CHAPTER 2. Seismology (continued)

CHAPTER 2 Seismology (continued) 2.1 A tour through the Earth. The gross structure of the Earth and its division into core, mantle and crust were determined by seismologists early in this century. More recently, attention has focused on the finer structure of the Earth and the evidence for lateral variations in properties. Generally, the largest variations in structure are found near the major discontinuities such as the surface and the core-mantle boundary (CMB), with comparatively smooth changes outside of these regions. We now take a closer look at Earth structure, starting at the center. Inner Core The radius of the inner core is defined by a small but sharp increase in P -wave velocity at a radius of about 1220 ± 10 km. This velocity increase is constrained by travel time data to be about 0.7 ± 0.15 km/s and is required to explain the triplications in the direct body waves which travel through the core (P KP waves) and the observations of reflected arrivals from the inner-core boundary (P KiKP waves). The various branches of the P KP travel times are illustrated in fig 2.44 and the ray paths are shown in fig 2.45. There is an alternate naming convention for P KP waves but note that P KP (DF ) is equivalent to P KIKP and P KP (CD) is equivalent to P KiKP and that the symbol P is sometimes used for P KP. Fig. 2.44 42

Fig. 2.45 Arrival times and waveforms of P KiKP at high frequencies provide the most direct constraints on the properties of the inner-core boundary (ICB). These data show that departures from the expected elliptical shape of the ICB are confined to a few kilometers and that the ICB transition must be complete in less than about 5 km. Waveform modeling experiments sampling different parts of the ICB have found velocity jumps varying from about 0.5 km/s to 0.8 km/s which may well reflect lateral variations in structure near the top of the inner core. Normal mode observations indicate a density jump at the ICB of about 0.75 g/cm 3, a result which is also consistent with P KiKP amplitudes. The average P -wave velocity in the inner core is about 11.2 km/s as determined by P KP travel times and normal modes. Constraints on the S-wave velocity in the inner core are weaker. Claims of observations of a body wave with an S leg through the inner core (P KJKP ) are now generally discarded but normal mode observations quite tightly constrain the average inner core shear velocity to be about 3.5 km/s. This gives a high Poisson ratio for the inner core of about 0.45 which has led some people to infer that this region may be close to its melting temperature. On the other hand, the high Poisson ratio may be simply a natural consequence of the fact that the ambient pressure is a significant fraction of the elastic moduli. There is now hard evidence that the inner core is also strongly anisotropic. Studies of P KIKP with paths nearly parallel to the rotation axis show that the waves travel anomalously quickly in this direction relative to more equatorial paths and are characterized by low-amplitude, complicated waveforms. Figure 2.46 shows some sample P KP waveforms in the distance range where the BC and DF branch arrive. Fig. 2.47 shows that these two arrivals have very similar paths in the mantle but the BC ray turns above the inner core while the DF ray turns within the inner core. 43

Fig. 2.46 Fig. 2.47 44

The differential travel time (BC DF ) is a particularly useful datum for probing the top of the inner core. Figure 2.46 shows that rays which sample the inner core in the equatorial plane of the Earth (ie sources and receivers near the equator) travel with "normal" travel times but rays which travel parallel to the rotation axis (e.g. South Sandwich Islands to a station at College, Alaska) have a DF phase which is anomalously fast (early). A simple model which fits most of these (and other) data has an anisotropic inner core which essentially behaves as a single crystal with a symmetry axis closely aligned with the rotation axis velocities are fast in this direction and slow for rays travelling perpendicular to this axis. The physical cause of the anisotropy is not currently understood, though alignment of iron crystals by convective flow is a possibility. In the past few years, several researchers have noticed that the (DF BC) differential travel times appear to change slowly with time at some stations (Figure 2.48). Fig. 2.48 This has been interpreted as a rotation of the inner core relative to the mantle (the inner core rotating faster than the mantle at a relative rate of as much as 1 degree per year). The fact that the fast axis of the anisotropy in the inner core is slightly tilted relative to the rotation axis makes the relative rotation of the inner core visible in the seismic travel times. It turns out that complexity in anisotropic structure in the inner core means that the relative rotation rate of the inner core is probably overestimated and is likely closer to 0.1 degree per year. This latter rate is more compatible with ideas that the inner core is locked to the mantle through gravitational forces arising from 3D structure in the mantle. Outer Core The outer core is assumed to be fluid since rapid convection is required to drive the geodynamo and no evidence has ever been found for outer-core shear waves. (It is possible that a very slow S-wave velocity (< 100 m/s) could escape seismic detection.) The P -wave velocity and density appear to increase smoothly with depth in the outer core, consistent with a well-mixed, vigorously convecting layer. However, there is some evidence for anomalous velocity gradients and/or weak heterogeneity in the uppermost 200 km and low velocity gradients close to the ICB. The region near the top of the core is particularly hard to study since few body waves turn here. The best data are mantle shear waves which convert to P -waves at the 45

