Seismic waves are transient elastic disturbances that transport vibrational energy through Earth and other planetary bodies, generated by abrupt mechanical events such as fault rupture, volcanic activity, magma migration, large landslides, and anthropogenic explosions. They are distinct from the continuous, low-amplitude background vibrations produced by natural and human activity and are characterized by measurable waveforms, arrival times and amplitudes recorded across observation networks.
Seismologists record these signals using land seismometers, underwater hydrophones and strong‑motion accelerometers; integration of data from distributed stations permits precise determination of phase arrivals and signal amplitudes. Different classes of seismic waves—principally body waves (compressional P and shear S phases) and various surface waves—propagate with different speeds and take different paths through the planet, enabling location of an event’s focus (hypocenter) and surface projection (epicenter) and providing constraints on source processes.
The physical behaviour of P and S waves is diagnostic of material properties: P waves, involving volumetric compression and dilatation, travel through solids and fluids, whereas S waves, which depend on a medium’s shear rigidity, cannot propagate where shear strength is absent. This contrast underlies global travel‑time anomalies and shadow zones that reveal internal layering; for example, the near‑vanishing of S‑wave propagation in the liquid outer core, together with changes in P‑wave speed at the core–mantle boundary, are foundational observations used to infer a silicate mantle overlying an iron‑dominated liquid outer core and a solid inner core.
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Seismic velocities vary with density and elastic moduli and typically increase with depth through crust and mantle owing to compositional and pressure‑related stiffening, but they undergo abrupt reductions where phase changes or melting occur. Refraction and reflection of seismic energy therefore form the basis of geophysical imaging: passive seismic tomography maps large‑scale internal structure from natural earthquakes, while controlled‑source surveys exploit generated vibrations to resolve shallow crustal stratigraphy and engineering-scale features.
Earthquake phenomena encompass a wide taxonomy—mainshocks, foreshocks, aftershocks, blind‑thrust and doublet events, interplate and intraplate quakes, megathrust ruptures, slow and supershear slip, submarine and tsunami‑generating events, remotely triggered events and clustered swarms—reflecting diverse rupture mechanics and contexts. Primary causative mechanisms include tectonic faulting, magmatic processes and induced seismicity related to human activities.
Core seismological concepts used in analysis and hazard assessment include hypocenter and epicenter location, epicentral distance, seismic phases and shadow zones; quantification employs seismometers alongside magnitude and intensity scales. Forecasting and coordinated prediction efforts operate at regional and national levels and through international bodies where organized, although deterministic earthquake prediction remains elusive.
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Seismic wave studies intersect many geophysical subdisciplines—electrodynamics (ionospheric and magnetospheric coupling), fluid dynamics (atmospheric and oceanic responses), geodynamics (mantle convection, plate tectonics and volcanism), gravity and geodesy, paleomagnetism and wave physics—reflecting the multidisciplinary nature of vibrational energy transfer. Applied and theoretical research topics include anisotropy diagnostics such as shear‑wave splitting, density–elasticity relations embodied in the Adams–Williamson framework, seismic regionalization (Flinn–Engdahl), earthquake engineering, recognition of seismites in stratigraphy and methodological developments in seismology.
The principles governing seismic propagation extend beyond Earth: planetary seismology of moons, planets and exoplanets uses waveform analysis from quakes, impacts and explosions to probe interior layering, phase boundaries and rheological behavior. The modern discipline has been built on the theoretical, observational and instrumental contributions of many geophysicists and pioneers whose work underpins current understanding and practice.
Types of seismic waves
Seismic energy at Earth is conventionally divided into body waves, which traverse the planet’s interior, and surface waves, which travel along the crustal interface. Because body waves propagate through a volumetric medium, their energy disperses in three dimensions and therefore diminishes more rapidly with distance than energy confined to a two‑dimensional surface layer. In contrast, surface waves concentrate energy near the boundary between solid Earth and atmosphere, so their amplitude decays more slowly with range.
Particle motions also differ: surface waves produce substantially larger ground displacements than body waves, a characteristic that explains their disproportionately large contribution to structural damage during earthquakes. While additional propagation modes exist, they are of limited relevance for terrestrial seismology but become important in contexts such as asteroseismology, where different internal regimes and waveguiding alter observable stellar oscillations. Practically, the slower attenuation and greater amplitudes of surface waves make them dominant in recorded ground shaking and thus central to seismic hazard assessment and engineering design.
Body waves
Body waves are seismic disturbances that travel through Earth’s interior along ray paths determined by the medium’s physical properties. Seismic wave speeds depend on density and elastic stiffness (moduli); because temperature, chemical composition and material phase (solid versus liquid) vary with depth and location, seismic velocities also vary spatially. These velocity gradients refract and bend ray paths in a manner analogous to optical refraction, so the trajectories of seismic rays record internal variations in material properties.
