Seismic velocity structure denotes the spatial distribution of seismic-wave speeds within the subsurface of Earth and other planetary bodies, providing a depth- and laterally varying description of how seismic energy propagates rather than a single bulk value. The principal observables in such profiles are compressional (P-) velocity, shear (S-) velocity, and bulk density; in the referenced dataset these are plotted as P-wave velocity (red), S-wave velocity (blue), and density (green), with the underlying numerical values drawn from the RockHound Python library.
Variations in P- and S-wave velocities and in density encode fundamental physical properties of the medium—mineralogical composition, porosity, fluid content, bulk density and elastic moduli, and temperature. Consequently, changes in the velocity and density curves signal lithological boundaries, phase transitions, variations in porosity or fluid saturation, and thermal gradients. Because seismic velocities are governed by elastic moduli and mass density, systematic trends (for example increases or decreases with depth or abrupt contrasts across interfaces) are routinely interpreted in terms of compaction, metamorphism, compositional layering, and temperature variations.
Quantitative interpretation typically proceeds by inverting observed seismic travel times and amplitudes to recover lateral and vertical contrasts in velocity and density. These reconstructed velocity models are central to delineating geological units and contacts, characterizing fault zones, and locating earthquake hypocenters. Beyond seismology, such models underpin applied tasks—hydrocarbon, mineral and groundwater exploration—and broader geodynamic and tectonic investigations into Earth’s internal structure and evolution. Visualizations and curated datasets (e.g., those provided by RockHound) therefore serve as essential tools for both qualitative assessment and quantitative modeling of subsurface properties.
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History
The 19th‑century invention of the seismogram, which produced continuous time‑series records of ground motion, transformed seismology from an observational pastime into an instrument‑based quantitative science. Systematic recording and archival of seismic waves supplied the empirical datasets necessary to investigate how propagation speeds vary with depth and across regions of the Earth. The term seismic velocity structure denotes these spatial and depth‑dependent variations in wave speed; by comparing waveforms, arrival times, amplitudes and phase information from archived seismograms, researchers can infer internal layering and variations in elastic properties. Continuous, instrumented observation thus enabled the resolution of internal heterogeneity, anisotropy and stratification and marked a decisive advance in understanding Earth’s internal physical structure.
The twentieth century established the fundamental framework for interpreting Earth’s seismic velocity structure by combining key observational discoveries, coordinated instrumental networks, and methodological advances. Early in the century, Andrija Mohorovičić identified a marked increase in seismic wave speeds that demarcates the crust–mantle boundary (the Moho), while Beno Gutenberg later recognized the seismic discontinuity at the core–mantle interface; together these discoveries defined the principal radial horizons that govern large‑scale velocity contrasts.
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Instrumental coordination amplified the impact of these conceptual breakthroughs. The World Wide Standardized Seismograph Network (WWSSN) of the 1960s provided a comparable, high‑quality global dataset that both improved the detection of systematic velocity variations and helped substantiate the emerging plate tectonics paradigm. Building on this legacy, the Global Seismic Network (GSN), established in 1984 under IRIS, deployed permanent broadband seismometers that further increased data coverage and fidelity, enabling more detailed tomographic studies, robust earthquake source analyses, and real‑time monitoring.
Methodological progress paralleled these data improvements. Seismic tomography—the inversion of travel times and amplitudes to produce three‑dimensional images of subsurface velocity—was advanced substantially by Keiiti Aki and Adam Dziewonski in the 1970s–1980s, making it possible to resolve lateral and radial heterogeneity in the mantle and lithosphere over multiple scales. The Preliminary Reference Earth Model (PREM, 1981) synthesized diverse seismic observations into a standardized radial profile of elastic and anelastic properties; PREM remains a baseline against which tomographic anomalies and alternative global models are compared.
Contemporary representations of the seismic monitoring infrastructure reflect this century of development: programmatic mapping of GSN station distributions using reproducible geospatial tools (for example, Python with the Cartopy library) and authoritative station inventories (e.g., USGS datasets) illustrates both the global coverage of modern seismometers and the reproducibility of current geoscientific workflows.
In the twenty‑first century seismic tomography has advanced rapidly through the combined effects of denser global observations, the development of ambient‑noise imaging, and a dramatic increase in computational capacity. Expansion of the Global Seismic Network has improved station density and geographic and azimuthal coverage for body and surface waves, yielding richer ray‑path sampling that reduces tomographic blind spots and strengthens constraints across regional to global scales. At the same time, ambient‑noise methods—which retrieve coherent surface‑wave signals from the cross‑correlation of continuous background seismic noise—now complement earthquake‑based data by enhancing crustal and upper‑mantle resolution and, when applied at long periods with dense, long‑duration records, contributing information useful for deeper mantle and core imaging. Greater computational power has enabled deployment of advanced inversion frameworks (notably full‑waveform inversion and adjoint techniques) that model three‑dimensional wave propagation, permitting resolution of smaller‑scale heterogeneity, reducing trade‑offs between structural geometry and velocity, and producing more robust models of the crust, mantle and core. Integrating teleseismic travel times, earthquake surface‑wave dispersion, ambient‑noise dispersion and full‑waveform modeling now yields multi‑scale velocity models that span the crust through the inner core, improves uncertainty quantification, and opens the door to time‑dependent (4‑D) studies of evolving structure. These methodological and observational gains have focused attention on the inner core—probing lateral heterogeneity, anisotropy and boundary topography to test competing ideas about composition, crystal alignment, growth and dynamics—and have sharpened our insights into mantle convection, plume structure and core–mantle boundary interactions. Improved velocity models also provide a firmer seismic framework for linking mineral‑physics constraints to estimates of temperature and composition and for refining regional seismic‑hazard assessments.