core-mantle boundary (e.g. SKS and SKKS). Using such data, Lay and Young [1988] find evidence for anomalously low velocities (by 1 2%) in a thin layer 50 100 km thick beneath the core-mantle boundary (CMB) under Alaska. Some studies have inferred weak lateral variation of structure in the outer core but SmKS data can also be affected by rapid lateral variations of structure at the base of the mantle, a region we know to be strongly heterogeneous. It seems preferable to assume the outer core is laterally homogeneous until more compelling observational evidence becomes available. The core-mantle boundary (CMB) is constrained by both body waves and normal modes to have a radius of 3483 ± 5 km. Attempts to resolve topography on the CMB from travel times of the reflected phase P cp have led to inconclusive results, primarily due to the difficulty in removing the effect of heterogeneity in the mantle on the travel times. The P cp times suggest it is unlikely that the CMB deviates by more than about 10 km from its hydrostatic shape. Short-period P cp waveforms appear undistorted, consistent with a sharp, smooth interface at the CMB. D region D is the name given to a region of reduced velocity gradients about 100 to 300 km thick immediately above the CMB. It is also known that the D region is characterized by strong lateral heterogeneity covering a broad spectrum of wavelengths. Fig. 2.49 The existence of large-scale S velocity anomalies with variations of up to 3% near the base of the mantle now seems to be well-established. They have been found in studies of ScS S and diffracted S. Such variations are also capable of explaining anomalous SmKS differential times in some areas. Observations of additional phases arriving slightly before ScS suggest the presence of a triplication caused by a velocity discontinuity about 280 km above the CMB (Figure 2.49). 46

Fig. 2.50 The data can be modeled with either a first-order discontinuity with a velocity contrast of about 3% or as a zone of high velocity gradient up to 100 km wide (Figure 2.50). This discontinuity seems to vary in depth and is probably not a global feature since it is not seen in some areas. A sharp gradient in shear velocity is unlikely to be explained by temperature effects so it is probable that a compositional stratification or a new phase transformation will have to be invoked to explain the data. A similar triplication has occasionally been observed in P wave data with the size of the inferred P -wave jump also being about 2 3%. Again, this P wave discontinuity is unlikely to be a global feature since reflections from it are rarely observed even under favorable recording conditions. Lateral variations of about 3% in P at the base of the mantle have also been inferred in studies of short period amplitude profiles and in studies of diffracted P Fig. 2.51 47