Two fundamental body-wave types arise from distinct particle motions. Primary (P) waves are compressional: particles oscillate mainly in the direction of propagation and their speed reflects both the bulk and shear stiffness as well as density. Secondary (S) waves are shear waves: particle motion is transverse to the ray and their propagation speed depends on the shear modulus and density. The conceptual separation of compressional and shear body waves was noted by Siméon Denis Poisson in 1830.
Observations of body-wave behavior through the mantle and core provide key constraints on Earth’s internal structure. Because liquids cannot sustain shear stress (their shear modulus is effectively zero), S waves do not propagate through the liquid outer core, producing a marked S‑wave shadow on the planet’s far side. P waves do transmit through the outer core, but abrupt changes in elastic properties at the mantle–core and core–inner‑core boundaries alter P‑wave velocities and refract their ray paths; this refraction creates P‑wave shadow zones and helps locate and characterize those internal interfaces.
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Primary waves (P waves)
Primary waves are compressional, longitudinal seismic waves in which particles oscillate back and forth parallel to the direction of travel. Because their propagation velocity exceeds that of other seismic phases, P waves are the earliest arrivals at seismographs following an earthquake and thus serve as the first indicator in seismic timing and detection.
These waves transmit pressure disturbances and can propagate through solids, liquids and gases; when traveling through the atmosphere they correspond to ordinary sound waves and move at the local acoustic speed. P-wave velocity varies strongly with the medium: typical values are on the order of 330 m s⁻¹ in air, about 1,450 m s⁻¹ in water, and roughly 5,000 m s⁻¹ in crystalline rock such as granite. Compared with shear (S) waves, P waves are substantially faster—commonly around 1.7 times the S-wave speed—accounting for their role as the primary seismic phase recorded after an event.
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Secondary (S) waves are transverse shear waves in which particle motion is orthogonal to the direction of propagation, transmitting shear stresses and producing lateral or transverse deformation rather than volumetric compression and expansion. On seismograms they follow the faster primary (P) waves, arriving as the second set of arrivals; in typical materials S-wave speeds are on the order of 60% of P-wave speeds (S ≈ 0.60 × P). The observed ground motion produced by S waves depends on their polarization and propagation direction—for example, horizontally polarized S waves generate alternately opposite lateral motions of the surface.
Because S waves require a medium capable of supporting shear stress, they travel only through solids and cannot propagate through fluids (liquids or gases). This property has been pivotal in Earth structure studies: the absence of S waves traversing the planet’s outer core provides direct evidence that the outer core is liquid.
Surface waves
Seismic surface waves are mechanical disturbances that propagate along the Earth’s exterior layers rather than through its interior. Distinct from body waves (P and S), they remain concentrated near the surface and therefore sample only the shallow elastic medium. Surface waves travel more slowly than P and S waves and consequently arrive after the body-wave phases on seismograms. Their amplitude decays with depth beneath the surface and attenuates along the propagation path as energy spreads and is dissipated in the medium; nevertheless, because they can sustain comparatively large amplitudes over long distances, surface waves often dominate recorded ground motion. In very large earthquakes these waves may be discernible worldwide, producing surface displacements on the order of centimeters. For these reasons surface waves are central to seismogram interpretation and to assessments of earthquake effects at the Earth’s surface.
Rayleigh waves
Rayleigh waves are a type of surface seismic wave—commonly termed “ground roll”—whose motion resembles waves on a water surface but is governed by elastic, not gravitational, restoring forces. At shallow depths particle trajectories are typically retrograde, so surface particles move opposite to the direction of wave propagation; the motion decays with depth. Their theoretical existence was demonstrated by J. W. Strutt (Lord Rayleigh) in 1885 within elastic‑wave theory.
In a homogeneous elastic half‑space Rayleigh waves travel more slowly than body waves, with a phase velocity on the order of ~0.9 times the S‑wave speed, which makes them a dominant low‑frequency, slow component in seismic records. In realistic layered Earth structures their propagation becomes dispersive: phase and group velocities vary with frequency (and therefore wavelength), so different frequency bands sample different depth ranges. As members of the surface‑wave family (cf. Lamb waves in platelike media), Rayleigh waves’ retrograde near‑surface particle motion, elastic restoring mechanism, slower speeds, and frequency‑dependent dispersion form the basis for surface‑wave seismology and are widely exploited to infer crustal and upper‑mantle structure.
