seismic properties of rocks

seismic properties of rocks The seismic properties of rocks are usually thought of in terms of P-wave velocity, V_p, and S-wave velocity, V_s, which are both functions of density (see seismic waves, principles). A knowledge of V_p, V_s, and density can tell us a great deal about the composition and physical state of materials in the earth. The Earth is, however, much more complex than this simple approach would indicate. Laboratory studies on individual mineral crystals are capable of great detail and precision. The situation is very different for measurements based on the analysis of body and surface waves travelling through the Earth. It has, for example, commonly been the practice to assume that materials are mechanically isotropic so that only two elastic constants are required. The constants measured are usually V_p and V_s. Modern studies are often able to go beyond this simple assumption but usually stop at determining V_p, V_s, density, Q, the quality factor (assumed to be a constant), and anisotropy expressed as a percentage. As a practical matter, this amounts to measuring from three to five elastic constants out of a possible 21, and recognizing that observable differences in velocity exist which are a function of the direction of travel.

Seismologists desire to measure physical properties to the greatest level of detail possible. Their aim is to determine not only the composition of the Earth but also its physical state. The question of composition is complex because rocks are combinations of minerals which each have their own seismic properties. In general, the velocities of the crystalline rocks which constitute most of the Earth's lithosphere are inversely proportional to the silicon dioxide content and directly proportional to the content of iron and magnesium oxides.

Many factors, such as porosity, pressure, and temperature, affect the seismic velocity of a particular rock. Figure 1, which is a compilation of typical values, illustrates some relationships which are generally true. Unconsolidated sediments can have very low velocities. Clastic sedimentary rocks (sandstone and shale) are ‘slower’ than carbonate sedimentary rocks (limestone and dolomite). For typical crystalline rocks, granite (felsic) is slower than gabbro (mafic), which is slower than peridotite (ultramafic). These relationships are generally reflected in the velocity structure of the Earth's lithosphere, in which the granitic upper crust generally has higher velocities than the sedimentary rocks which cover it but has lower velocities than the more mafic lower crust. The ultramafic mantle, which is very rich in iron, has even higher velocities.

Such factors as the degree of alignment of particular minerals govern properties such as the level of anisotropy. For example, an early large-scale observation of anisotropy was provided by P-wave velocities measured in the mantle near ocean spreading centres. Here, alignment of the highly anisotropic mineral olivine is sufficient to cause velocities measured from refraction profiles that are recorded in the direction of spreading to be higher than those for profiles recorded parallel to the spreading centre. This alignment is particularly interesting because it is related to the flow which reflects plate movements. As a result there is much interest in measuring anisotropy elsewhere in the mantle. Some metamorphic rocks and shales have mineral alignments which are clear in hand specimens and which are reflected in significant anisotropy, but when viewed on a larger scale most crustal rocks do not appear to be very anisotropic. However, detailed velocity measurements, such as those made by logging devices which are lowered down boreholes, often reveal significant anisotropy in individual rock units, which is sometimes a result of the alignment of fractures.

Other properties of rocks can dominate composition, especially in the sedimentary rocks found near the Earth's surface. Porosity (percentage of pore space) is particularly important. Burial at depth, giving rise to high overburden pressures, causes sedimentary rocks in particular to compact. In the process, their porosity decreases and their seismic velocity increases correspondingly. For example, pressure due to burial, accompanied by cementation, causes sand and mud to evolve into sedimentary rocks (sandstone and shale respectively), and their velocity usually increases as this evolution proceeds. Increasing age also causes the velocity of sedimentary rocks to increase because many processes that take place in the Earth tend to decrease the porosity. Crystalline rocks also exhibit an increase in velocity with increasing pressure, as micro-cracks in the rock close, reducing their porosity. In the mantle, phase transformations of olivine result in more compact crystal structures which are believed to cause the seismic discontinuities that are consistently observed at several depths on a global basis. Temperature is another factor that affects the seismic properties of rocks. If other factors are held constant, an increase in temperature generally causes a decrease in seismic velocity. Since temperature increases with depth in the Earth, we might expect seismic velocity to decrease with depth. Except in small regions, this is not, however, the case because in general the temperature effect is offset by the effects of pressure and composition.

In many cases instances it is important to know V_p, V_s, and density (r) in order to study some phenomenon; for example, the variation in the amplitude of a wave reflected from a discontinuity in the Earth with the angle at which the wave is approaching. We may, however, be able to measure only V_p. Since we have good values for Poisson's ratio (s) for typical rock types, we can calculate V_s from a standard equation.

This relationship becomes very useful when we have independent information on density from gravity measurements or logging devices which measure the density of rocks penetrated by a borehole. In addition to Poisson's ratio, there is a good correlation between V_p and density. This relationship is based mostly on measuring the density and V_p for many different rock types. It has been presented in several forms.

These relationships are useful, but only approximate. One should not lose sight of the fact that many types of rocks share the same P-wave velocity, V_p (Fig. 1). More independent measurements of other seismic properties are thus highly desirable so that the type of rock and its physical state can be better determined.

The attenuation of seismic waves as they travel through the Earth is a complex subject which is the target of much research. In general, we find that the amplitude of a seismic wave dies off in proportion to the factor e^−ax, where x is the distance travelled and a is the attenuation coefficient. The attenuation coefficient is a function of frequency, and it becomes larger as the frequency increases. This preferential attenuation of higher frequencies is a fundamental limitation in seismology that restricts our ability to resolve (i.e. see) deep structures because we need the short wavelengths associated with high frequencies (see seismic waves, principles). It would be a major task to tabulate a for many materials as a function of frequency, so it is fortunate that a is an approximately linear function of frequency for typical seismic waves. This relationship leads to the quality factor, Q, being a constant. The quality factor is thus a convenient measure of the degree to which a material absorbs seismic energy; high values of Q mean that attenuation is low. An early large-scale observation was that the cold down-going slabs in subduction zones had high Q values while the hot volcanic arcs above the subduction zones had low Q values.

G. R. Keller

Bibliography

Telford, W. M.,, Geldart, L. P.,, and and Sheriff, R. E. (1990) Applied geophysics. Cambridge University Press.