Banana Doughnut theory

Short description: Model in seismic tomography

Schematic illustration of the first Fresnel zone for one source-receiver pair. W indicates the width of the first Fresnel zone.

The banana doughnut theory[1][2] \- also sometimes known as Born-Fréchet kernel theory, or finite-frequency theory \- is a model in seismic tomography that describes the shape of the Fresnel zone along the entire ray path of a body wave. This theory suggests that the area that influences the ray velocity is the surrounding material and not the infinitesimally small ray path. This surrounding material forms a tube enclosing the ray, but does not incorporate the ray path itself.

The name was coined by Princeton University postdoc Henk Marquering.[3] This theory gets the name "banana" because the tube of influence along the entire ray path from source to receiver is an arc resembling the fruit. The "doughnut" part of the name comes from the ring shape of the cross-section. The ray path is a hollow banana, or a banana-shaped doughnut.[4]

Mohammad Youssof and colleagues (Youssof et al., 2015)[5] of Rice University and the University of Copenhagen conducted one of the studies that compared both the Born-Fréchet kernel theory and the infinitesimal geometrical ray theory when they used the same datasets to see the resolving power on real datasets from the South African Seismic Array [SASE] in Kalahari (Carlson et al., 1996)[6] and compared their results when using one and multiple frequencies to previous studies by Fouch et al. (2004),[7] Priestley et al. (2006),[8] and Silver et al. (2001).[9] Youssof et al. (2015) models are similar in some ways, but they also have significant differences which include new results of cratonic boundaries, the keels' depth, and their structures.

## References

1. ↑ Dahlen, F. A.; Hung, S.-H.; Nolet, Guust (April 2000). "Fréchet kernels for finite-frequency traveltimes-I. Theory". Geophysical Journal International 141 (1): 157–174. doi:10.1046/j.1365-246X.2000.00070.x. Bibcode: 2000GeoJI.141..157D.
2. ↑ van der Hilst, Robert D.; de Hoop, Maarten V. (December 2005). "Banana-doughnut kernels and mantle tomography". Geophysical Journal International 163 (3): 956–961. doi:10.1111/j.1365-246X.2005.02817.x. Bibcode: 2005GeoJI.163..956V.
3. ↑ "The Banana-Doughnut Debate Explained". https://www.geoazur.fr/GLOBALSEIS/nolet/BDdiscussion.html. [self-published source?]
4. ↑ An image of the model can be found here.
5. ↑ Youssof, M.; Thybo, H.; Artemieva, I.M.; Levander, A. (June 2015). "Upper mantle structure beneath southern African cratons from seismic finite-frequency P- and S-body wave tomography". Earth and Planetary Science Letters 420: 174–186. doi:10.1016/j.epsl.2015.01.034. Bibcode: 2015E&PSL.420..174Y.
6. ↑ Carlson, Richard W.; Grove, Timothy L.; De Wit, Maarten J.; Gurney, John J. (16 July 1996). "Program to study crust and mantle of the Archean craton in southern Africa". Eos, Transactions American Geophysical Union 77 (29): 273–277. doi:10.1029/96EO00194. Bibcode: 1996EOSTr..77Q.273C.
7. ↑ Fouch, M. J. (June 2004). "Mantle seismic structure beneath the Kaapvaal and Zimbabwe Cratons". South African Journal of Geology 107 (1–2): 33–44. doi:10.2113/107.1-2.33. Bibcode: 2004SAJG..107...33F.
8. ↑ Priestley, Keith; McKenzie, Dan; Debayle, Eric (April 2006). "The state of the upper mantle beneath southern Africa". Tectonophysics 416 (1–4): 101–112. doi:10.1016/j.tecto.2005.11.024. Bibcode: 2006Tectp.416..101P.
9. ↑ Silver, Paul G.; Gao, Stephen S.; Liu, Kelly H. (July 2001). "Mantle deformation beneath southern Africa". Geophysical Research Letters 28 (13): 2493–2496. doi:10.1029/2000GL012696. Bibcode: 2001GeoRL..28.2493S.

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