Principle of seismic velocity structure
Seismic velocity structure interprets spatial variations in the speeds of seismic waves to infer the Earth’s internal layering, material composition and physical state with depth. Variations in velocity—produced by changes in mineralogy, density and temperature—alter seismic raypaths through refraction and generate returns by reflection; these effects concentrate and redirect seismic energy at boundaries and thereby encode the location and contrast of subsurface interfaces.
Refraction at an interface is governed by Snell’s Law, which links the angles of incidence and refraction to the velocities in the two media (qualitatively, the sines of the angles are proportional to the velocities). That relation predicts a critical condition in which the refracted ray propagates along the boundary (angle of refraction = 90°), a phenomenon exploited in seismic refraction surveys when incidence angles are sufficient for critically refracted phases to develop.
Compressional (P) and shear (S) waves provide complementary constraints. P‑waves travel through solids, liquids and gases and vary systematically with medium properties, so they sample a wide range of depths and constrain radial velocity and mass distribution. S‑waves propagate only in solids and therefore directly inform on shear rigidity and the presence of solid phases; the failure of S‑waves to traverse the outer core is a primary line of evidence for its liquid state.
Practical reconstruction of velocity structure relies on analysis of travel times, arrival sequences and reflected phases and their inversion into layered models. Such travel‑time and reflection analyses yield depth‑resolved velocity profiles and delineate major transitions—for example the crust–mantle discontinuity (Moho) and the core–mantle boundary—thereby linking seismic observables to the mechanical and compositional structure of the Earth.
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Average seismic velocity structure of planetary bodies
Seismic profiles of terrestrial planets and the Moon exhibit layered variations in compressional (P) and shear (S) wave speeds that reflect compositional and rheological differences with depth. P-waves travel faster than S-waves in all solid regions, and the presence or absence of S-wave propagation is a primary indicator of liquid versus solid phases.
On Earth, continental crustal P-wave speeds generally fall between ~6.0 and 7.0 km s−1 (oceanic crust ~5.0–7.0 km s−1), with corresponding crustal S-wave speeds near 3.5–4.0 km s−1. The upper mantle is characterized by P velocities of roughly 7.5–8.5 km s−1 and S velocities of about 4.5–5.0 km s−1, while the lower mantle shows substantially higher P speeds (~10–13 km s−1) and S speeds in the range ~5.5–7.0 km s−1. Seismology identifies an outer core in which S-waves are absent and P-waves slow to ~8.0–10 km s−1, consistent with a fluid layer, and an inner core in which P-waves reach ≈11 km s−1 and weak S-wave signals of ~3.5 km s−1 are observed, indicating a solid inner region.
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Lunar velocity structure is lower in absolute magnitude than Earth’s but retains a layered character. Reported crustal P velocities lie between ~5.1 and 6.8 km s−1 with S speeds near 2.96–3.9 km s−1. A mantle velocity around P ≈7.7 km s−1 and S ≈4.5 km s−1 has been inferred, although a deeper region has been reported with P velocities near 5.5 km s−1 and no corresponding S-wave phase, implying a localized low-velocity (partially molten or fluid) zone. The Moon’s outer core is inferred from an absence of S-waves and reduced P speeds (~4 km s−1), while limited evidence for an inner lunar core gives P ≈4.4 km s−1 and S ≈2.4 km s−1.
Mars displays generally lower crustal velocities (P ≈3.5–5.0 km s−1; S ≈2–3 km s−1). Its upper mantle is estimated to have P-wave speeds near 8 km s−1 and S-waves around 4.5 km s−1. Martian seismic observations indicate a core in which S-waves are not transmitted and P-wave speeds are about 5 km s−1, consistent with a predominantly liquid core; inner-core properties remain unconstrained by the data summarized here.
Comparatively, Earth shows the highest deep-mantle velocities and a well-resolved solid inner core, the Moon exhibits lower velocities with evidence for both liquid and solid inner regions at reduced contrasts, and Mars is characterized by relatively low crustal speeds and a liquid core inferred from the lack of transmitted S-waves.
Velocity structure of the Earth is principally radial: a thin, variable crust overlies the silicate mantle (divided into upper and lower regions with an intervening transition zone), beneath which lie a liquid iron–nickel outer core and a solid inner core. Material properties and physical state change systematically with depth, so elastic-wave speeds vary accordingly. Seismic velocities are controlled by pressure (depth), temperature, mineral composition and crystal structure; increasing pressure and density generally raise P- and S-wave speeds, whereas elevated temperature or partial melt reduce them.
Two body-wave types provide complementary constraints on internal structure. Compressional (P) waves are the fastest and travel through both solids and liquids; shear (S) waves travel only through solids and are slower. The absence of S-wave transmission beneath ~2,900 km depth is a primary indicator of a liquid outer core. Quantitative differences in P- and S-wave speeds, and their gradients with depth, therefore diagnose material state as well as elastic moduli.
Sharp, empirically observed changes in seismic velocities—seismic discontinuities—mark boundaries where mineralogy or physical state changes abruptly. Notable examples include the Mohorovičić (Moho) discontinuity separating crust and mantle (typically ~7–10 km beneath oceans and ~25–70 km beneath continents, mean continental ≈35 km); the mantle transition-zone boundaries near 410 km and 660 km depth associated with the olivine→wadsleyite and ringwoodite→bridgmanite + ferropericlase transformations; the core–mantle (Gutenberg) boundary at ~2,900 km, which delineates solid silicate mantle from the liquid outer core; and the inner–outer core boundary near ~5,150 km (with the Earth’s centre at ~6,371 km). Changes in S-wave behavior signal melting or liquid layers, while stepwise changes in both P- and S-wave speeds across the transition zone reflect pressure-induced phase changes.
