Shadow zone

The earth is made up of different structures: the crust, the mantle, the inner core and the outer core. The crust, mantle, and inner core are typically solid; however, the outer core is entirely liquid.[1] A liquid outer core was first shown in 1906 by Geologist Richard Oldham.[2] Oldham observed seismograms from various earthquakes and saw that some seismic stations did not record direct S waves, particularly ones that were 120° away from the hypocenter of the earthquake.[3]

In 1913, Beno Gutenberg noticed the abrupt change in seismic velocities of the P waves and disappearance of S waves at the core-mantle boundary. Gutenberg attributed this due to a solid mantle and liquid outer core, calling it the Gutenberg discontinuity.[4]

The main observational constraint on identifying liquid layers and/or structures within the earth come from seismology. When an earthquake occurs, seismic waves radiate out spherically from the earthquake's hypocenter.[5] Two types of body waves travel through the Earth: primary seismic waves (P waves) and secondary seismic waves (S waves). P waves travel with motion in the same direction as the wave propagates and S-waves travel with motion perpendicular to the wave propagation (transverse).[6]

The P waves are refracted by the liquid outer core of the Earth and are not detected between 104° and 140° (between approximately 11,570 and 15,570 km or 7,190 and 9,670 mi) from the hypocenter.[7][8] This is due to Snell's law, where a seismic wave encounters a boundary and either refracts or reflects. In this case, the P waves refract due to density differences and greatly reduce in velocity.[7][9] This is considered the P wave shadow zone.[10]

The S waves cannot pass through the liquid outer core and are not detected more than 104° (approximately 11,570 km or 7,190 mi) from the epicenter.[7][11][12] This is considered the S wave shadow zone.[10] However, P waves that travel refract through the outer core and refract to another P wave (PKP wave) on leaving the outer core can be detected within the shadow zone. Additionally, S waves that refract to P waves on entering the outer core and then refract to an S wave on leaving the outer core can also be detected in the shadow zone (SKS waves).[7][13]

The reason for this is P wave and S wave velocities are governed by different properties in the material which they travel through and the different mathematical relationships they share in each case. The three properties are: The three properties are: incompressibility (${\displaystyle k}$), density (${\displaystyle p}$) and rigidity (${\displaystyle u}$).[11][14]

P wave velocity is equal to:

${\displaystyle {\sqrt {(k+{\tfrac {4}{3}}u)/p}}}$

S wave velocity is equal to:

${\displaystyle {\sqrt {u/p}}}$

S wave velocity is entirely dependent on the rigidity of the material it travels through. Liquids have zero rigidity, making the S-wave velocity zero when traveling through a liquid. Overall, S waves are shear waves, and shear stress is a type of deformation that cannot occur in a liquid.[11][12][14] Conversely, P waves are compressional waves and are only partially dependent on rigidity. P waves still maintain some velocity (can be greatly reduced) when traveling through a liquid.[7][8][14][15]

Although the core-mantle boundary casts the largest shadow zone, smaller structures, such as magma bodies, can also cast a shadow zone. For example, in 1981, Páll Einarsson conducted a seismic investigation on the Krafla Caldera in Northeast Iceland.[16] In this study, Einarsson placed a dense array of seismometers over the caldera and recorded earthquakes that occurred. The resulting seismograms showed both an absence of S waves and/or small S wave amplitudes. Einarsson attributed these results to be caused by a magma reservoir. In this case, the magma reservoir has enough percent melt to cause S waves to be directly affected.[16] In areas where there are no S waves being recorded, the S waves are encountering enough liquid, that no solid grains are touching.[17] In areas where there are highly attenuated (small aptitude) S waves, there is still a precent of melt, but enough solid grains are touching where S waves can travel through the part of the magma reservoir.[12][15][18]

Between 2014 and 2018, a geophysicist in Taiwan, Cheng-Horng Lin investigated the magma reservoir beneath the Tatun Volcano Group in Taiwan.[19][20] Lin's research group used deep earthquakes and seismometers on or near the Tatun Volcano Group to identify changes P and S waveforms. Their results showed P wave delays and the absence of S waves in various locations. Lin attributed this finding to be due to a magma reservoir with at least 40% melt that casts an S wave shadow zone.[19][20] However, a recent study done by National Chung Cheng University used a dense array of seismometers and only saw S wave attenuation associated with the magma reservoir.[21] This research study investigated the cause of the S wave shadow zone Lin observed and attributed it to either a magma diapir above the subducting Philippine Sea Plate. Though it was not a magma reservoir, there was still a structure with enough melt/liquid to cause an S wave shadow zone.[21]

The existence of shadow zones, more specifically S wave shadow zones, could have implications on the eruptibility of volcanoes throughout the world. When volcanoes have enough percent melt to go below the rheological lockup (percent crystal fraction when a volcano is eruptive or not eruptive), this makes the volcanoes eruptible.[22][23] Determining the percent melt of a volcano could help with predictive modeling and assess current and future hazards. In an actively erupting volcano, Mt. Etna in Italy, a study was done in 2021 that showed both an absence of S-waves in some regions and highly attenuated S-waves in others, depending on where the receivers are located above the magma chamber.[24] Previously, in 2014, a study was done to model the mechanism leading to the December 28th, 2014 eruption. This study showed that an eruption could be triggered between 30-70% melt.[25]

• Seismic wave
• Ray tracing (physics)
• P wave
• S wave
• Snell's Law
• Structure of Earth
• Core-mantle boundary