P wave — Introduction
The P wave (primary or pressure wave) is the fastest seismic body wave and therefore normally constitutes the first clear phase recorded at a site following an earthquake. It is a compressional wave that propagates by alternately compressing and dilating material in the direction of travel, and unlike shear waves it can transmit through solids, liquids and gases. In simple seismological illustrations a P wave is often shown as a planar compressional disturbance with particle motion aligned perpendicular to the advancing wavefront, a convenient visualization for its kinematics.
P waves comprise one of the two principal body-wave types used in seismology (the other being S waves); together with surface waves they form the principal categories by which seismic radiation is analyzed to infer source characteristics and internal Earth structure. Virtually every seismic source—ranging from foreshocks, mainshocks and aftershocks to megathrust ruptures, intraplate events, slow and tsunami‑related slips, induced earthquakes and swarm activity—radiates compressional energy that is observed as P‑wave arrivals. The primary geophysical mechanisms producing these waves include fault rupture, magmatic processes, and anthropogenic triggers such as fluid injection.
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P‑wave arrival times and amplitudes are central to routine seismological practice: they are used, together with the concepts of hypocenter (the subsurface focus), epicenter (the surface projection) and epicentral distance, to locate earthquakes and estimate focal depths. Because P waves travel through the core they are refracted rather than fully blocked, a behavior that, in contrast with the disappearance of S waves through liquid layers, produces characteristic body‑wave shadowing that has been essential in demonstrating the existence of a liquid outer core and layered mantle structure. Instrumentally, P waves are recorded by seismometers and enter into phase identification, magnitude computation and intensity assessments that document both the energy released and its effects at particular sites.
In applied contexts P‑wave detection underpins early‑warning and short‑term forecasting systems that exploit the lead time between the first compressional arrivals and the subsequently more damaging S and surface waves. Analytical and modeling tools linked to P‑wave study include full‑waveform and shear‑wave analyses, geophysical inversion methods (for example those using equations governing density and elastic moduli), regional cataloging frameworks, and applications in earthquake engineering and sedimentary earthquake proxies (seismites). Together these observational, theoretical and practical strands situate P waves as a foundational element of seismology and geophysical interpretation.
Nomenclature
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P waves are longitudinal, compressional seismic waves in which particles oscillate back and forth parallel to the direction of travel; this mode of motion transmits energy efficiently through both solids and liquids, giving P waves the highest body-wave velocities and causing them to be the first seismic arrivals on a seismogram. The label “primary” denotes their early arrival, while “pressure” refers to the alternating compressions and dilatations that generate them, making P phases crucial for rapid detection and initial localization of earthquakes.
By contrast, S waves are transverse, shear waves whose particle motion is perpendicular to propagation. Called “secondary” because they reach stations after P waves, S waves typically produce larger lateral ground displacements and thus more damaging shaking. Because shear deformation cannot be supported by fluids, S waves do not travel through liquid layers; this dichotomy between P- and S-wave transmissivity underpins seismic inference of fluid zones, most notably the liquid outer core.
The two wave types also differ in boundary behavior. P waves refract and reflect at interfaces where elastic properties change; S waves are limited to solids, undergo mode conversion at contrasts (e.g., P↔S), and split into two orthogonal polarizations—SV (vertical shear) and SH (horizontal shear)—which affect the orientation of ground motion and the response of seismic instruments. Differences in P–S arrival times across networks are routinely used to triangulate epicenters and estimate focal depths, while the presence, absence, or timing anomalies of P and S phases constrain material properties and major discontinuities such as the mantle–outer core boundary.
Finally, both P and S signals experience attenuation, scattering, and frequency-dependent dispersion as they traverse heterogeneous crustal and mantle structure. Reflected, refracted, and converted phases combine to produce complex seismograms that seismologists exploit to image subsurface structure and to model earthquake source processes. The temporal sequence and relative amplitudes of P and S arrivals also govern shaking intensity, building response, and secondary hazards (for example, landslides and liquefaction where S-wave energy couples strongly with near-surface sediments).
Seismic-wave velocities increase and decrease in systematic ways with depth, and abrupt changes in the velocity–depth profile mark transitions in physical state or composition of Earth’s internal layers. Body waves—primary (P) and secondary (S) waves—propagate through the interior by different physical mechanisms and thus sample complementary material properties: P waves are compressional (longitudinal) disturbances that travel through both solids and liquids, with speeds sensitive to pressure, temperature and composition, whereas S waves are shear (transverse) disturbances that require elastic shear strength and therefore vanish where material behaves as a fluid. The liquid outer core is revealed by an effective zero S‑wave velocity and a sharp seismic‑velocity discontinuity at the core boundary; the solid inner core restores shear rigidity and exhibits distinct P‑ and S‑wave speeds that produce further discontinuities in the profile. By recording motion, amplitude and arrival times of P and S phases across networks of stations, seismologists exploit differences in travel times and ray geometries—produced by waves following different paths through layers of varying velocity—to locate internal boundaries and infer physical state. Interpretations of velocity discontinuities as phase changes (solid↔liquid) or compositional contrasts are tested by matching observed travel‑time patterns and ray paths to theoretical models of elastic wave propagation.