Lateral variations in seismic velocity, revealed by tomographic imaging, record thermal and compositional heterogeneity within the crust and mantle. By analysing the depths, magnitudes and spatial patterns of velocity anomalies and discontinuities, geophysicists infer temperature, composition and phase distributions, constrain mantle convection, plume and slab dynamics, and thereby link seismic observations to the planet’s thermal history and geodynamic evolution.
Crust
Seismic velocities in the Earth’s crust vary systematically with tectonic setting, composition and depth. Mean compressional (P‑) wave speeds in continental crust are typically 6.0–7.0 km s⁻¹, whereas oceanic crust exhibits a broader range centered around 5.0–7.0 km s⁻¹; shear (S‑) wave speeds in crustal rocks are generally near 3.5–4.0 km s⁻¹. These values conceal strong lateral and vertical heterogeneity controlled by lithology: the upper crust, often dominated by sedimentary rocks, commonly shows low P‑wave velocities of roughly 2.0–5.5 km s⁻¹, while the lower crust—frequently composed of denser basaltic to gabbroic material—produces substantially higher velocities.
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Velocity increases with depth throughout the crust primarily because overburden pressure rises with burial. Increasing load compacts pore space, raises density and can induce changes in crystal fabrics or phase assemblages; each of these processes tends to accelerate seismic-wave propagation. Temperature exerts an opposing influence: the geothermal gradient thermally weakens and expands minerals, reducing elastic moduli and thus lowering seismic speeds. In typical crustal conditions the pressure-driven stiffening usually outweighs the thermal softening, so net velocities increase downward.
A one‑dimensional seismic‑velocity model of the Earth encapsulates these depth trends as progressive velocity growth with depth punctuated by zones of rapid gradient where compositional changes or phase transformations occur. At much greater depths, the core–mantle boundary produces a dramatic discontinuity: S‑waves vanish across the mantle-to-fluid outer‑core transition and P‑wave behavior alters abruptly because of the loss of shear strength. The inner‑core boundary is marked by a converse jump in velocity as material freezes from the fluid outer core into a solid inner core, reflecting sudden increases in rigidity and changes in compressibility.
Upper mantle
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Seismic-wave speeds in the upper mantle are typically on the order of 7.5–8.5 km s⁻¹ for compressional (P) waves and 4.5–5.0 km s⁻¹ for shear (S) waves, providing a quantitative baseline for mantle propagation. A systematic increase of velocity with depth is chiefly driven by growing lithostatic (overburden) pressure, which raises the elastic moduli and compacts mantle minerals more strongly than in the crust and therefore increases seismic velocities. Superimposed on this monotonic pressure effect are discrete, pressure‑induced mineral phase changes: under higher pressures olivine reorganizes into denser polymorphs, first to wadsleyite near ~410 km depth and then to ringwoodite near ~660 km. The interval between ~410 and ~660 km—the mantle transition zone—thus records abrupt changes in physical properties and a measurable acceleration of seismic-wave speeds relative to shallower mantle levels because the denser polymorph assemblage transmits elastic waves more efficiently.
Lower mantle
The lower mantle exhibits markedly higher seismic speeds than shallower layers: compressional (P) waves typically travel at about 10–13 km s⁻¹, while shear (S) waves have velocities in the range 5.5–7.0 km s⁻¹. The clear separation between P‑ and S‑wave ranges reflects the distinct elastic and mechanical controls on compressional versus shear wave propagation in deep mantle minerals.
The dominant control on this velocity structure is the progressive rise of pressure with depth, which increases material density and elastic moduli and thus accelerates both P and S waves. Temperature-dependent weakening, which tends to lower seismic velocities, is present but subordinate in the lower mantle; the observed speed ranges therefore record a net effect in which pressure‑driven compaction and stiffening outweigh thermal softening.
Outer Core
Seismic observations indicate that compressional (P) waves travel through the outer core at approximately 8.0–10 km s⁻¹, while shear (S) waves are not transmitted—an absence that reflects the outer core’s liquid state. At the core–mantle boundary (commonly identified with the D″ layer or the Gutenberg discontinuity) there is a marked drop in seismic velocity: the phase change to a fluid causes wave speeds to decrease sharply despite the extreme pressures at those depths. The outer core’s reduced velocities and its inferred density deficit relative to pure iron require the presence of lighter alloying elements (notably oxygen, silicon, sulfur and hydrogen), which lower bulk density and modify elastic properties and thus account for the observed seismic signatures. Seismic studies probing deeper still reveal anisotropic behavior in the innermost regions of the core (the proposed “inner” inner core), where travel times are faster along the planet’s rotation axis than along equatorial directions, implying localized structural or compositional variations that affect wave propagation directionally.
Inner‑core seismic observations indicate compressional (P) wave speeds near 11 km s−1 and shear (S) wave speeds around 3.5 km s−1, magnitudes that are characteristic of a very dense, mechanically rigid material at Earth’s center. These velocities are consistent with a solid, crystalline assemblage dominated by iron and nickel; the metal‑rich lattice provides the elastic strength necessary for both P‑ and S‑wave propagation.
The marked contrast in wave behavior between the inner and outer core—detectable S‑wave transmission in the former but not in the latter—reflects the inner core’s ability to support shear stresses, whereas the liquid outer core cannot. Seismic speed differences therefore directly signal higher elastic moduli and rigidity in the inner core relative to the surrounding fluid layer. Minor concentrations of lighter elements are present within the iron‑nickel matrix and slightly modify the observed velocities, but the overall seismic signature remains governed by the dense metallic composition.
