Introduction
When seismic waves travel through Earth, they do not move in straight lines. Like light rays entering a glass lens, seismic waves bend (refract) whenever they cross a boundary where velocity changes, and reflect whenever the velocity contrast is sharp enough. Because seismic velocity generally increases with depth in the mantle — pressure increases K and μ faster than ρ — wave paths curve continuously, bending away from the vertical and eventually turning back toward the surface. This continuous refraction creates curved ray paths that were first analysed mathematically by Karl Zoeppritz and Beno Gutenberg in the early twentieth century.
The most important velocity boundaries in Earth are the Mohorovičić discontinuity (Moho), the 410 km (255 mi) and 660 km (410 mi) transition zone discontinuities, and the core-mantle boundary (CMB) at 2,891 km (1796 mi) depth. At the Moho, P-wave velocity jumps abruptly from ~6.5 km/s (continental crust) to ~8.0 km/s (uppermost mantle), first detected by Croatian seismologist Andrija Mohorovičić in 1909 by analysing a local Croatian earthquake: at stations close to the earthquake, direct crustal P-waves arrived first; at greater distances, waves that had refracted along the top of the faster mantle ("head waves") overtook them and arrived first, revealing the faster layer below. The crossover distance (where head waves overtake direct waves) gave Mohorovičić the depth to his discontinuity — about 54 km (34 mi) beneath Croatia — and the principle he established is now used globally. The Moho marks the boundary between crust and mantle — but a far more dramatic velocity boundary lies deeper, at the outer edge of the core, where wave bending creates the shadow zones that first revealed Earth's liquid outer core.
The shadow zones are perhaps the most dramatic demonstration of seismic wave bending. P-waves traveling toward Earth's opposite side reach a region called the P-wave shadow zone between 105° and 140° of angular distance from the earthquake — no direct P-waves arrive there because the core-mantle boundary refracts the waves sharply downward (the P-wave velocity drops from ~13.7 km/s in the base of the lower mantle to ~8.1 km/s in the outer core — a large velocity decrease that bends waves toward the core's centre rather than through the shadow zone). S-waves cannot penetrate the liquid outer core at all, creating an even larger S-wave shadow zone beyond 105° from the earthquake. Within the P-wave shadow zone at 105°-140°, very weak P-wave arrivals called PKP phases can still be detected — these are waves that entered and exited the outer core but took more complex curved paths. Richard Dixon Oldham first recognised these shadow zones in 1906, proving Earth had a distinct core.
The inner core adds another layer of seismic complexity. P-waves that travel all the way through the inner core (PKIKP phases) arrive within the shadow zone at distances beyond 150°. The inner core's P-wave velocity (~11 km/s, higher than the outer core's ~10 km/s) and the detection of weak S-waves (PKJKP phases) transmitted through the inner core confirm it is solid. Danish seismologist Inge Lehmann discovered the inner core in 1936 from careful analysis of PKIKP arrivals. Furthermore, the inner core appears to be seismically anisotropic — P-waves traveling parallel to Earth's rotation axis are ~3-4% faster than those traveling through the equatorial plane — probably because iron crystals in the inner core are aligned by the magnetic field or by slow differential rotation (~0.3-0.5°/yr faster than the mantle).
Key Terms
Snell's Law describes how seismic waves bend at a velocity boundary — the greater the velocity contrast, the sharper the bend. Mathematically: sin(i₁)/v₁ = sin(i₂)/v₂, where i is the angle of incidence measured from vertical and v is wave speed in each layer. It causes waves to bend away from regions of low velocity toward regions of high velocity. In Earth's mantle, where velocity increases continuously with depth, Snell's law produces concave-upward ray arcs that curve progressively away from vertical until they turn back toward the surface, allowing body waves from a single earthquake to return to the surface at a range of epicentral distances.
The seismic and chemical boundary between Earth's crust and mantle, where P-wave velocity jumps abruptly from ~6.5 km/s to ~8.0 km/s. Depth varies: ~7 km (4.3 mi) beneath oceanic crust and ~35-70 km (43 mi) beneath continents (global average ~35 km (22 mi)). Discovered in 1909 by Croatian seismologist Andrija Mohorovičić, who identified the velocity jump from the crossover distance at which mantle head waves overtook direct crustal P-waves in travel-time records from a local earthquake. The Moho defines the base of the crust both chemically (change from felsic/mafic crustal rock to ultramafic peridotite) and seismically.
A region at 105°-140° of angular distance from an earthquake where direct P-waves do not arrive at the surface. The shadow zone is caused by refraction at the core-mantle boundary: as P-wave velocity drops sharply from ~13.7 km/s at the base of the lower mantle to ~8.1 km/s in the outer core, Snell's law bends incoming rays steeply downward, deflecting them away from the 105°-140° angular range. Waves arriving shallower than the critical angle return to the surface at less than 105°; waves entering the core emerge beyond 140°. First identified by Richard Dixon Oldham in 1906, the shadow zone was the original proof that Earth has a distinct core.
A seismic phase in which a P-wave travels down through the mantle (P), refracts into the liquid outer core (K), transmits through the solid inner core (I), exits the inner core back into the outer core (K again), and returns through the mantle to the surface (P). PKIKP phases arrive within the P-wave shadow zone at distances of 150°-180° from the source. The velocity increase encountered in the inner core (~11 km/s vs. ~10 km/s in the outer core) causes inner-core-crossing rays to be focused back toward the surface, producing real arrivals where the simple outer-core model predicts silence. Inge Lehmann used these anomalous arrivals in 1936 to discover the inner core.
A property of a material or region in which the velocity of seismic waves varies depending on the direction of propagation or polarisation. In Earth's inner core, P-waves traveling parallel to the rotation axis are ~3-4% faster than those traveling through the equatorial plane, probably due to preferential alignment of hexagonal close-packed iron (hcp ε-iron) crystals. The crust and upper mantle also exhibit anisotropy from aligned olivine crystals or fluid-filled fractures, which seismologists use to infer past strain history and present-day mantle flow directions.