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.{{Cite book|url=https://www.worldcat.org/oclc/745002805|title=Encyclopedia of solid earth geophysics|date=2011|publisher=Springer|others=Harsh K. Gupta|isbn=978-90-481-8702-7|location=Dordrecht|oclc=745002805}} A liquid outer core was first shown in 1906 by Geologist Richard Oldham.{{Cite journal|last=Bragg|first=William|date=1936-12-18|title=Tribute to Deceased Fellows of the Royal Society|url=https://www.science.org/doi/10.1126/science.84.2190.539|journal=Science|language=en|volume=84|issue=2190|pages=539–546|doi=10.1126/science.84.2190.539|pmid=17834950 |issn=0036-8075}} 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.{{Cite journal|last=Brush|first=Stephen G.|date=September 1980|title=Discovery of the Earth's core|url=http://aapt.scitation.org/doi/10.1119/1.12026|journal=American Journal of Physics|language=en|volume=48|issue=9|pages=705–724|doi=10.1119/1.12026|issn=0002-9505}}

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.{{Cite book |title=A dictionary of earth sciences.|date=2008|author=Michael Allaby|isbn=978-0-19-921194-4|edition=3rd |location=Oxford|oclc=177509121}}

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.{{Cite web|title=Earthquake Glossary|url=https://earthquake.usgs.gov/learn/glossary/?term=seismic%20wave|access-date=2021-12-10|publisher=United States Geological Survey}} 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).{{Cite book|last=Fowler|first=C. M. R. |title=The solid earth: an introduction to global geophysics|date=2005|publisher=Cambridge University Press|isbn=0-521-89307-0|edition=2nd |location=Cambridge, UK|oclc=53325178}}

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.{{Cite web|title=CHAPTER 19 NOTES Earth's (Interior)|url=https://uh.edu/~geos6g/1330/interior.html|access-date=2021-12-10|website=uh.edu}}{{Cite web|title=Earthquake Glossary|url=https://earthquake.usgs.gov/learn/glossary/?termID=170&alpha=S|access-date=2021-12-10|publisher=United States Geological Survey}} 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.{{Cite web|title=Snell's Law -- The Law of Refraction|url=https://personal.math.ubc.ca/~cass/courses/m309-01a/chu/Fundamentals/snell.htm|access-date=2021-12-10|website=personal.math.ubc.ca}} This is considered the P wave shadow zone.{{Cite web|title=Seismic Shadow Zone: Basic Introduction- Incorporated Research Institutions for Seismology|url=https://www.iris.edu/hq/inclass/animation/seismic_shadow_zone_basic_introduction|access-date=2021-12-10|publisher=IRIS Consortium}}

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.{{Cite web|title=Why can't S-waves travel through liquids?|url=https://www.earthobservatory.sg/faq-on-earth-sciences/why-cant-s-waves-travel-through-liquids|access-date=2021-12-10|website=Earth Observatory of Singapore|language=en}}{{Cite journal|last1=Greenwood|first1=Margaret Stautberg|last2=Bamberger|first2=Judith Ann|author2-link= Judith Bamberger |date=August 2002|title=Measurement of viscosity and shear wave velocity of a liquid or slurry for on-line process control|url=https://linkinghub.elsevier.com/retrieve/pii/S0041624X02003724|journal=Ultrasonics|language=en|volume=39|issue=9|pages=623–630|doi=10.1016/S0041-624X(02)00372-4|pmid=12206629 }} This is considered the S wave shadow zone. 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).{{Citation|last=Kennett|first=Brian|title=Seismic Phases|date=2007|url=https://doi.org/10.1007/978-1-4020-4423-6_290|encyclopedia=Encyclopedia of Geomagnetism and Paleomagnetism|pages=903–908|editor-last=Gubbins|editor-first=David|place=Dordrecht|publisher=Springer Netherlands|language=en|doi=10.1007/978-1-4020-4423-6_290|isbn=978-1-4020-4423-6|access-date=2021-12-10|editor2-last=Herrero-Bervera|editor2-first=Emilio}}

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: incompressibility ($k$), density ($p$) and rigidity ($u$).{{Cite journal|last1=Dziewonski|first1=Adam M.|last2=Anderson|first2=Don L.|date=June 1981|title=Preliminary reference Earth model|url=https://linkinghub.elsevier.com/retrieve/pii/0031920181900467|journal=Physics of the Earth and Planetary Interiors|language=en|volume=25|issue=4|pages=297–356|doi=10.1016/0031-9201(81)90046-7}}

P wave velocity is equal to:

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

S wave velocity is equal to:

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

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. 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.{{Cite journal|last=Båth|first=Markus|date=1957|title=Shadow zones, travel times, and energies of longitudinal seismic waves in the presence of an asthenosphere low-velocity layer|url=https://onlinelibrary.wiley.com/doi/abs/10.1029/TR038i004p00529|journal=Eos, Transactions American Geophysical Union|language=en|volume=38|issue=4|pages=529–538|doi=10.1029/TR038i004p00529|issn=2324-9250}}