Anisotropy of the inner core
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Seismic observations demonstrate that the solid inner core is anisotropic: compressional waves travel faster along directions close to Earth’s rotation axis than through the equatorial plane. This directional dependence of P-wave speed implies an internal fabric rather than an isotropic aggregate, and it is most readily interpreted as a preferred alignment of iron and its crystal lattices at depth.
The alignment likely reflects geodynamic processes tied to rotation and solidification. As the inner core grows, rotationally influenced crystallization or deformation could orient iron crystals, producing systematic velocity variations with direction. Such a process provides a plausible mechanistic link between large-scale rotational forcing and microscopic lattice texture.
Seismic travel-time anomalies furthermore indicate a possible distinct “inner” inner core beneath the inner-core boundary: rays sampling the deepest ~250–400 km beneath the boundary require a model with a transition approximately 100–200 km thick. This innermost zone may record changes in crystal preferred orientation, lateral or radial variations in light-element content within the Fe-alloy, or relics of discrete stages in accretional and early thermal–chemical evolution.
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Characterizing the inner core remains intrinsically challenging. It occupies under 1% of Earth’s volume and is shielded by the mantle and liquid outer core, so seismic coverage is sparse and uneven. Constraints on shear-wave speeds are especially weak because P–S and S–P conversions at the inner-core boundary are rare and shear energy is strongly attenuated in the inner core, leaving S-wave velocities poorly resolved and motivating continued focused seismological and geophysical efforts.
Lateral variation of seismic velocity structure
Lateral variation in seismic velocity denotes horizontal contrasts in wave speed within the crust, describing map‑like changes across the Earth’s surface rather than vertical stratification alone. These contrasts reflect spatial differences in rock composition and fabric (mineralogy, porosity, degree of consolidation), gradients in temperature (with higher temperatures generally reducing elastic moduli and wave speeds) and the occurrence, pressure and saturation of fluids, which strongly affect S‑wave speeds and modulate P‑wave velocities and Vp/Vs ratios.
Such horizontal heterogeneity measurably alters seismic observations: it modifies travel times, amplitudes and waveforms of P‑ and S‑phases, redirects energy through lateral refraction and reflection, and produces velocity anomalies in tomographic and profile datasets that betray subsurface complexity. Lateral structure exists over a broad spectrum of scales, from metre‑to‑kilometre variability in near‑surface deposits to tens or hundreds of kilometres associated with crustal blocks and plate boundaries, and it must be evaluated in concert with vertical layering when interpreting seismic surveys.
Mapping these variations relies on a suite of imaging techniques—travel‑time and waveform tomography for body and surface waves, reflection and refraction profiling, and ambient‑noise tomography—each inverting observed arrivals and waveforms to generate two‑ or three‑dimensional lateral velocity maps. Interpreting anomalies requires diagnostic use of velocity magnitudes, Vp/Vs ratios and independent geological or petrophysical constraints: reduced velocities often indicate elevated temperature, partial melt or fluid saturation, whereas increased velocities point to colder, denser mafic or crystalline materials.
The resulting lateral velocity maps are central to delineating tectonic boundaries, faults, basins and sutures, and they inform exploration for hydrocarbons, minerals, groundwater and geothermal resources, as well as models of crustal structure and regional heat flow. However, map resolution and reliability depend critically on data coverage, station geometry and ray‑path sampling; inversions are inherently non‑unique and subject to trade‑offs (for example between lateral velocity and interpreted depth). Robust interpretation therefore requires integration of seismic results with geological, petrophysical and thermal information.
Discontinuity
Discontinuities are internal surfaces or thin zones where seismic velocities change abruptly, reflecting sharp contrasts in composition, phase, or physical state and thereby delineating the major structural layers of the Earth. The Mohorovičić discontinuity (Moho) marks the crust–mantle interface: it lies roughly 30–50 km beneath continental regions and about 5–10 km beneath ocean basins and is expressed as a sudden increase in P‑ and S‑wave speeds at the base of the crust. Within the mantle, a suite of phase‑transition boundaries produces prominent velocity steps: at ~410 km depth olivine transforms to wadsleyite, at ~520 km wadsleyite converts to ringwoodite, and at ~660 km ringwoodite reacts to form bridgmanite plus ferropericlase; each transition yields measurable changes in seismic wave propagation and together define the mantle transition zone. The Gutenberg discontinuity, at approximately 2,890 km depth, separates the solid silicate mantle from the liquid outer core and is manifested by a marked alteration in seismic behavior at the core–mantle interface. Deeper still, the Lehmann discontinuity or inner‑core boundary (ICB) at about 5,150 km depth delineates the transition from the fluid outer core to the solid inner core and is identified by distinct changes in seismic velocities transmitted through the core.
Velocity structure of the Moon
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Between 1969 and 1972 Apollo missions deployed five passive seismic experiment (PSE) stations on the lunar surface; the instrument placed by Apollo 11 failed soon after deployment, while four stations continued to operate until 1977. Those four long‑duration stations were all sited on the Moon’s near side and were positioned roughly at the vertices of an equilateral triangle, with a pair of instruments colocated at one vertex. This configuration produced a triangular seismic array with a denser cluster at a single vertex, which nevertheless provided the principal spatial sampling available from the lunar surface.
