Math 2.0

Geophysics Seismology: waves and rays Object

Preliminary reference Earth model

Builds on Normal modes of the EarthTravel-time curveDispersion of surface wavesSeismic anisotropyP-waveS-wave

Description

The Preliminary reference Earth model (PREM) is a one-dimensional model of the Earth, published by Dziewonski and Anderson in 1981. It gives the density ρ\rho, the P-wave and S-wave speeds, and the seismic attenuation as functions of the radius rr only. The Earth is cut into shells by discontinuities, such as the core–mantle boundary at r=3480r = 3480 km and the inner core boundary at r=1221.5r = 1221.5 km. In each shell, each quantity is a polynomial of degree at most 33 in the normalised radius x=r/ax = r/a, with a=6371a = 6371 km. In the upper mantle the model is transversely isotropic, an instance of seismic anisotropy.

Remarks

The model was fitted at once to several kinds of data. These are the frequencies of the normal modes of the Earth and the travel-time curves of body waves. They also include the dispersion of surface waves and the mass and moment of inertia of the Earth. Check of one formula: in the inner core PREM takes ρ(x)=13.0885−8.8381 x2\rho(x) = 13.0885 - 8.8381\, x^2 in g/cm³. At the centre this gives 13.0913.09 g/cm³. At the inner core boundary, x=1221.5/6371≈0.1917x = 1221.5/6371 \approx 0.1917, so x2≈0.0368x^2 \approx 0.0368 and ρ≈13.0885−0.325≈12.76\rho \approx 13.0885 - 0.325 \approx 12.76 g/cm³. Just above the boundary, in the liquid outer core, the density is lower, about 12.1712.17 g/cm³.

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Dispersion of surface waves, concept, no evidence levelDispersion of surface…conceptNormal modes of the Earth, concept, no evidence levelNormal modes of the E…conceptP-wave, concept, no evidence levelP-waveconceptS-wave, concept, no evidence levelS-waveconceptSeismic anisotropy, concept, no evidence levelSeismic anisotropyconceptTravel-time curve, concept, no evidence levelTravel-time curveconceptPreliminary reference Earth model, object, no evidence levelPreliminary reference…object
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  • no evidence level
  1. Dispersion of surface waves concept
  2. Normal modes of the Earth concept
  3. P-wave concept
  4. S-wave concept
  5. Seismic anisotropy concept
  6. Travel-time curve concept
  7. Preliminary reference Earth model object

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Further reading

  1. Web https://en.wikipedia.org/wiki/Preliminary_reference_Earth_model
About this page
Tag20FVNS391E
URIm2://20FVNS391E
Kindobject
WritingW0 stub
MSC86A15, 86A22
UsesNormal modes of the Earth, Travel-time curve, Dispersion of surface waves, Seismic anisotropy, P-wave, S-wave
Same as
Changed3 November 2026

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