Love waves
Love waves are surface-guided shear waves with horizontal transverse particle motion confined to a plane parallel to the ground; seismologically they are classed as SH waves. They arise only in a stratified elastic medium: contrasts in elasticity or density produce a waveguide that supports Love-mode propagation, so they do not exist in a homogeneous half‑space. The theoretical description was derived by A. E. H. Love in 1911, hence the eponym. Kinematically, Love waves generally travel somewhat faster than Rayleigh waves and have phase and group velocities that are frequency- and structure‑dependent; in many cases their speed is on the order of 0.9 times the local shear (S‑wave) velocity. Because of their horizontal shear character and strong sensitivity to vertical and lateral layering, Love waves are particularly valuable for imaging near‑surface elastic structure and for interpreting seismic records.
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Stoneley waves
Stoneley waves are seismic interface waves that travel bound to the contact between two media, most commonly along a solid–fluid boundary but, for specific combinations of material properties and boundary conditions, also able to propagate along solid–solid interfaces. Their particle motion and energy are concentrated at the interface and diminish rapidly with distance into the adjoining media, producing an evanescent, strongly localized wavefield whose amplitude is maximal at the boundary.
In subsurface acoustics these waves are frequently generated on the walls of fluid-filled boreholes, where the borehole wall serves as an efficient waveguide. In borehole geophysics they therefore appear prominently in vertical seismic profiles (VSPs) and in sonic logging: Stoneley arrivals often dominate the low-frequency portion of recorded signals, acting as coherent noise that can obscure other phases while simultaneously representing a distinctive component of the source–receiver wavefield.
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Because their energy is confined to the vicinity of the interface, Stoneley waves are highly sensitive to near-boundary mechanical and hydraulic properties—borehole wall condition, formation permeability, and cement or bonding quality among them. This sensitivity makes them both a nuisance for conventional travel-time analysis and a useful diagnostic: their amplitude, dispersion, and attenuation can be exploited to infer boundary conditions and fluid/rock coupling in the near-wellbore region.
The theoretical description of these boundary waves was first developed by Robert Stoneley (1894–1976), whose formulation of the governing equations established the foundation for understanding this class of interface-confined seismic waves.
Normal modes of the Earth
Free oscillations of the Earth manifest as standing-wave patterns that arise when surface waves travel in opposite directions and interfere. Interference of Rayleigh-type motion produces spheroidal standing modes (S), characterized by radial and volumetric deformation, whereas interference of Love-type motion yields toroidal modes (T), characterized by transverse, twisting motion. Mode visualizations commonly mark nodal lines (zero-displacement loci) and use arrows to indicate the local sense of motion at successive instants.
Modes are designated by the triplet nSlm (or nTlm for toroidal modes). The letter S or T identifies the spheroidal or toroidal class; l is the angular degree (spherical-harmonic order) and determines the number of nodal great circles; m is the azimuthal order, taking integer values from −l to +l (so each l gives 2l+1 azimuthal variants); and n is the radial overtone number, equal to the number of radial nodes. In an ideal, spherically symmetric Earth the eigenperiod depends only on (n, l) and is independent of m, so each set of 2l+1 azimuthal components is degenerate in frequency unless symmetry is broken by rotation, ellipticity, or lateral heterogeneity.
Representative spheroidal modes include the fundamental breathing mode 0S0, in which the whole planet expands and contracts nearly uniformly (period ≈ 20 min), and the quadrupolar 0S2 “rugby” mode, involving alternating elongation along orthogonal axes (period ≈ 54 min). The would-be 0S1 mode is not physically realized because it would correspond to a net displacement of the Earth’s center of mass and therefore would require an external force. Among toroidal modes, the trivial 0T1 corresponds to a change in global rotation rate (a quasi-static rotational perturbation) whose timescale is too long to be useful seismologically, while 0T2 represents a torsional twist between hemispheres with a period of roughly 44 minutes.
Earth’s free oscillations were first identified following the 1960 Chile earthquake; subsequent observations have recorded thousands of distinct modal periods across many (n, l) combinations. Measured eigenperiods provide direct, large-scale constraints on interior properties and are a foundational observational dataset for seismological models of mantle and core structure.
P and S waves in the mantle and core
Seismograms commonly show both the compressional P arrival and the subsequent shear S arrival at stations close to an earthquake, but at greater epicentral distances the first S arrival often loses its high‑frequency content or disappears altogether. This distance‑dependent modification reflects intrinsic differences in propagation: P waves (longitudinal/compressional) can traverse both solid and liquid media, whereas S waves (transverse/shear) cannot propagate through liquids. When shear energy encounters a liquid layer it is blocked, refracted, and strongly attenuated—effects that preferentially remove higher frequencies and create characteristic S‑wave shadow zones and azimuthal patterns of diminution.