The near‑side network recorded in excess of 13,000 seismic events, constituting the primary empirical dataset for inferring lunar seismic velocities and internal structure. Careful examination of the records has yielded a consistent classification of moonquakes into four types: shallow moonquakes, deep moonquakes, thermal events driven by the diurnal temperature cycle, and discrete impact signals from meteoroids. Continued reanalysis of the Apollo PSE archive remains essential for refining velocity models, constraining internal layering, and clarifying the physical mechanisms that generate the observed seismicity.
Crust
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Seismic observations indicate a remarkably consistent, one‑dimensional velocity structure for the lunar crust, which is commonly modeled as roughly 60 km thick. Compressional (P) waves travel faster than shear (S) waves throughout this column: global mean P velocities lie between about 5.1 and 6.8 km s−1, whereas S velocities range from approximately 2.96 to 3.9 km s−1. From the surface downward the profile is steep: an extremely low‑velocity, highly porous regolith (~100 m s−1) grades rapidly to ~4 km s−1 by 5 km depth and to ~6 km s−1 by ~25 km, where a pronounced discontinuity raises velocities to ≈7 km s−1; below that horizon velocities remain essentially constant with further depth.
The near‑surface low velocities reflect unconsolidated, porous material; the rapid increase with depth is attributable to progressive lithification and mechanical compaction that reduce porosity and stiffen the rock fabric. The sharp ∼25 km impedance jump denotes a substantive change in material or mechanical state—interpreted as transition to dense, low‑porosity anorthositic and gabbroic lithologies under near‑hydrostatic overburden—so that velocities below this boundary are characteristic of sealed, high‑velocity crustal rocks. The contrasting shapes of P‑ and S‑velocity curves and the occurrence of abrupt versus gradual velocity changes therefore serve as diagnostics of porosity loss, rock‑type boundaries, and mechanical sealing. Thermal effects on these speeds are minor: the Moon’s geothermal gradient reduces velocities by only ~0.1–0.2 km s−1, so mechanical compaction and lithologic variation are the dominant controls on the observed seismic velocity structure.
Mantle
Seismic constraints on the lunar mantle are limited by a sparse dataset of moonquake waveforms, yielding significant uncertainty in structure, particularly beneath ~480 km. Measured bulk velocities for representative lunar materials—an average P-wave speed near 7.7 km s−1 and an S-wave speed near 4.5 km s−1—provide baseline values against which depth- and regionally dependent variations are assessed. In the upper mantle (roughly 60–400 km depth) observations indicate a modest negative velocity gradient: S-wave speeds decrease with depth at rates on the order of −6×10−4 to −13×10−4 km s−1 per km, and similar downward trends for P-waves have been inferred from waveform studies. Thermal effects, most notably increasing temperature with depth, are generally invoked to explain these upper-mantle velocity reductions, with thermal gradients considered more influential than compositional heterogeneity for the observed seismic behavior.
A sharper change in seismic properties occurs across a transition zone between ≈400 and 480 km, marked by a pronounced drop in both P- and S-wave speeds and interpreted as a major structural or compositional boundary separating upper and lower mantle domains. This velocity decrease is consistent both with thermal variations and with a model of chemical stratification—specifically an increase in iron concentration at greater depth under high-pressure, high-temperature conditions, which would reduce elastic moduli and lower seismic velocities relative to the overlying mantle. Below the transition (≈480–1100 km) seismic interpretations diverge: some analyses report continued S-wave attenuation or strong scattering consistent with absorption or partial melt, whereas others infer velocity increases with depth. Near ~1000 km depth a hypothesis of partial melting has been proposed to account for pronounced S-wave attenuation; such a molten or partially molten layer could promote material segregation (for example concentrating Mg‑rich olivine at greater depth), thereby altering seismic velocities through both compositional sorting and changes in physical state. Overall, limited data and competing explanations leave the deep lunar mantle structure and its controlling processes incompletely resolved.
Core
Seismic and geophysical constraints indicate a geometrically and compositionally complex lunar core but remain limited and model‑dependent. Seismic observations and schematic cross‑sections suggest the deep liquid and partially molten regions are not perfectly concentric, implying an aspherical core geometry and possible lateral heterogeneity in material distribution.
Across the mantle–core boundary there is an abrupt reduction in P‑wave speed from about 7.7 km s⁻¹ in the lowermost mantle to ~4.0 km s⁻¹ in the outer core, accompanied by an absence of transmitted S‑waves; these features are most simply explained by a fluid outer layer, commonly interpreted as a molten iron–sulphur–rich melt. The outer core’s mean P‑wave velocity near 4.0 km s⁻¹ and its inability to transmit S‑waves together confirm its liquid state and place constraints on its thermal and compositional state.
Evidence for a distinct inner core comes from a modest rise in seismic speeds: mean P‑wave velocities increase to ≈4.4 km s⁻¹ and S‑wave speeds to ≈2.4 km s⁻¹, consistent with a solid phase. These higher velocities are compatible with an iron‑nickel dominated solid, probably alloyed with lighter elements. Contemporary geophysical models generally favor a relatively small lunar core: estimates place the liquid outer core at roughly 1–3% of the Moon’s mass and the total core mass on the order of 15–25% of the lunar mass. Nonetheless, given the sparseness of direct seismic data and inherent model trade‑offs, some analyses find that a core with specific properties is not uniquely required by the available observations.
