Earth:Shadow zone

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Short description: Area not reached by seismic waves from an earthquake
Seismic shadow zone (from USGS)
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A seismic shadow zone is an area of the Earth's surface where seismographs cannot detect direct P waves and/or S waves from an earthquake. This is due to liquid layers or structures within the Earth's surface. The most recognized shadow zone is due to the core-mantle boundary where P waves are refracted and S waves are stopped at the liquid outer core; however, any liquid boundary or body can create a shadow zone. For example, magma reservoirs with a high enough percent melt can create seismic shadow zones.

Background

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]

Seismic wave properties

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: incompressibility ([math]\displaystyle{ k }[/math]), density ([math]\displaystyle{ p }[/math]) and rigidity ([math]\displaystyle{ u }[/math]).[11][14]

P wave velocity is equal to:

[math]\displaystyle{ \sqrt{(k+\tfrac{4}{3}u)/p} }[/math]

S wave velocity is equal to:

[math]\displaystyle{ \sqrt{u/p} }[/math]

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]

Other observations and implications

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 Volcanic Group in Taiwan.[19][20] 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.[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]

See also

References

  1. ↑ Encyclopedia of solid earth geophysics. Harsh K. Gupta. Dordrecht: Springer. 2011. ISBN 978-90-481-8702-7. OCLC 745002805. https://www.worldcat.org/oclc/745002805. 
  2. ↑ Bragg, William (1936-12-18). "Tribute to Deceased Fellows of the Royal Society" (in en). Science 84 (2190): 539–546. doi:10.1126/science.84.2190.539. ISSN 0036-8075. PMID 17834950. https://www.science.org/doi/10.1126/science.84.2190.539. 
  3. ↑ Brush, Stephen G. (September 1980). "Discovery of the Earth's core" (in en). American Journal of Physics 48 (9): 705–724. doi:10.1119/1.12026. ISSN 0002-9505. http://aapt.scitation.org/doi/10.1119/1.12026. 
  4. ↑ Michael Allaby (2008). A dictionary of earth sciences. (3rd ed.). Oxford. ISBN 978-0-19-921194-4. OCLC 177509121. 
  5. ↑ "Earthquake Glossary". https://earthquake.usgs.gov/learn/glossary/?term=seismic%20wave. 
  6. ↑ Fowler, C. M. R. (2005). The solid earth: an introduction to global geophysics (2nd ed.). Cambridge, UK: Cambridge University Press. ISBN 0-521-89307-0. OCLC 53325178. 
  7. ↑ 7.0 7.1 7.2 7.3 7.4 "CHAPTER 19 NOTES Earth's (Interior)". https://uh.edu/~geos6g/1330/interior.html. 
  8. ↑ 8.0 8.1 "Earthquake Glossary". https://earthquake.usgs.gov/learn/glossary/?termID=170&alpha=S. 
  9. ↑ "Snell's Law -- The Law of Refraction". https://personal.math.ubc.ca/~cass/courses/m309-01a/chu/Fundamentals/snell.htm. 
  10. ↑ 10.0 10.1 "Seismic Shadow Zone: Basic Introduction- Incorporated Research Institutions for Seismology". https://www.iris.edu/hq/inclass/animation/seismic_shadow_zone_basic_introduction. 
  11. ↑ 11.0 11.1 11.2 "Why can't S-waves travel through liquids?" (in en). https://www.earthobservatory.sg/faq-on-earth-sciences/why-cant-s-waves-travel-through-liquids. 
  12. ↑ 12.0 12.1 12.2 Greenwood, Margaret Stautberg; Bamberger, Judith Ann (August 2002). "Measurement of viscosity and shear wave velocity of a liquid or slurry for on-line process control" (in en). Ultrasonics 39 (9): 623–630. doi:10.1016/S0041-624X(02)00372-4. PMID 12206629. https://linkinghub.elsevier.com/retrieve/pii/S0041624X02003724. 
