Seismic modelling of the Earth’s large-scale three-dimensional structure

Abstract
Several different kinds of seismological data, spanning more than three orders of magnitude in frequency, have been employed in the study of the Earth’s large-scale three-dimensional structure. These yield different but overlapping information, which is leading to a coherent picture of the Earth’s internal heterogeneity. In this article we describe several methods of seismic inversion and intercom pare the resulting models. Models of upper-mantle shear velocity based upon mantle waveforms (Woodhouse & Dziewonski ( J. geophys. Res . 89 , 5953-5986 (1984))) ( f ≲ 7 mHz) and long-period body waveforms ( f ≲ 20 mHz; Woodhouse & Dziewonski ( Eos, Wash . 67 , 307 (1986))) show the mid-oceanic ridges to be the major low-velocity anomalies in the uppermost mantle, together with regions in the western Pacific, characterized by back-arc volcanism. High velocities are associated with the continents, and in particular with the continental shields, extending to depths in excess of 300 km. By assuming a given ratio between density and wave velocity variations, and a given mantle viscosity structure, such models have been successful in explaining some aspects of observed plate motion in terms of thermal convection in the mantle (Forte & Peltier ( J. geophys. Res . 92 , 3645-3679 (1987))). An im portant qualitative conclusion from such analysis is that the magnitude of the observed seismic anomalies is of the order expected in a convecting system having the viscosity, tem perature derivatives and flow rates which characterize the mantle. Models of the lower mantle based upon P-wave arrival times ( f ≈ 1 Hz; Dziewonski ( J. geophys. Res . 89 , 5929-5952 (1984)); Morelli & Dziewonski ( Eos, Wash . 67 , 311 (1986))) SH waveforms ( f ≈ mHz; Woodhouse & Dziewonski (1986)) and free oscillations (Giardini et al . ( Nature, Lond . 325 , 405-411 (1987); J. geophys. Res. 93 , 13716—13742 (1988))) ( f ≈ 0.5-5 mHz) show a very long wavelength pattern, largely contained in spherical harmonics of degree 2, which is present over a large range of depths (1000-2700 km). This anomaly has been detected in both compressional and shear wave velocities, and yields a ratio of relative perturbations in v s and v P in the lower mantle in the range 2-2.5. Such values, which are much larger than has sometimes been assumed, roughly correspond to the case that perturbations in shear modulus dominate those in bulk modulus. It is this anomaly that is mainly responsible for the observed low-degree geoid undulations (Hager et al. Nature, Lond . 313 , 541-545 (1985))). In the upper part of the lower mantle this pattern consists of a high-velocity feature skirting the subduction zones of the Pacific and extending from Indonesia to the Mediterranean, with low velocities elsewhere; thus it appears to be associated with plate convergence and subduction. The pattern of wave speeds in the lowermost mantle is such that approximately 80% of hot spots are in regions of lower than average velocities in the D" region. The topography of the core-mantle boundary, determined from the arrival times of reflected and transmitted waves (Morelli & Dziewonski ( Nature, Lond . 325 , 678-683 (1987))), exhibits a pattern of depressions encircling the Pacific, having an amplitude of approximately ± 5 km, which has been shown to be consistent with the stresses induced by density anomalies inferred from tom ographic models of the lower mantle (Forte & Peltier ( Tectonphysics (In the press.) (1989))). By using both free oscillations (Woodhouse et al . ( Geophys. Res. Lett . 13 , 1549-1552 (1986))) and travel-time data (Morelli et al . ( Geophys. Res. Lett . 13 , 1545—1548 (1986))), the inner core has been found to be anisotropic, exhibiting high velocities for waves propagating parallel to the Earth ’s rotation axis and low velocities in the equatorial plane. Tomographic models represent an instantaneous, low-resolution image of a convecting system. They require for their detailed interpretation knowledge of mineral and rock properties that are, as yet, poorly known but that laboratory experiments can potentially determ ine. The fact that the present distribution of seismic anomalies must represent the current configuration of therm al and compositional heterogeneity advected by m antle flow, imposes a complex set of constraints on the possible modes of convection in the m antle of which the implications have not yet been worked out; this will require num erical modelling of convection in three dimensions, which only recently has become feasible. Thus the interpretation of the ‘geographical’ information from seismology in terms of geodynamical processes is a matter of considerable complexity, and we may expect that a number of the conclusions to be drawn from the seismological results lie in the future.