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Lateral variation of seismic velocity structure
The lunar crust displays significant lateral heterogeneity in seismic velocities, such that wave speeds vary markedly with geographic location rather than forming a laterally uniform layer. Large impact basins are primary loci of this heterogeneity: the mechanical effects of basin-forming collisions—chiefly the compaction and densification of near-surface materials—produce higher compressional and shear-wave velocities within and around basins than in surrounding highland or mare terrains. Mechanistically, impact-induced collapse reduces pore space and increases bulk density and elastic moduli, so that both P‑ and S‑wave speeds rise in basin floors and uplifted rims relative to less-altered adjacent regions; contrasts also reflect differences in fracturing intensity, layering, and porosity. Seismic datasets returned by lunar missions provide the empirical framework for mapping these spatial variations, showing location-specific velocity profiles that permit inferences about subsurface compaction, stratification, and impact-related heterogeneities. Interpreting lateral velocity contrasts is therefore critical for reconstructing the sequence and effects of basin-forming events, constraining mechanical properties of the crust, and informing models of the Moon’s thermal and structural evolution.
Velocity structure of Mars
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The one‑dimensional seismic velocity profile for Mars describes how seismic wave speeds vary with depth beneath a single site (or in a radially averaged sense). Variations in that depth‑dependent velocity are interpreted as indicators of changing physical state (temperature, porosity, fracturing, presence of volatiles or partial melt) and/or compositional differences (mineralogy, bulk rock density) with depth. In general, higher seismic velocities imply cooler, mechanically strong and/or more mafic (denser) materials, whereas lower velocities point to elevated temperatures, increased porosity or cracking, fluids or melts, or a shift toward less dense mineral assemblages; discriminating thermal effects from compositional ones requires joint analysis of travel times, amplitudes and waveform characteristics.
Knowledge of Mars’s radial velocity structure has been developed through a combination of numerical/theoretical modelling and the sparse seismic observations available. Models provide priors and permit forward modelling and inverse experiments, while observed marsquakes and impact‑generated signals are used to update one‑dimensional models via inversion and tomographic approaches. The InSight mission, which landed in 2018, supplies the principal modern dataset: by 30 September 2019 InSight had recorded 174 seismic events, enabling constraints on shallow and intermediate depth structure beneath the landing site. Earlier attempts (notably Viking 2 in the 1970s) yielded only very limited, locally constrained detections and did not meaningfully constrain deeper structure.
Combining InSight’s event set, the legacy Viking observations and modelling has produced first‑order constraints on Mars’s 1‑D velocity profile, but spatial coverage and vertical resolution remain limited. As a result, inferences about composition, thermal state and internal layering retain substantial uncertainty; resolving these ambiguities will require more seismic events, wider spatial sampling (additional stations), and integrated geophysical modelling that jointly exploits travel times, amplitudes and waveforms.
Crustal seismic velocities on Mars are moderate, with compressional (P) waves typically propagating at roughly 3.5–5 km s−1 and shear (S) waves at about 2–3 km s−1. Crustal thickness is estimated between ~10 and 50 km, and velocities increase with depth as rising lithostatic pressure closes pore space and mechanically stiffens rock. The very near surface is characterized by low bulk density and high porosity, producing reduced seismic speeds and a pronounced near-surface velocity gradient. Seismic profiles resolve an internal discontinuity at ~5–10 km depth, indicative of a change in porosity or lithology within the crust, and a deeper discontinuity at ~30–50 km that is interpreted as the crust–mantle boundary—the Martian analogue of the terrestrial Moho—separating higher-density, lower-porosity mantle material. Altogether, the observed absolute velocities, their depth dependence, and the two discontinuities support models of a porous, low-density surficial layer overlying progressively compacted, higher-velocity rock toward the base of a 10–50 km crust.
Mantle
Mars’s mantle is characterized by an iron-rich, relatively high‑velocity upper layer that transmits compressional waves at about 8 km s⁻¹ and shear waves near 4.5 km s⁻¹. Seismic observations and modeling indicate a layered mantle structure: a pronounced low‑velocity zone (LVZ) between roughly 400 and 600 km depth, two abrupt seismic discontinuities near 1,100 km and 1,400 km, and evidence for extensive partial melt or a molten layer at greater depths in addition to a liquid core.
The LVZ is marked primarily by reduced S‑wave speeds while P‑wave speeds remain steady or increase slightly; this pattern is consistent with elevated temperatures under moderate pressure and with a relatively stagnant layer lying above a more vigorously convecting interior. The two deeper discontinuities are interpreted as pressure‑driven mineral phase changes—olivine → wadsleyite near ~1,100 km and wadsleyite → ringwoodite near ~1,400 km—analogous in mechanism to Earth’s mantle transitions but occurring at different depths because of Mars’s distinct pressure‑temperature regime and composition. Unlike Earth, Mars lacks a bridgmanite‑dominated lower mantle, a compositional difference that helps explain contrasting seismic velocity profiles and shifted phase‑transition depths.
Seismic measurements of the deeper mantle yield a P‑wave velocity of about 5.5 km s⁻¹ while S‑wave observations are effectively absent or “not applicable,” implying widespread partial melt or a liquid layer that would preclude shear transmission. Together, the iron‑rich upper mantle, the thermal LVZ, the phase‑change discontinuities, and possible deep molten zones strongly influence seismic wave propagation and impose important constraints on models of Martian convection and thermal evolution, while also complicating the interpretation of seismic data used to infer the planet’s internal structure.
Core seismic structure of Mars is constrained primarily by compressional- and shear-wave observations. Average P-wave speeds within the interior are ~5 km s−1; because P-waves travel through both solids and liquids, this velocity provides a baseline constraint on the bulk elastic properties used in interior models. In contrast, shear waves are not observed to traverse the region interpreted as the outer core. The loss and strong attenuation of S-wave energy on core-crossing paths constitutes the principal seismological evidence for a low-rigidity, liquid outer core rather than a wholly solid central region.
