Wave travel, refraction and transmission constrain an interior model.
Key knowledge
Seismic travel times, refraction and shadow regions constrain Earth's layered interior. The transmission of both P and S waves through the mantle supports solid behaviour on seismic timescales; the absence of transmitted S waves through the outer core supports its liquid character.
Conditions and scope
Wave speed depends on elastic properties and density; travel times do not uniquely identify chemical composition.
Solid seismic behaviour does not exclude slow mantle deformation on geological timescales.
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References
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Seismic travel times, refraction and shadow regions constrain Earth's layered interior. The transmission of both P and S waves through the mantle supports solid behaviour on seismic timescales; the absence of transmitted S waves through the outer core supports its liquid character.
Seismic waves constrain interior layers relevant to the lithosphere and slowly deforming mantle.
Geodynamo models describe generation and maintenance of Earth's intrinsic magnetic field by motion of electrically conducting fluid in the outer core. Numerical models and surface or satellite observations constrain the evolving field and core dynamics.
The dynamo model concerns the fluid outer core; field and seismic constraints are distinct observations.
Accretion, impacts, gravitational redistribution and radioactive decay contributed to early-Earth heating. Separation of dense metallic material from silicate-rich material produced a differentiated interior. Geological evidence constrains this history indirectly; a schematic fully molten stage is not a measured instantaneous state of the whole planet.
Modern interior observations constrain the differentiated result.
Terrestrial planets are dominated by rock and metal; giant planets contain larger proportions of light gases and volatile-rich material. Compression changes material state at depth, including electrically conducting hydrogen under giant-planet conditions. Gravitational fields, density and magnetic evidence constrain interiors through models rather than direct imaging.
For a homogeneous isotropic linearly elastic solid of densityρ, P waves have vP²=(λ+2μ)/ρ=(K+4μ/3)/ρ and S waves have vS²=μ/ρ. The tensor-strain convention is ε_ij=(∂_iu_j+∂_ju_i)/2 with σ_ij=λtr(ε)δ_ij+2με_ij and K=λ+2μ/3. Wave propagation is distinct from particle displacement.
Travel times constrain interior structure under a response model.
In a high-frequency ray model, travel time along a pathγ is t=∫_γ ds/v. Across a stationary planar interface, matching phase along the interface gives sinθ₁/v₁=sinθ₂/v₂ for propagating branches, with angles from the normal. For v₂>v₁ the transmitted grazing angle occurs at sinθ_c=v₁/v₂. Reflection and converted elastic branches require their own speeds and boundary conditions.
Refraction, conversion and travel times constrain an interior model.
For source and receiver on a flat surface a horizontal distance x apart above a uniform layer of depth h and speed v₁, direct travel time is x/v₁ and reflection from its horizontal base has time 2√(h²+x²/4)/v₁. If the lower medium has v₂>v₁, the ideal critically refracted head-wave branch has t=x/v₂+2h√(v₁⁻²−v₂⁻²), where its geometric path exists. Observed first arrivals are the minimum among available detectable branches, not a single universal straight line.
Layer travel-time models add quantitative context to interior inference.
Crust, mantle and core primarily distinguish composition. Lithosphere and asthenosphere distinguish mechanical behavior: the lithosphere includes crust and a rigid upper-mantle portion, above a weaker, predominantly solid mantle region. A solid mantle can transmit seismic shear waves while deforming over geological time. The liquid outer core and solid inner core are distinct from this mantle layering.
Short-timescale seismic response and slow solid-mantle deformation are compatible, not evidence for a wholly liquid mantle.