Chapter 2
The geophysical observables

The basic constraints on the first order geodynamic processes that have shaped the modern Earth are provided by the observed long-wavelength variations in topography, the geoid (which contains information about the distribution of potential energy), heat flow, seismicity and the in-situ stress field. The main features of each of these geophysical observables at the global scale is summarised below.

2.1  Topography

At the global-scale the distribution of topography is strongly bimodal (Fig. 2.1) with continental topography having a mean elevation of several hundred m and ocean bathymetry having a mean depth of about -4 km.

Figure 2.1: Histograms of topographhy (and bathymetry) at the plate and global scales.

Morphology of the ocean floor

The floors of the ocean basins have a relatively simply morphology (at least when considered at long wavelengths, being dominated by narrow ridges (the mid-ocean ridges), abyssal plains and trenches. The mid-ocean ridges represent submerged volcanic mountain ranges, with an average depth beneath sea level of 2-3 km. Broad swells in the elevation of the ridges occur along their length and locally the ridges are exposed, as is the case in Iceland. The depth of the ocean floor increases systematically away from the ridges, corresponding to time dependent changes in the density structure of the upper mantle beneath the ageing oceanic lithosphere, as reflected for example in the geoid (see Section 7.1). The depth beneath the ridges above 40 Ma oceanic crust is about 2 km, while for 80 Ma old oceanic crust it is about 3 km. The average depth of the ocean waters is therefore clearly related to the age of the oceanic lithosphere, which in turn is related to the rate of generation (spreading rate) of new oceanic lithosphere at ridges (see Section 5.2). In trenches, which mark the sight of subduction of old oceanic lithosphere water depths may reach 10 km.

This regular pattern of oceanic bathymetry is disturbed by:

Continental topography

The continents have a mean elvation of several hundered meters above sea-level with a range from about 300 meters below sea-level (at the break in the continental shelf) up to about 8 km at Mt. Everest. At the 100 km - scale,the highest average elevation is only 5 km.

Continental landscapes provide one of the most dramatic of natural fractal surfaces. The characteristic feature of the fractal is the statitiscal scale-invariance, that is the general character of the surface looks the same independent of the scale of observation. For landscapes this is strictly true only over a limited range of scales (10-1m - 105 m). The invariance of landscapes on this range of scales suggests that the processes operating to sculpt the landscape (i.e., erosion, mass wastage and deposition) are either scale-invariant themselves or that when acting together produce the scale-invariant effect. Erosion acts to roughen landscape at a wide range of scales while both mass wastage and deposition act to smooth the landscape, at the short and long-wavelength, respectively.

2.2  The geoid

Because of the inviscid nature of water (when viewed at geological time-scales) the mean sea-level represents gravitational equipotential surface in the earths gravitational field and therefore its elevation can be related to the density distribution at depth (as well as the the orbital dynamics of the Earth which cause an ellipticity in mass distribution and hence in the equipotential surfaces). The observed geoid height, as determined from the mean sea-level elevation, is expressed in terms of an anomaly relative to some fixed elevation (i.e., the predicted geoid for an idealised sphercially symmetric, rotating mass distribution).

Variations in the gravitational potential energy of the lithosphere, DUl, correlate with the dipole moment of the near-surface density distribution and therefore they can be directly related to the lithospheric component of the observed geoid anomalies, DNl :

DUl = g2
2  p G

where g is the gravitational acceleration, and G is the gravitational constant (note that the potential energy varies with the geoid anomaly as approximately 0.23 x 1012 N m-1 per meter). The main problem with using this relationship is resolving the lithospheric contribution of the geoid anomalies from the much larger amplitude anomalies associated with the dynamic processes of plate tectonics and mantle convection.

Positive geoid anomalies of up to 10 - 15 m associated with a number of mid-ocean ridge segments, as well as age-correlated geoid offsets across fracture zones imply that ageing of the ocean lithosphere is accompanied by a decline in potential energy. The geoid anomaly predicted for the cooling half-space model (as well as the thermal plate model) for young ocean lithosphere is about d  (DNo )/d  t = - 0.15 m/Ma, which compares favourably with the observed geoid anomaly over the Mid-Atlantic Ridge at 44.5oN, and elsewhere, as well as with the geoid offsets across fracture zones. The total geoid anomaly of -12.7 m over 84 Ma corresponds decline in Ul of 2.9 x 1012 N m-1.

In comparison with the mid-ocean ridges, the geoid anomalies associated with continental margins and the interior of continents are far less clear. On the basis of averages taken over large areas there appears to be no systematic difference in the geoid height between old ocean basins (older than Cretaceous) and continental masses. Such an interpretation implies that the mean potential energy of the continental lithosphere is equivalent to old ocean basins. However, the data show very substantial differences between continents, with the mean geoid of the African continent some 40 m higher than the North American continent and 10 m higher than the mean for the Atlantic and Pacific ocean basins older than Cretaceous. This observed intercontinental variation far exceeds the plausible lithospheric contributions to geoid anomalies and therefore must reflect long-wavelength sub-lithospheric contributions. Moreover, a number of continental margins are characterized by distinct positive anomalies of the order 6 m across the transition from the ocean basin to sea-level continent and imply that a continental lithospheric column supporting sea level elevation has the potential energy equivalent to ocean lithosphere of age about 44 Ma.

Since the lithospheric contribution to the geoid anomaly reflects the dipole moment of the near-surface density distribution, the observed geoid anomalies across continental margins can also be used to constrain the continental lithospheric density structure. A lithospheric thickness of 125 km and a crustal density of 2750 kg /m3 is consistent with a continental marginal geoid anomaly of + 6 m. Moreover, such a density structure is consistent with the interpretation that an isostatically compensated continental lithospheric column supporting about 1 km of surface elevation above sea level is in potential energy balance with the mid-ocean ridges. While the generally poor resolution of the geoid in mountainous regions precludes definitive correlation between topography and potential energy within the continents, some evidence of the correlation is provided by the lithospheric contribution to the geoid anomaly of 24 - 27 m for the Andean Altiplano. Such inferences are consistent with a geoid that varies with continental topography as 6 - 7 m/km, corresponding to a potential energy variation of about 1.3 x 1012 N m-1. For a continent with an average elevation of 500 m, this correlation suggests a mean continental potential energy of 0.997 x UMOR

2.3  Heat flow

Since the lithosphere represents a conductive lid to mantle convection the variation in heat flow measured at the surface provides insight into the vertical structure of the lithosphere.

In the ocean lithosphere, the highest heat flow regions are associated with mid-ocean ridges, where absolute values are very variable (50-300 mW m-2) due to intense, but localised, hydrothermal activity. In older, deeper lithosphere the heat flow measurements become less variable and gradually decline. The decline in heat flow approximates the same dependence on t0.5 as bathymetry. This age-bathymetry-heatflow law for ocean lithosphere which provides one of the most profound insights into the structure of the lithosphere (see Chapter 7).

2.4  Active seismicity

The distribution of seismicity in the lithosphere provides a direct ßnapshot" of the active deformation.

2.5  The in-situ stress field

The orientation of the stress field in the lithsophere provides an imprtant constraint on mechanisms driving plate motion (see Chapter 10).