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When seismic constraints are combined with geochemical and bulk-density bounds, the most consistent compositional interpretation is an iron–nickel–dominant core enriched in lighter elements. The reduced mean core density relative to a pure Fe–Ni alloy requires appreciable light-element admixture to match Mars’ mass and moment-of-inertia constraints. By contrast, the existence and dimensions of a solid inner core analogous to Earth’s remain unresolved: current seismic coverage and signal resolution do not permit definitive detection of an inner solid phase, so its presence and detailed properties continue to be the subject of modelling and future observational efforts.
Lateral variation of velocity structure
Seismic data returned by the InSight mission reveal that Mars’s interior is laterally heterogeneous: seismic waves travel at different speeds in different regions, demonstrating that subsurface elastic properties vary horizontally as well as vertically. These lateral velocity contrasts are best explained by a stratified crust and upper mantle comprising multiple discrete or gradational layers rather than a uniform stratigraphy.
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Spatial changes in seismic-wave speeds are principally attributed to variations in crustal thickness and in rock composition. Differences in layer thickness, mineralogy and the presence of intrusive or extrusive volcanic materials produce measurable contrasts in elastic moduli and density. The observed patterns of velocity heterogeneity are consistent with a geological history dominated by localized volcanic construction and tectonic modification—such as volcanic edifices, lava flows, intrusive bodies and structural deformation—that has produced lateral complexity in lithology and structure.
InSight seismic signatures also indicate a low-velocity, liquid-bearing layer overlying the metallic core, implying a molten or partially molten zone that influences seismic propagation and constrains Mars’s present thermal regime. Together, the lateral seismic contrasts and the inferred liquid layer point to a coupled set of thermal and compositional processes—variable heat flow, partial melting, chemical differentiation and lateral compositional heterogeneity—that have governed the planet’s internal evolution.
Ongoing and more detailed analyses of marsquake datasets aim to link these surface and crustal heterogeneities to mantle convective processes. Correlating lateral velocity variations with patterns of mantle upwelling, downwelling and persistent thermal anomalies offers a path to understanding the geodynamic mechanisms that produced Mars’s present-day internal structure.
Velocity structure of Enceladus
Enceladus is commonly represented by a three-layer internal model—an outer ice shell, a global subsurface ocean, and an underlying rocky core—though the detailed internal geometry and properties remain only weakly constrained by existing observations. The study reproduces theoretical one‑dimensional seismic velocity profiles (Dapré and Irving, 2024) for three end‑member configurations—Single Core, Thick Ice, and Layered Core—chosen to bracket plausible ranges of layer thicknesses, material contrasts, and boundary depths that control seismic wave speeds. Across all models, predicted seismic behavior follows a consistent pattern: velocities fall moving downward from the brittle, porous or fractured ice shell into the subsurface ocean, reflecting the transition from a mechanically weakened solid to an essentially fluid medium. Deeper in the rocky interior, velocities rise substantially in solid silicate material, creating a pronounced high‑velocity domain that contrasts strongly with the low‑velocity ocean and the fractured ice above. This interpretation rests on the physical linkage between seismic speed and material state: porosity, fracturing and liquid phases reduce wave speeds relative to intact crystalline ice and dense silicate rock, so velocity minima are expected to mark the ocean and velocity maxima to indicate solid‑core regions. These 1‑D profiles and their end‑member variants are intended as practical guides for mission planning and data analysis, identifying likely depth ranges and seismic signatures for the ice shell, ocean, and core and thereby aiding detection of layer boundaries, subsurface reservoirs, and possible core layering.
Future work in planetary seismology seeks to move beyond the limited dataset obtained from the Moon and Mars by deploying seismic instruments across additional Solar System bodies to constrain internal structure and ongoing tectonic or cryoseismic processes. Foremost among planned efforts is the Europa Lander Mission (launch window 2025–2030), which is designed to record seismicity on Jupiter’s moon in order to characterize the mechanical properties of its ice shell and to quantify how surface and putative subsurface liquid layers are mechanically coupled. Central to that payload is the Seismometer to Investigate Ice and Ocean Structure (SIIOS), developed at the University of Arizona and engineered to operate under Europa’s extreme cold and radiation; SIIOS aims specifically to resolve the physical structure of the icy crust and to detect signals indicative of a subsurface ocean.
On the lunar front, NASA’s Artemis-driven return to the surface is accompanied by the Development and Advancement of Lunar Instrumentation (DALI) program, which prioritizes maturation of technologies for lunar science — seismology being a key area for reconstructing the Moon’s interior and geological evolution. A highlighted DALI initiative, the Seismometer for a Lunar Network (SLN), proposes embedding seismometers on future landers and rovers to establish a distributed seismic network. Such a network is intended to provide the spatial coverage required for systematic geophysical investigations and to inform sustained exploration and scientific planning.
Methods for determining seismic velocity structure rely on observing seismic waves and solving inverse problems: subsurface models are iteratively adjusted until predicted waveforms or travel times reproduce observed records, thereby inferring layering, material properties, and the temperature–composition controls on P‑ and S‑wave speeds across scales.
Near‑surface and engineering applications commonly use controlled‑source techniques. Seismic refraction employs man‑made impulsive sources to generate waves that bend at velocity contrasts; the earliest arrivals are direct waves, followed by refracted headwaves that emerge from critically refracting interfaces. Analysis of refracted travel‑time trends and the crossover between direct and headwave arrivals yields layer depths and contrasts, but resolution is limited by seismic wavelength (typical refraction study wavelengths are on the order of 200 m to 1 km) and the expense of acquiring dense source–receiver coverage. Seismic reflection records energy echoed from impedance boundaries (where density times velocity changes) and uses travel‑time and amplitude variations of those reflections to map stratigraphy and structure; reflection imaging complements refraction by resolving layer geometry and is a staple of hydrocarbon and shallow subsurface investigations.
