# Gravity effect of spreading ridges: comparison of 2D and spherical models

- 125 Downloads
- 4 Citations

## Abstract

Because of its importance to many Earth science analyses, it is worth assessing whether gravity modelling can be simplified depending on the intended purpose and required precision. While it is obvious that large-scale gravity studies should account for the sphericity of the Earth, each case should be examined on its own merits. Demonstrations are useful for providing estimates of the errors in much simpler 2D modelling. The example of the Mid-Atlantic Ridge serves to compare “large” 2D and spherical 3D models. My model extends horizontally ±2,000 km (±18°) from the model profile across and along the straight ridge axis (along a great circle) and to a depth of 82 km across the axis. 3D modelling would generally be considered obligatory, but this is not clearly necessary from this study. The density structure is highly idealised, the asthenospheric uplift or lithosphere thinning is simplified. The Bouguer anomaly is fitted by least-squares for the density contrast, and the 2D–3D difference of the results is taken as the error. A lithosphere–asthenosphere density contrast of 86.56 kg/m^{3} was computed for the 2D model, and 84.14 kg/m^{3} for the spherical model. The difference is small, in the order of 3%, well within all the other uncertainties. My study shows that despite the significant sphericity of the structure, 2D models are well suited for such ridge studies, or generally for models with a laterally extended layered structure, and that spherical modelling can be applied discriminately.

## Keywords

2D Spherical gravity modelling Ocean ridges## Notes

### Acknowledgments

I thank my former advisor, Prof. Dr. Wolfgang Jacoby for his suggestions, encouragement and efforts with helping me formulate this work in English. I thank Dr Horst Holstein, from whom I have benefited through helpful discussions. I also thank Dr. Peter Clift for his suggestions. The reviewers gave further helpful criticism.

## References

- Artemieva IM, Mooney WD (2002) Thermal thickness and evolution of Precembrian lithosphere: a global study. J Geophys Res 106:16387–16416. doi: 10.1029/2000JB900439 CrossRefGoogle Scholar
- Çavşak H (1992) Dichtemodelle für den mitteleuropäischen Abschnitt der EGT aufgrund der gemeinsamen Inversion von Geoid, Schwere und refraktionsseismisch ermittelter Krustenstruktur (in German: Density models for the central European Section of EGT on the basis of joint inversion of geoid, gravity and refraction seismic crustal structure). Ph.D. Thesis, Mainz UniversityGoogle Scholar
- Chapman ME (1979) Techniques for interpretation of geoid anomalies. J Geophys Res 84:3793–3801. doi: 10.1029/JB084iB08p03793 CrossRefGoogle Scholar
- Cochran JR, Talwani M (1978) Gravity anomalies, regional elevation, and the deep structure of the North Atlantic. J Geophys Res 83:4907–4924. doi: 10.1029/JB083iB10p04907 CrossRefGoogle Scholar
- Fischer HJ (1984) Erfassung der Schwereanomalie über ozeanischen Rücken und ihre Deutung. Diploma thesis, Geophys, FrankfurtGoogle Scholar
- Holstein H (2002a) Gravimagnetic similarity in anomaly formulas for uniform polyhedra. Geophysics 67:1126–1133. doi: 10.1190/1.1500373 CrossRefGoogle Scholar
- Holstein H (2002b) Invariance in gravimagnetic anomaly formulas for uniform polyhedra. Geophysics 67:1134–1137. doi: 10.1190/1.1500374 CrossRefGoogle Scholar
- Holstein H, Schürholz P, Starr AJ, Charkraborty M (1999) Comparison of gravimetric formulas for uniform polyhedra. Geophysics 64:1438–1446. doi: 10.1190/1.1444648 CrossRefGoogle Scholar
- Jacoby WR, Çavşak H (2005) Inversion of gravity anomalies over spreading oceanic ridges. J Geodyn 39:461–474. doi: 10.1016/j.jog.2005.04.011 CrossRefGoogle Scholar
- Jonson LR, Litehiser JJ (1972) A method for computing the gravitational attraction of three-dimensional bodies in a spherical or ellipsoidal Earth. J Geophys Res 77:6999–7009. doi: 10.1029/JB077i035p06999 CrossRefGoogle Scholar
- Pohánka V (1988) Optimum expression for computation of the gravity field of a homogeneous polyhedral body. Geophys Prospect 36:733–751. doi: 10.1111/j.1365-2478.1988.tb02190.x CrossRefGoogle Scholar
- Rapp RH (1977) Potential Coefficient Determination from Terrestrial Gravity Data. Rep. Dept. Geodetic Science, 251, Ohio State University, 1977Google Scholar
- Takin M, Talwani M (1966) Rapid computation of the gravitation attraction of topography on a spherical Earth. Geophys Prospect 14:119–142. doi: 10.1111/j.1365-2478.1966.tb01750.x CrossRefGoogle Scholar
- Talwani M (1973) Computer usage in the computation of gravity anomalies. In: Methods in computational physics, vol 13. Academic Press, New York, NY, pp 343–389Google Scholar
- Talwani M, Lamar WJ, Landisman M (1959) Rapid gravity computations for two-dimensional bodies with application to the Mendocino submarine fracture zone. J Geophys Res 64(1), 49–59, 1Google Scholar
- Vesper H (1984) Erfassung von Schwereanomalien über ozeanischen Rücken und ihre Deutung. Diploma thesis, Geophys, FrankfurtGoogle Scholar
- von Frese RRB, Hinze WJ, Braile LW, Luca AJ (1981) Spherical Earth gravity and magnetic anomaly modeling by Gauss–Legendre quadrature integration. J Geophys 49:234–242Google Scholar
- Vyskocil V, Burda M (1976) On the computation of the gravitational effect of three-dimensional density models of the Earth’s crust. Stud Geophys Geod 3:213–218. doi: 10.1007/BF01601900 CrossRefGoogle Scholar