle have led to some surprises. In particular, geoscientists have discovered that old continental regions, like Eastern North America and Arabia, still bear the stretch-marks of mountain-building events that occurred up to 600 million years ago.
Shear-wave splitting is similar to altering the propagation of visible light with a polarizing filter. Like electromagnetic radiation, an S wave has two independent polarizations. (Why? A solid material has two independent directions in which it can vibrate and still move perpendicular to the direction of wave motion.) If an S wave travels through an anisotropic volume of rock, the aligned minerals in the rock will induce two distinct wavespeeds for two distinct polarizations, one "fast" and one "slow." The two polarizations will accumulate a traveltime difference as they travel, and distort the motion of the wave as recorded by the seismometer. Typical fast-slow time delays are 0.5-1.5 seconds, and are observed in S waves with typical oscillation periods of 5-10 seconds. With these timing parameters, the fast and slow waves do not appear distinct. Rather, the wave motion becomes slightly elliptical in the horizontal plane.
With computer processing, it is possible to retrieve the apparent "fast" axis of anisotropy from "split" shear waves. When such measurements are made over a "small" region like the US Northeast, the gross consistency of fast-axis orientation suggests that the source of the signal is geographically broad, associated with properties that are more deeply seated than the local surface rocks. Nevertheless, if one compares splitting data from two earthquakes that approach the US Northeast at markedly different approach angles a more complex structure under the region is suggested. Notice that the fast-axis direction is consistent among stations for each event. The data can be modelled successfully with a two-layer model of mantle strain. This two-layer model has an interpretation that makes sense in a plate-tectonic sense. The lower-layer fast axis aligns with the long-term drift of the North American Plate over the deeper mantle, suggesting that the lower layer records the developing skidmark of our own plate's migration over the Earth. The upper layer of anisotropy has a fast axis that aligns perpendicular to the Appalachian mountains in the northeast US. It is hypothesized that this upper layer of anisotropy developed during the original formation of the Appalachians about 390 million years before present.
P-to-S scattering by anisotropic mantle shear zones follows this schematic. P waves from distant earthquakes approach a seismometer steeply, and convert some of their energy to S waves at each major transition in rock properties. The S waves travel upwards as well, but more slowly, and so trail the main P wave. The trailing S waves can be reconstructed by time-series processing of multiple earthquakes, such as here for a station in Ar Rayn, Saudi Arabia. The two columns of traces in the figure correspond to the two perpendicular directions of motion in the horizontal plane. The wiggle marked PMs is generated by the Moho discontinuity that markes the boundary between the Earth's crusdt and mantle. The second bump (PHs) is internal to the mantle, and is interpreted to be a shear zone that developed as the Arabian subcontinent was assembled from a rag-tag collection of volcanic islands and oceanic plateaus about 550-600 million years ago. Field geologists had previously hypothesized that a chunk of Arabia had been squeezed northward during the final collision of crustal fragments, pinched along the ancient Najd fault lines now exposed in the west-Arabian interior. The seismic anisotropy study confirms this hypothesis, because the inferred fast-axis is aligned north-south.
Other seismic anisotropy and mantle flow results:
Combined tomography and shear-wave splitting tracks the motion of the Yellowstone mantle "hotspot."
Results
from the Yale-OMSP joint seismic deployment in the Kamchatka
peninsula, Russian Far East.