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For deeper and regional to global imaging, methods based on natural seismicity predominate. Seismic tomography uses travel times (and raypath geometry) from earthquakes recorded at many stations to invert for three‑dimensional variations in P‑ and S‑wave speed; tomographic models reveal heterogeneity related to composition, temperature, and dynamic processes such as mantle convection and plate interactions. Receiver‑function analysis treats single‑station converted phases and reverberations — for example P‑to‑S conversions at the Moho — to estimate interface depths and impedance contrasts, enabling mapping of crustal thickness, basin sediment depths, and internal discontinuity topography, especially where dense broadband networks are available.
Ambient Noise Tomography (ANT) extracts empirical Green’s functions by cross‑correlating continuous background seismic noise between station pairs; coherent surface‑ and body‑wave signals recovered from oceanic, atmospheric, or anthropogenic noise permit high‑resolution imaging of shallow to mid‑crustal structure in regions lacking sufficient earthquake sources. Full Waveform Inversion (FWI) is a data‑intensive, iterative approach that fits the entire observed wavefield rather than only travel times; by exploiting amplitude and phase information across frequencies, FWI attains finer structural and physical parameter resolution and is applied from reservoir‑scale studies to regional tectonic models when dense, broadband data and large computational resources are available.
In practice, controlled‑source refraction and reflection are most effective for near‑surface and reservoir targets (subject to wavelength and acquisition limits), tomographic and receiver‑function techniques probe deeper lithospheric and mantle structure using natural earthquakes, ANT fills observational gaps where seismicity is sparse, and FWI offers the highest resolution where data quality and computing permit. Each method therefore occupies a complementary niche in depth penetration, spatial resolution, and operational cost.
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Applications of seismic velocity structure
Seismic velocity structure—the three-dimensional variation of seismic wave speeds in the crust and mantle—provides quantitative constraints on subsurface composition and state (e.g., lithology, temperature, porosity, and fluids). By converting travel-time, amplitude and waveform data into velocity models, geoscientists obtain high-resolution images of internal layering and heterogeneity that serve as the foundation for interpreting geological architecture and physical conditions at depth.
Across scales, velocity imaging elucidates both local and large-scale tectonic features. At imaging scales it resolves faults, folds and lithological contrasts that control deformation and seismic behaviour; at regional to plate scales it reveals major elements such as subducting slabs, mantle plumes and rift systems. These models therefore inform interpretations of crustal structure, mantle flow patterns and plate-dynamics processes that govern deformation and distribution of seismicity.
In exploration geoscience, velocity models are indispensable for locating and characterizing hydrocarbon reservoirs and mineral deposits. Seismic-derived velocities delineate reservoir geometry and internal heterogeneity, guide well placement and drilling strategies, and reduce exploration risk by constraining rock properties and fluid distributions—information that underpins reservoir modelling and recovery planning.
Velocity structure is central to seismic-hazard assessment and volcanic risk management. Accurate crustal and near-surface velocity models control propagation, amplification and attenuation of seismic waves and thus are required inputs to rupture simulation and ground-shaking forecasting. Beneath volcanoes, detailed velocity images can map magma chambers, conduits and plumbing systems, improving assessments of eruption probability and potential magnitude and enabling targeted mitigation and preparedness measures.
Finally, velocity-based methods are critical in engineering and environmental applications and extend beyond Earth to planetary geophysics. In site investigations they identify discontinuities and weak or compressible layers that affect foundation design and infrastructure safety; they also permit monitoring of contaminant plumes and groundwater pathways for remediation and resource management. On the Moon, Mars and other bodies, seismic velocity studies similarly constrain internal layering, thermal state and tectonic history and can indicate the presence of volatiles or exploitable horizons relevant to planetary evolution and in situ resource utilization.
Limitations in measuring seismic velocity structure arise from both physical signal constraints and methodological assumptions. For the Earth’s inner core, shear-phase observation is hindered by weak wave conversion at the core boundaries and by substantial intrinsic attenuation within the core, which together reduce the amplitude and clarity of core-transmitted shear energy. Novel approaches such as late-coda correlation—which leverages the tail of seismograms to extract weak core signals—show promise but remain hampered by low signal‑to‑noise ratios and by dependence on particular scattering and noise models.
Common simplifications in seismic modeling introduce additional uncertainty. Many inversions assume isotropy and adopt one‑dimensional (depth‑only) structure to reduce computational complexity; however, both mantle and inner‑core materials are likely anisotropic and laterally heterogeneous, so these assumptions can bias retrieved velocities and misrepresent true wave propagation. The inversion itself is inherently non‑unique and sometimes ill‑conditioned: multiple disparate models can fit the same observations, and small data errors can induce large variations in inferred structure.
These issues are compounded for other planetary bodies where instrumentation is sparse. Lunar and Martian velocity models rely on very limited seismometer networks—Apollo-era instruments for the Moon and the InSight lander for Mars—so spatial and temporal coverage are inadequate to resolve three‑dimensional heterogeneity robustly. Collectively, weak core signals, attenuation, simplifying model assumptions, inverse non‑uniqueness, and sparse extraterrestrial datasets produce substantial, model‑dependent uncertainty in estimates of inner‑core shear velocity for Earth and far greater uncertainty for the Moon and Mars; consequently seismic inferences about internal structure must be interpreted with caution.