Recently, evidence for an extremely low-velocity layer or transition region right at the CMB has been found in certain places. The best data use an interesting phase called SP dks which has a short difracted P leg along the CMB (Figure 2.51). These data indicate a thin (10 40km) thick layer with very reduced velocities (10 40%) though they can also be modelled by a smooth transition between mantle and core (Figure 2.52). It is possible that these regions represent areas of partial melt which allows chemical interaction of the mantle with the core. Fig. 2.52 Lower mantle The lower mantle is usually taken to be all the mantle from the top of D to the 660-km discontinuity. Up to a depth of about 750 km, the lower mantle appear to be relatively homogeneous with no significant discontinuities in structure of global extent. Tomography results indicate shear-velocity variations of 1% or less though recently it has become clear that there are anomalies associated with descending slabs that sometimes penetrate throughout the whole mantle. Above 750 km, we enter the region where upper mantle minerals are still undergoing phase changes to their high pressure forms and there may be an anomalously steep velocity gradient just below the 660-km discontinuity. Transition zone This is usually taken to be the region between the two major seismic discontinuities in the upper mantle the 410- and 660-km discontinuities. Most Earth models have first-order discontinuities at these depths with 4 7% jumps in velocity and density. Both discontinuities are now generally explained as resulting from phase changes in olivine, but controversy remains regarding whether small compositional changes might also occur. Most seismological observations of the discontinuities cannot distinguish between abrupt discontinuities and gradual transitions over a depth interval up to about 20 km. An exception are shortperiod precursors to the phase P KP P KP (generally termed P P which result from underside reflections off mantle discontinuities at near-vertical incidence fig. 2.53, 2.54). These observations suggest that, at least in some regions, a significant part of the velocity and density jumps at 410 and 660 km must occur within a depth interval of less than 5 km. 48

Fig. 2.53 Fig. 2.54 An seismogram made by averaging all traces recorded by the dense networks in the western US Depths to the major discontinuities have varied between different studies and it now appears that at least some of this variation is due to topography on the discontinuities. Recent observations of long-period S-wave reflections (fig 2.55,fig 2.56) from the underside of the discontinuities which arrive as precursors to SS suggest depth variations of up to 30 km (Figure 2.57). These studies also indicate a minor discontinuity near 520 km depth and show no evidence of a global discontinuity at 220 km. Uppermost mantle This is the highly heterogeneous region between the crust and the 410-km discontinuity. In most models, the shear velocity (and sometimes the compressional velocity) decreases at a depth of 50 80 km beneath the oceans and at depth of greater than 150 km under the shields. The evidence for this low velocity zone (LVZ) comes from surface waves and body waves, the region above the LVZ is sometimes called the lid. Isotropic models of the Earth require deep LVZs with velocity drops of 5 10% in shear velocity. Such models presumably imply that substantial partial melting is present, a result consistent with observations of high attenuation in surface waves that sample this region. 49

Fig. 2.55 Fig. 2.56 (The introduction of transverse isotropy can substantially reduce the magnitude of the inferred velocity drop of the LVZ at the cost of adding additional free parameters to the inversion). A 220-km discontinuity, marking the bottom of the LVZ, has occasionally been observed (e.g. under Australia) and is a conspicuous feature of PREM (see Figure 2.43). However, in most areas such an interface is not seen, and recent stacks of long-period seismograms confirm that a 220-km discontinuity cannot be a global feature unless it is extremely variable in depth. At the top of the lid is a sharp change in composition and seismic velocity (the Mohorovicic discontinuity or Moho ) which separates the mantle from the overlying crust. The oceanic 50

crust is about 7 km thick, while continental crust varies from 20 to 70 km in thickness. Fig. 2.57 A suite of upper mantle velocity models for different regions are shown in fig 2.58. Such models are often found by careful modelling of triplications seen in seismograms at regional distances (fig. 2.59). Overplotting some of the models in fig. 2.60 shows that most of the lateral variations in velocity occur above 400 km depth though the difference between shield structures and tectonically active areas (such as the western US) can be quite large (>10%). 51

Fig. 2.58 2.2 Global seismic models. At the beginning of the 80 s, almost all research in seismology was concerned with the properties of the spherically-averaged Earth. Two factors led to a sudden explosion of interest in full three-dimensional models. One was the easy availability of the computing power required to analyze large seismic datasets and the second was the ever-expanding database of high quality digital seismic recordings. Travel times of seismic body waves have played a prominent role in this research. Instead of thinking of the travel time of a body wave as an integral over depth (in the form we derived earlier in this chapter equation 2.6), we think of the travel time as an integrated effect of the velocity structure along the raypath. If we have enough intersecting raypaths, we can use the measured travel times of rays to reconstruct the three-dimensional velocity structure within the Earth. This technique is called seismic tomography by analogy with medical tomography where CAT scans are used to reconstruct cross-sections of the head. 52