Seismology—through analysis of seismic body waves, normal modes, travel times, reflections, refractions and phase changes—provides the principal empirical basis for inferring the Earth’s radial layering and material properties. P waves (compressional waves) can traverse both solids and fluids and therefore pass into and through the fluid outer core; however, refraction at the mantle–outer core boundary bends P‑wave ray paths so that first‑arrival P waves are not observed over an angular belt of focal (great‑circle) distances between about 103° and 142° (the P‑wave shadow zone). S waves (shear waves) cannot propagate through liquids, so direct S arrivals are absent at stations whose ray paths intersect the outer core. The coincident observation of a P‑wave shadow zone produced by core refraction and the disappearance of direct S phases where paths enter the core constitutes direct seismological evidence for a liquid outer core underlying a semisolid mantle and underpins the reconstruction of the Earth’s internal radial structure.
P waves as the basis for earthquake early warning
Primary (P) waves are the fastest, compressional seismic phase and generally do not produce the strong ground motions that cause damage; the later-arriving shear (S) waves and surface waves (e.g., Rayleigh waves) are responsible for most of the hazardous shaking. Early-warning systems exploit this separation in arrival times by detecting P-wave onsets and using the intervening interval before destructive phases reach a site to issue alerts or initiate protective measures. The warning interval available at a given location equals the time between the first P-wave detection and the arrival of the damaging waves and can range from only a few seconds up to on the order of one to one and a half minutes in the case of very large, deep, and distant earthquakes (for example, the 2011 Tohoku event). Longer lead times tend to occur when earthquakes are larger, deeper, or farther from the protected area because the P phase arrives well before the more energetic later phases. Reliable early warning therefore depends on extremely rapid and accurate discrimination of true P-wave signals from local non‑seismic noise (such as heavy traffic or construction) to avoid false alarms and missed events. When P-wave detections are validated, systems can be automated to trigger immediate safety actions—public alerts, elevator stops at the nearest floor, utility shutdowns and other procedures—to reduce exposure and secondary hazards.
P waves are compressional body waves in which particle motion is parallel to wave propagation; in isotropic, homogeneous solids they travel along straight rays as material elements oscillate back and forth on the direction of energy transmission. The propagation speed v_p is determined by the elastic response and density of the medium and may be written exactly as
v_p = sqrt((K + 4/3 μ)/ρ) = sqrt((λ + 2μ)/ρ),
where K is the bulk modulus, μ (or G) the shear modulus, λ the first Lamé parameter, and ρ the mass density. Because density within the Earth varies relatively little compared with the elastic moduli, it is convenient to define the P‑wave (elastic) modulus M = K + 4/3 μ and express v_p = sqrt(M/ρ), which highlights that elastic stiffness typically controls P‑wave velocity more strongly than density.
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Seismological observations and laboratory measurements yield typical earthquake P‑wave speeds of roughly 5–8 km s−1; speeds increase with depth from under ~6 km s−1 in much of the crust to about 13.5 km s−1 in the lower mantle and on the order of 11 km s−1 through the inner core, reflecting systematic changes in elastic moduli and phase state with pressure and temperature. Representative laboratory/field velocities for common lithologies include: unconsolidated sandstone ~4,600–5,200 m s−1 (15,000–17,000 ft s−1); consolidated sandstone ~5,800 m s−1 (19,000 ft s−1); shale ~1,800–4,900 m s−1 (6,000–16,000 ft s−1); limestone ~5,800–6,400 m s−1 (19,000–21,000 ft s−1); dolomite ~6,400–7,300 m s−1 (21,000–24,000 ft s−1); anhydrite ~6,100 m s−1 (20,000 ft s−1); granite ~5,800–6,100 m s−1 (19,000–20,000 ft s−1); and gabbro ~7,200 m s−1 (23,600 ft s−1).
Empirical relations are used to relate v_p and ρ across diverse rocks and conditions; one common form (Birch’s law) casts velocity as v_p = a(M̄) + b ρ, with a(·) an empirically determined function of a mean modulus M̄ and b an empirical coefficient, providing practical fits for seismic interpretation and rock‑property estimation.