Preliminary reference Earth model
The Preliminary Reference Earth Model (PREM) is a one-dimensional, spherically symmetric representation of Earth's average internal structure, providing radial profiles of key physical properties such as compressional-wave velocity (VP), shear-wave velocity (VS), density (ρ), and attenuation quality factor (Q) as functions of depth from the surface to the center of the planet.[1] Developed in 1981 by seismologists Adam M. Dziewonski and Don L. Anderson, PREM was constructed to serve as a standardized reference for interpreting global seismic data and facilitating comparisons across geophysical studies.[1] It incorporates transverse isotropy (azimuthal anisotropy) in the uppermost 220 km of the mantle to account for observed discrepancies in Love and Rayleigh wave dispersion, while assuming isotropy in the deeper mantle, outer core, and inner core.[1] PREM's development relied on an extensive dataset, including approximately 1,000 normal-mode periods, 500 body-wave travel time summaries, 100 normal-mode Q values, as well as constraints from Earth's total mass and moment of inertia.[1] This was supplemented by over 1.75 million P and S wave travel times from 12 years of International Seismological Centre (ISC) bulletins, enabling a least-squares inversion that fits the data with high precision—typically within 2-4% for upper-mantle velocities.[1] The model divides Earth into distinct layers: an averaged crust approximately 35 km thick (with a discontinuity at 10 km depth), lithosphere (to ~220 km), low-velocity zone (80-220 km), upper mantle transition zone (410-660 km with discontinuities at 410 km and 660 km), lower mantle (to 2,891 km), liquid outer core (2,891-5,150 km), and solid inner core (to 6,371 km).[2][3] Notably, it features a nearly constant velocity gradient in the lowermost mantle (D'' layer) and a core-mantle boundary at 2,891 km depth, reconciling observations from free oscillations and surface waves.[1] Since its publication, PREM has become the most widely adopted one-dimensional Earth model in seismology, underpinning research in geodesy, geodynamics, and planetary science due to its excellent agreement with global travel-time curves (e.g., for epicentral distances of 22°-90°) and its parametric formulation using low-order polynomials for smooth radial variations.[2] It includes frequency-dependent anelastic dispersion, allowing velocities to vary slightly with period (e.g., 1 Hz reference), and has been instrumental in resolving long-standing debates, such as the radius of the inner core (approximately 1,221 km).[1] Despite refinements in later models like AK135 or IASP91, PREM remains a benchmark for forward modeling of seismic wave propagation and inversion of Earth's heterogeneity.[4]History and Development
Origins and Motivation
Prior to the development of the Preliminary Reference Earth Model (PREM), Earth models such as the Jeffreys-Bullen (JB) model from 1940 relied on limited seismic data collected between 1930 and 1939 from sparse global seismometer networks, resulting in travel-time tables that were found to be 2-4 seconds slow compared to more accurate observations.[3] These early models struggled to accommodate the growing volume of high-quality seismic data emerging in the post-World War II era, particularly after the establishment of the World Wide Standardized Seismograph Network (WWSSN) in the 1960s, which provided unprecedented coverage and enabled detailed studies of Earth's interior.[5] By the 1950s and 1960s, advances in computational seismology led to a proliferation of incompatible radial Earth models, with researchers often mixing properties from different sources, such as Bullen's density profiles or Herrin et al.'s travel-time revisions, creating inconsistencies that hindered unified geophysical interpretations.[6] The motivation for PREM arose from the need for a comprehensive, standardized one-dimensional (1D) radial Earth model to integrate diverse observations, including normal mode periods, body-wave travel times, attenuation (Q values), mass, and moment of inertia, amid the expansion of global seismic networks and computational capabilities.[6] This unification was essential for consistent applications in seismology, geodesy, and astronomy, where discrepancies in prior models complicated the analysis of Earth's elastic properties and density distribution.[6] The model addressed key limitations of isotropic assumptions by incorporating transverse isotropy in the upper mantle and anelastic dispersion, providing a benchmark to reconcile global data sets and facilitate comparisons across studies.[6] Development of PREM was initiated in the mid-1970s through international collaboration, primarily at the California Institute of Technology (Caltech) and Harvard University, driven by key figures Don L. Anderson and Adam M. Dziewonski.[3] The effort stemmed from a 1971 International Union of Geodesy and Geophysics (IUGG) symposium in Moscow on Earth tides, where a Standard Earth Model Committee was formed under K.E. Bullen to establish an internationally adopted reference.[6] Subsequent milestones included the 1973 International Association of Seismology and Physics of the Earth's Interior (IASPEI) meeting in Lima, which renamed it a "reference model" and formed sub-committees; the 1975 IUGG in Grenoble, emphasizing Q values; the 1977 IASPEI in Durham reviewing proposals; the 1978 Caracas meeting presenting an initial Anderson-Dziewonski model using International Seismological Centre (ISC) data; and the 1979 IUGG in Canberra, where an interim model was shared, culminating in the final PREM publication in 1981.[6] As a "preliminary" model, PREM was explicitly designed as an accessible benchmark for ongoing refinements, encouraging future iterations based on emerging data while standardizing calculations in geophysical research.[6][3]Data Sources and Fitting Process