Fig. 2.59 Fig. 2.60 53

Seismic tomography isn t the only technique that is used. It is possible to (approximately) calculate the effect on a seismic waveform of a small perturbation in Earth structure at some point inside the Earth so it is possible to directly model whole waveforms rather than travel times. We can also use surface-wave dispersion and free oscillation frequencies to help constrain structure. These techniques are beginning to reveal the nature of the large-scale aspherical structure of the Earth. As with the discussion of inner core structure, "differential" travel times can play a useful role as they are often less sensitive to uncertainties in earthquake location and are typically insensitive to structure under the source and receiver (where the two ray paths are very similar). Consider Fig 2.61 which shows the ray geometry for the differential times SS S and ScS S. Fig. 2.61 Considering this diagram, it makes sense to plot the travel time "residuals" (i.e., the measured differential time minus the differential time computed for a spherically symmetric standard Earth model) at the bouncepoint of SS for SS S and of ScS for ScS S since neither differential time is sensitive to near-source or near-receiver structure and we know that there is large-amplitude structure near both boundaries of the mantle. The result is shown in fig. 2.62 where we also show P P P (the P equivalent of SS S) for good measure. The top two panels of this figure (P P P and SS S) show very similar patterns which are clearly related to near-surface tectonics. Residuals corresponding to bouncepoints under young ocean regions and back-arc regions are very slow (hot), while those under cratons are fast. The SS S residuals are roughly three times the P P P residuals (note the difference in scales) which is what you would expect for normal sub-solidus thermal effects. The bottom panel (ScS S) shows a quite differnt pattern with very slow (hot?) regions under the central Pacific (but on the core-mantle boundary) and under Africa, with a ring of negative (fast=cold?) residuals in a ring around the Pacific. We suspect this has something to do with subduction. It turns out that we can also plot S and P times in a similar way if we make the assumption that such data are mainly sensitive to structure in the vicinity of the turning point of the ray (in equation 2.6, we noted a square-root singularity at the turning point of the ray which implies great sensitivity to structure there). The results are shown in fig 2.63 where the data have been binned for various turning depth ranges in the mantle. 54

Fig. 2.62 The important parts of the figure are at the bottom where rays are bottoming in the lowermost mantle. The patterns are similar but it turns out that the "red" parts of the bottom two figures (under the central Pacific and Africa) show that the S residuals are much larger than the corresponding P residuals. This is characteristic of an effect like partial melting and cannot be achieved by normal sub-solidus thermal effects. 55

You should also note the similarity between the deep-turning S residuals of fig. 2.63 and the ScS S residuals in the bottom part of fig 2.62. Clearly, any model of S velocity in the lowermost mantle wil have a slow region below the mid-pacific and Africa surrounded by fast velocities. One such model is shown in fig. 2.64. Such models are dominated by long-wavelength, large-amplitude structure near the surface and near the base of the mantle. This pattern is characteristic of whole-mantle convection with no significant barriers to convection in the mid mantle. Near-surface structure obviously has something to do with tectonics (shields are associated with fast velocities in the mantle while ocean ridges tend to be associated with low velocities). The amplitude of three-dimensional structure is quite high throughout the upper mantle (5 7% anomalies in shear velocity are common) but is smaller in the lower mantle. All models show an increase in the amplitude of anomalies in the lowermost mantle with perturbations reaching a level of 2 3%. The pattern of three dimensional structure near the base of the mantle is particularly well-defined by the seismic datasets. Clearly, there are continental-scale structures near the base of the mantle and some authors are led to speculate about continents on the core-mantle boundary. Fig. 2.63 Continents at the surface are caused by the continual separation of light material from the mantle (mainly through island arc volcanism). The buoyancy of this material makes it difficult for it to be reassimilated into the mantle and it eventually accumulates into the large continental structures we see today. It is also possible that heavy material can sink out of the mantle and accumulate at the core mantle boundary (if it is not heavy enough to enter the core). Another possibility is that we are seeing a graveyard of subducted slabs which 56

have thickened and folded as they have reached the base of the mantle (the coincidence of the regions of fast velocity at the CMB with areas of historical subduction is highly suggestive). This presupposes that slabs are capable of penetrating into the lower mantle (something that many geochemists are nervous about) but the seismological evidence is now very strong that penetration occurs (fig 2.65 shows a perspective view of the model shown in fig. 2.64 and it is clear that there are fast velocity regions extending from zones of current subduction into the lower mantle.) Fig 2.64 Cross sections of the Earth at various depths showing perturbations of shear velocity in percent. 57