  13. ↑ Kennett, Brian (2007), Gubbins, David; Herrero-Bervera, Emilio, eds. (in en), Seismic Phases, Dordrecht: Springer Netherlands, pp. 903–908, doi:10.1007/978-1-4020-4423-6_290, ISBN 978-1-4020-4423-6, https://doi.org/10.1007/978-1-4020-4423-6_290, retrieved 2021-12-10 
  14. ↑ 14.0 14.1 14.2 Dziewonski, Adam M.; Anderson, Don L. (June 1981). "Preliminary reference Earth model" (in en). Physics of the Earth and Planetary Interiors 25 (4): 297–356. doi:10.1016/0031-9201(81)90046-7. https://linkinghub.elsevier.com/retrieve/pii/0031920181900467. 
  15. ↑ 15.0 15.1 Båth, Markus (1957). "Shadow zones, travel times, and energies of longitudinal seismic waves in the presence of an asthenosphere low-velocity layer" (in en). Eos, Transactions American Geophysical Union 38 (4): 529–538. doi:10.1029/TR038i004p00529. ISSN 2324-9250. https://onlinelibrary.wiley.com/doi/abs/10.1029/TR038i004p00529. 
  16. ↑ 16.0 16.1 Einarsson, P. (September 1978). "S-wave shadows in the Krafla Caldera in NE-Iceland, evidence for a magma chamber in the crust". Bulletin Volcanologique 41 (3): 187–195. doi:10.1007/bf02597222. ISSN 0258-8900. http://dx.doi.org/10.1007/bf02597222. 
  17. ↑ Asimow, Paul D. (2016), White, William M., ed. (in en), Partial Melting, Encyclopedia of Earth Sciences Series, Cham: Springer International Publishing, pp. 1–6, doi:10.1007/978-3-319-39193-9_218-1, ISBN 978-3-319-39193-9, https://doi.org/10.1007/978-3-319-39193-9_218-1, retrieved 2021-12-10 
  18. ↑ Sheriff, R. E. (1975). "Factors Affecting Seismic Amplitudes*" (in en). Geophysical Prospecting 23 (1): 125–138. doi:10.1111/j.1365-2478.1975.tb00685.x. ISSN 1365-2478. https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1365-2478.1975.tb00685.x. 
  19. ↑ 19.0 19.1 Lin, Cheng-Horng (2016-12-23). "Evidence for a magma reservoir beneath the Taipei metropolis of Taiwan from both S-wave shadows and P-wave delays" (in en). Scientific Reports 6 (1): 39500. doi:10.1038/srep39500. ISSN 2045-2322. PMID 28008931. 
  20. ↑ 20.0 20.1 Lin, Cheng-Horng; Lai, Ya-Chuan; Shih, Min-Hung; Pu, Hsin-Chieh; Lee, Shiann-Jong (2018-11-06). "Seismic Detection of a Magma Reservoir beneath Turtle Island of Taiwan by S-Wave Shadows and Reflections" (in en). Scientific Reports 8 (1): 16401. doi:10.1038/s41598-018-34596-0. ISSN 2045-2322. PMID 30401817. 
  21. ↑ 21.0 21.1 Yeh, Yu-Lien; Wang, Wei-Hau; Wen, Strong (2021-01-13). "Dense seismic arrays deny a massive magma chamber beneath the Taipei metropolis, Taiwan". Scientific Reports 11 (1): 1083. doi:10.1038/s41598-020-80051-4. ISSN 2045-2322. PMID 33441717. PMC 7806728. http://dx.doi.org/10.1038/s41598-020-80051-4. 
  22. ↑ Cooper, Kari M.; Kent, Adam J. R. (2014-02-16). "Rapid remobilization of magmatic crystals kept in cold storage". Nature 506 (7489): 480–483. doi:10.1038/nature12991. ISSN 0028-0836. PMID 24531766. http://dx.doi.org/10.1038/nature12991. 
  23. ↑ Marsh, B. D. (October 1981). "On the crystallinity, probability of occurrence, and rheology of lava and magma". Contributions to Mineralogy and Petrology 78 (1): 85–98. doi:10.1007/bf00371146. ISSN 0010-7999. http://dx.doi.org/10.1007/bf00371146. 
  24. ↑ De Gori, Pasquale; Giampiccolo, Elisabetta; Cocina, Ornella; Branca, Stefano; Doglioni, Carlo; Chiarabba, Claudio (2021-10-12). "Re-pressurized magma at Mt. Etna, Italy, may feed eruptions for years" (in en). Communications Earth & Environment 2 (1): 1–9. doi:10.1038/s43247-021-00282-9. ISSN 2662-4435. 
  25. ↑ Ferlito, C.; Bruno, V.; Salerno, G.; Caltabiano, T.; Scandura, D.; Mattia, M.; Coltorti, M. (2017-07-13). "Dome-like behaviour at Mt. Etna: The case of the 28 December 2014 South East Crater paroxysm" (in en). Scientific Reports 7 (1): 5361. doi:10.1038/s41598-017-05318-9. ISSN 2045-2322. PMID 28706233. 



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