The construction of the Preliminary Reference Earth Model (PREM) relied on a comprehensive empirical dataset compiled from seismological observations and geophysical constraints. Primary data included approximately 1000 normal-mode periods, which provided insights into Earth's eigenfrequencies across various degrees and orders, derived from global free-oscillation analyses following major earthquakes. Additionally, around 500 summary travel-time observations for P and S body waves were incorporated, aggregating phase picks from extensive catalogs such as those from the International Seismological Centre (ISC), encompassing roughly 1.75 × 10^6 individual P and S wave arrivals over 12 years. About 100 normal-mode Q values were used to model attenuation properties, ensuring the model captured anelastic effects in seismic wave propagation. These seismological inputs were supplemented by fundamental geophysical constraints, including Earth's total mass of 5.973 × 10^{24} kg and moment of inertia factor of 0.3307 MR^2, which anchored the density profile to observed gravitational and rotational properties. The data were primarily sourced from observations of large earthquakes in the 1960s and 1970s, such as those summarized in travel-time studies by Herrin et al. (1968) and Hales et al. (1968), which utilized events like the 1960 Chile earthquake and subsequent global shocks to build robust averages of wave propagation. These summaries focused on body-wave arrivals and surface-wave dispersions, with baseline corrections applied to account for source and receiver effects, enabling a global representation of radial structure. The fitting process employed a least-squares inversion framework that integrated forward modeling of normal-mode frequencies and body-wave travel times to derive radial profiles of density, P-wave velocity (V_P), S-wave velocity (V_S), and attenuation (Q). Iterative adjustments were made to low-order polynomial parameterizations of these properties within discrete layers, minimizing residuals between observed and predicted data through successive refinements that balanced trade-offs among velocity, density, and anisotropy. Although PREM is fundamentally a radial model, transverse isotropy was parameterized up to 220 km depth in the upper mantle. This methodology ensured a data-driven fit without overparameterization, yielding root-mean-square residuals on the order of a few percent for key observables.Model Structure
Layering and Discontinuities
The Preliminary Reference Earth Model (PREM) divides the Earth radially into seven primary layers based on seismic observations of velocity and density contrasts, extending from the center to the surface at a mean radius of 6371 km. These layers reflect major structural and compositional transitions inferred from global seismic data, with discontinuities marking sharp changes in physical properties. The model assumes radial symmetry and incorporates an averaged crustal structure rather than distinct oceanic or continental crusts, with a conventional crustal thickness of 24.4 km, representing an average adjusted to fit global seismic and gravitational data, without separate oceanic (typically ~7 km thick over two-thirds of the surface) or continental (~35 km thick) profiles.[7] The innermost layer is the solid inner core, spanning from the center (0 km) to a radius of 1221.5 km, bounded by the inner-outer core discontinuity where shear wave velocities emerge due to solidification. This boundary, at a depth of approximately 5149.5 km from the surface, signifies a transition from liquid to solid iron-nickel alloy. Adjacent to it lies the liquid outer core, extending from 1221.5 km to 3480 km radius (depth 2891 km), characterized by the absence of shear waves and dominated by fluid dynamics. The core-mantle boundary (CMB) at 3480 km radius represents a profound discontinuity, separating the metallic core from the silicate mantle, with significant jumps in density and seismic velocities observed in reflected and converted waves.[7][8] Above the CMB, the lower mantle occupies the region from 3480 km to 5701 km radius (depths 670 km to 2891 km), comprising predominantly bridgmanite and ferropericlase under high pressure. This layer transitions into the mantle transition zone at the 670 km discontinuity (radius 5701 km), a major boundary linked to the ringwoodite to bridgmanite + ferropericlase phase transformation (with possible dehydration effects), causing velocity increases for both P- and S-waves.