Fig 2.65 Isovelocity surfaces for values of -1.0% (light) and +0.6% (dark reveal the general nature of structure in the mantle: large-scale low velocity regions surrounded by fast slab-like regions which extend across the whole mantle A barrier to convection somewhere in the mantle would drastically change the thermal history of the Earth. If convection is unimpeded, the Earth is able to get rid of its heat easily and will rapidly evolve. The latest detailed tomographic images of subduction zones show that some slabs seem to accumulate on the 660 km discontinuity. The current best model is one where slab penetration is impeded (perhaps due to a large viscosity increase across the 660 km discontinuity) but significant mixing occurs. It is also possible that large-scale mixing of the upper and lower mantles is intermittent in time. Seismology shows a snapshot of the mantle as it is now and perhaps it is merely a matter of luck that most slabs seem to be penetrating the lower mantle seismology 20 Myr into the future could show a significantly layered planet (I hope it is obvious that your author is skeptical). The geochemical arguments for "layered" convection and modern efforts to reconcile the geochemical and geophysical data are discussed in the Kellogg et al. paper. The upshot is that few people believe that the 660km discontiuity is the location of layering but a deeper (more contorted) interface may exit at about 1600km. Again, your author is not convinced. The need for a primitive geochemical reservoir can be accomodated by having many non-simply-connected bodies in the lower or even the upper mantle which are cooled by a general mantle circulation but don t necessarily get carried along with it. One final point: by comparing the relative velocity variations in P and S, we can get some idea of the physical cause of the velocity anomalies that we image. From laboratory measurements, we have a good idea of what the relative perturbation in shear and compressional velocity should be for simple sub-solidus thermal effects. We find that shear velocity perturbations (measured in percent) should be roughly 1.6 2.0 times the compressional velocity perturbations. This is what we observe throughout the mantle except for the bottom three to five hundred kilometers of the mantle in the strong low-velocity regions benath the Pacific and Africa. Here, shear velocity perturbations are four times or more the compressional velocity perturbations. This could perhaps be achieved by partial melting though why this should happen in these locations and not others is unclear. In fact, one might expect locations of historic subduction (typically around the Pacific) to have increased levels of volatiles and, so, reduced melting temperatures but the middle of the Pacific is about as far as one can get from a region of historic subduction. An alternative, speculative, idea is that interaction of the mantle and core under an upwelling can 58

lead to chemical changes which are swept up into the mantle. This is somewhat supported by the identification of ULVSs at the CMB under the Pacific. On the other hand, there appears to be no geochemical signal associated with such mixing. The studies we have just discussed use earthquakes as the source of seismic energy and a global distribution of seismic observatories as receivers. You are probably aware that seismic techniques can be used on a much smaller scale, with man-made sources and dense arrays of portable receivers, to investigate the local structure of the crust (e.g. in the search for structures that will trap oil). Since we are concerned with global geophysics in this class, we do not treat this subject in any detail. Marine seismic techniques have recently been used with great effect to ellucidate the structure of mid-ocean ridges. Marine seismology typically uses either explosive sources or arrays of air guns which inject air at high pressure into the sea generating a bubble pulse which is then transmitted through the water and into the oceanic crust. These pulses are received on streamers of hydrophones which are towed behind ships or on specially built ocean bottom seismometers (OBS) which sit on the ocean floor. Careful modelling of such data collected around the East Pacific Rise shows that a magma chamber does exist under the midocean ridge and is remarkably continuous along the ridge axis. On the other hand, the chamber is very narrow and much smaller than previously thought. Such observations are making us rethink the mechanisms for generation of oceanic crust. 59