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.{{Cite journal|last=Einarsson|first=P.|date=September 1978|title=S-wave shadows in the Krafla Caldera in NE-Iceland, evidence for a magma chamber in the crust|url=http://dx.doi.org/10.1007/bf02597222|journal=Bulletin Volcanologique|volume=41|issue=3|pages=187–195|doi=10.1007/bf02597222|s2cid=128433156 |issn=0258-8900|hdl=20.500.11815/4200|hdl-access=free}} 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. In areas where there are no S waves being recorded, the S waves are encountering enough liquid, that no solid grains are touching.{{Citation|last=Asimow|first=Paul D.|title=Partial Melting|date=2016|url=https://doi.org/10.1007/978-3-319-39193-9_218-1|encyclopedia=Encyclopedia of Geochemistry: A Comprehensive Reference Source on the Chemistry of the Earth|series=Encyclopedia of Earth Sciences Series |pages=1–6|editor-last=White|editor-first=William M.|place=Cham|publisher=Springer International Publishing|language=en|doi=10.1007/978-3-319-39193-9_218-1|isbn=978-3-319-39193-9|access-date=2021-12-10}} In areas where there are highly attenuated (small aptitude) S waves, there is still a percentage of melt, but enough solid grains are touching where S waves can travel through the part of the magma reservoir.{{Cite journal|last=Sheriff|first=R. E.|date=1975|title=Factors Affecting Seismic Amplitudes*|url=https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1365-2478.1975.tb00685.x|journal=Geophysical Prospecting|language=en|volume=23|issue=1|pages=125–138|doi=10.1111/j.1365-2478.1975.tb00685.x|issn=1365-2478}}

Between 2014 and 2018, a geophysicist in Taiwan, Cheng-Horng Lin investigated the magma reservoir beneath the Tatun Volcanic Group in Taiwan.{{Cite journal|last=Lin|first=Cheng-Horng|date=2016-12-23|title=Evidence for a magma reservoir beneath the Taipei metropolis of Taiwan from both S-wave shadows and P-wave delays|journal=Scientific Reports|language=en|volume=6|issue=1|pages=39500|doi=10.1038/srep39500|pmid=28008931 |pmc=5180088 |s2cid=968378 |issn=2045-2322|doi-access=free}}{{Cite journal|last1=Lin|first1=Cheng-Horng|last2=Lai|first2=Ya-Chuan|last3=Shih|first3=Min-Hung|last4=Pu|first4=Hsin-Chieh|last5=Lee|first5=Shiann-Jong|date=2018-11-06|title=Seismic Detection of a Magma Reservoir beneath Turtle Island of Taiwan by S-Wave Shadows and Reflections|journal=Scientific Reports|language=en|volume=8|issue=1|pages=16401|doi=10.1038/s41598-018-34596-0|pmid=30401817 |pmc=6219605 |s2cid=53228649 |issn=2045-2322|doi-access=free}} Lin's research group used deep earthquakes and seismometers on or near the Tatun Volcanic 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. 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.{{Cite journal|last1=Yeh|first1=Yu-Lien|last2=Wang|first2=Wei-Hau|last3=Wen|first3=Strong|date=2021-01-13|title=Dense seismic arrays deny a massive magma chamber beneath the Taipei metropolis, Taiwan|url=http://dx.doi.org/10.1038/s41598-020-80051-4|journal=Scientific Reports|volume=11|issue=1|page=1083 |doi=10.1038/s41598-020-80051-4|pmid=33441717 | pmc=7806728 |issn=2045-2322}} 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.

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.{{Cite journal|last1=Cooper|first1=Kari M.|last2=Kent|first2=Adam J. R.|date=2014-02-16|title=Rapid remobilization of magmatic crystals kept in cold storage|url=http://dx.doi.org/10.1038/nature12991|journal=Nature|volume=506|issue=7489|pages=480–483|doi=10.1038/nature12991|pmid=24531766 |s2cid=4450434 |issn=0028-0836}}{{Cite journal|last=Marsh|first=B. D.|date=October 1981|title=On the crystallinity, probability of occurrence, and rheology of lava and magma|url=http://dx.doi.org/10.1007/bf00371146|journal=Contributions to Mineralogy and Petrology|volume=78|issue=1|pages=85–98|doi=10.1007/bf00371146|s2cid=73583798 |issn=0010-7999}} 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.{{Cite journal|last1=De Gori|first1=Pasquale|last2=Giampiccolo|first2=Elisabetta|last3=Cocina|first3=Ornella|last4=Branca|first4=Stefano|last5=Doglioni|first5=Carlo|last6=Chiarabba|first6=Claudio|date=2021-10-12|title=Re-pressurized magma at Mt. Etna, Italy, may feed eruptions for years|journal=Communications Earth & Environment|language=en|volume=2|issue=1|pages=1–9|doi=10.1038/s43247-021-00282-9|s2cid=238586951 |issn=2662-4435|doi-access=free}} Previously, in 2014, a study was done to model the mechanism leading to December 28, 2014, eruption. This study showed that an eruption could be triggered between 30 and 70% melt.{{Cite journal|last1=Ferlito|first1=C.|last2=Bruno|first2=V.|last3=Salerno|first3=G.|last4=Caltabiano|first4=T.|last5=Scandura|first5=D.|last6=Mattia|first6=M.|last7=Coltorti|first7=M.|date=2017-07-13|title=Dome-like behaviour at Mt. Etna: The case of the 28 December 2014 South East Crater paroxysm|journal=Scientific Reports|language=en|volume=7|issue=1|pages=5361|doi=10.1038/s41598-017-05318-9|pmid=28706233 |pmc=5509668 |s2cid=10170141 |issn=2045-2322|doi-access=free}}

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

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Category:Seismology