[9] The transition zone itself spans 5701 km to 5971 km radius (depths 400 km to 670 km), featuring a prominent discontinuity at 400 km depth (radius 5971 km) associated with the olivine to wadsleyite phase transformation, which sharpens P-wave velocities more than S-waves. Further upward, from 5971 km to 6151 km radius (depths 220 km to 400 km), lies a zone of relatively smooth gradients, often considered part of the upper mantle.[7][10] The uppermost mantle includes the low-velocity zone from 6151 km to 6291 km radius (depths approximately 80 km to 220 km), where partial melting or anisotropy leads to reduced velocities, though PREM models this with continuous polynomials rather than a sharp break. The lithosphere follows from 6291 km to 6346.6 km radius (depth about 24.4 km to 80 km), representing the rigid upper layer. Finally, the crust is modeled as a thin explicit layer from 6346.6 km to 6371 km radius (0 to 24.4 km depth), averaging oceanic (about 7 km thick, covering two-thirds of the surface) and continental (about 35 km thick) contributions to yield a global mean of 24.4 km, without separate oceanic or continental profiles. This crustal representation simplifies lateral variations for a reference model, focusing on radial averages. The 220 km discontinuity at radius 6151 km (depth 220 km) marks the base of the lithosphere and top of the asthenosphere, with PREM incorporating transverse isotropy in this upper mantle region to fit surface wave data.[7][3]| Layer | Radius Range (km) | Depth Range (km) | Key Discontinuity |
|---|---|---|---|
| Inner Core | 0–1221.5 | 5149.5–6371 | Inner-outer core boundary (1221.5 km radius) |
| Outer Core | 1221.5–3480 | 2891–5149.5 | Core-mantle boundary (3480 km radius) |
| Lower Mantle | 3480–5701 | 670–2891 | 670 km discontinuity (5701 km radius) |
| Transition Zone | 5701–5971 | 400–670 | 400 km discontinuity (5971 km radius) |
| Upper Mantle (LVZ to Lithosphere) | 5971–6346.6 | 24.4–400 | 220 km discontinuity (6151 km radius) |
| Crust | 6346.6–6371 | 0–24.4 | Moho (averaged at 24.4 km depth) |
Key Physical Parameters
The Preliminary Reference Earth Model (PREM) provides radial profiles for the primary elastic properties of Earth's interior, including density \rho(r), compressional-wave velocity V_p(r), and shear-wave velocity V_s(r), which are parameterized as functions of radius r from Earth's center. These profiles are derived from inversions of seismic travel times, normal mode data, and moment tensor solutions, yielding a spherically symmetric model that captures the average structure across major layers. Derived quantities such as pressure P(r), gravitational acceleration g(r), and bulk modulus K(r) are computed by integrating the primary parameters using equations of hydrostatic equilibrium and elastic theory, ensuring consistency with observed free-oscillation frequencies.[7] Density \rho(r) exhibits a monotonic increase with depth, reflecting the compression and compositional stratification of Earth's layers, ranging from approximately 13.0 g/cm³ in the inner core to 2.9 g/cm³ in the upper crust and 1.0 g/cm³ in the oceans. In the mantle, density rises gradually from about 3.3 g/cm³ in the upper mantle to 5.6 g/cm³ at the core-mantle boundary (CMB), with a sharp discontinuity at the CMB where it jumps to 9.9 g/cm³ in the outer core; within the core, it peaks at 12.2 g/cm³ near the inner core boundary before stabilizing in the solid inner core. V_p(r) shows a similar deepening trend but with notable decreases at fluid-core boundaries, starting at 11.0 km/s in the inner core, dipping to 8.0 km/s at the top of the outer core, and reaching maxima of 13.7 km/s in the lower mantle and 7.8 km/s in the upper mantle. V_s(r) is zero throughout the liquid outer core, approximately 3.5 km/s in the inner core, and varies from 4.5 km/s in the upper mantle to 7.3 km/s in the lower mantle, highlighting the shear strength of solid regions.[7][3] PREM's derived parameters further elucidate the model's physical realism: pressure P(r) accumulates to about 136 GPa at the CMB and 364 GPa at the center, driven by overlying mass; gravity g(r) decreases from 9.8 m/s² at the surface to near zero at the center, with subtle inflections at discontinuities; and bulk modulus K(r) increases from around 100 GPa in the upper mantle to over 300 GPa in the core, indicating rising incompressibility with depth. A distinctive feature of PREM is its inclusion of attenuation profiles, with quality factors Q_\kappa (bulk) averaging 1000–3000 in the mantle and much higher (up to 10,000) in the core, while Q_\mu (shear) is lower at 80–600 in the mantle to account for anelastic dissipation, assuming implicitly adiabatic gradients through the elastic parameterization. These parameters are tabulated at 29 discrete depths, enabling interpolation for radial variations, and exhibit abrupt changes at key boundaries like the CMB, where density jumps by over 4 g/cm³ and V_s drops to zero, underscoring the model's representation of phase transitions and compositional contrasts.[7][3]| Layer | Depth Range (km) | \rho (g/cm³) | V_p (km/s) | V_s (km/s) |
|---|---|---|---|---|
| Upper Crust | 0–15 | 2.6 | 5.8 | 3.2 |
| Lower Crust | 15–24.4 | 2.9 | 6.8 | 3.9 |
| Upper Mantle | 24.4–220 | 3.4–3.5 | 7.8–8.1 | 4.5–4.7 |
| Transition Zone | 220–670 | 3.6–4.0 | 8.9–10.0 | 4.8–5.5 |
| Lower Mantle | 670–2891 | 4.4–5.6 | 10.2–13.7 | 5.8–7.3 |
| Outer Core | 2891–5153 | 9.9–12.2 | 8.0–10.4 | 0 |
| Inner Core | 5153–6371 | 12.8–13.0 | 11.0 | 3.5 |