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The selective disappearance or damping of S‑wave energy is therefore a direct diagnostic of liquid regions within a planetary interior. Early seismological analyses used these patterns to demonstrate that Earth has a liquid outer core: the absence and refraction of shear arrivals at particular distances and directions provided the key observational constraint, famously established in the work of R. D. Oldham. Analogous reasoning has been applied to the Moon, where seismic data have been interpreted variously as indicating a solid core, while more recent geodetic measurements favor a partially molten or fluid core. The apparent disagreement underscores the need to integrate seismic observations with geodetic and other constraints to resolve the physical state of deep interiors.
Notation
Seismic-phase names compactly encode both the physical wave type and the geometric sequence of legs a wave follows between the earthquake focus and a station. Conventionally these paths are drawn as ray diagrams and recorded as a letter string; because a theoretically large number of path permutations exist, the naming system evolved historically and remains subject to formal standardization (see the IASPEI Standard Seismic Phase List).
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The basic convention treats the phase string as an ordered record of successive legs and boundary interactions. Uppercase letters identify legs that transmit through a region, while lowercase letters normally mark reflections or upgoing legs, though a few letters and mixed-case forms are special cases and must be interpreted on their own terms. A direct reflection from the free surface is not given an extra letter in the string. Mixed-case forms (for example Lt versus LT) can carry distinct meanings and should be read with care.
Specific letters map to propagation regions and boundary events. In the mantle P and S waves are labeled P and S respectively; P propagation in the outer core is denoted K, transmission through the inner core by I, and an S-phase in the inner core by J. Reflections from the outer- and inner-core boundaries are indicated by c and i. Additional inner-core notations include h for an internal inner‑core reflector and d for a reflection from a discontinuity at some depth. Shallow and crustal identifiers include g for waves confined to the crust and n for waves guided along the crust–mantle interface (Moho); surface-wave types are R (Rayleigh) and L (Love). The lowercase p and s mark P‑ and S‑legs that travel up toward and reflect from the free surface, and w denotes reflection from the seafloor.
Examples of reading concatenated strings: ScP — an S leg travels inward, reflects at the outer‑core boundary (c), and the subsequent transmitted leg through the mantle is recorded as P. sPKIKP — an upgoing S leg (s) reflects at the surface as a P (no extra surface letter), then that P transmits through the outer core (K), inner core (I), back through the outer core (K) and out through the mantle as a P, the full sequence being recorded in the symbol string.
Usefulness of P and S waves in locating an event
P and S arrivals provide the fundamental observables for determining earthquake hypocenters. For nearby events the S–P time difference at a single station yields a direct distance estimate; practitioners commonly use the rule of thumb distance (km) ≈ (P–S time difference in s) × 8 km s–1 for events within roughly 200 km. Locating the event in space requires combining distance estimates from at least three geographically separated stations: each station defines a circle of possible epicentral locations, and the intersection of three such circles gives the epicenter (triangulation). For global-scale (teleseismic) earthquakes, unique origin time and position are instead found by fitting P-wave arrival times from three or more widely distributed, clock-synchronized stations; in routine practice seismologists use dozens to hundreds of P arrivals to increase robustness.
The fit between observed and predicted arrival times is quantified by the residual, and typical residuals are substantially smaller for local events (≈0.1–0.2 s) than for distant teleseismic events (≈0.5 s or less). Because compressional P waves propagate at several kilometres per second, even subsecond errors in travel-time modeling map to kilometer-scale errors in inferred distance, so precise travel-time calculation and timing are essential. Using many independent P picks tends to average down individual errors, producing global hypocenter uncertainties on the order of 10–50 km; by contrast, dense regional networks (for example in California) can routinely locate events to roughly 1 km.
Depth is estimated as part of the inversion: location algorithms commonly start from a reference depth (often ~33 km) and adjust depth along with origin time and horizontal coordinates to minimize residuals. Most earthquakes occur at shallow crustal depths (<~40 km), although subduction-zone events can reach depths approaching 700 km. Teleseismic P waves traverse deep mantle paths and may be refracted at discontinuities or into the outer core; because seismic velocity generally increases with depth (elastic moduli increase faster than density), curved refracted paths can be faster than straight-line trajectories, an effect explained by Huygens’ principle and accounted for in travel-time modeling.
Improved precision depends on both measurement and modeling advances. Arrival-time shifts measured by waveform cross-correlation yield far greater timing precision than manual picks and simple difference rules, and modern array processing and inversion schemes outperform basic geometric triangulation. Operationally robust hypocenter determination therefore requires broad and diverse station coverage, precise clock synchronization, accurate three-dimensional velocity models for mantle and core structure, and iterative minimization of arrival-time residuals to refine origin time, epicenter and depth.