Testing Linear Regressions by StatsModel Library of Python for Oceanological Data Interpretation

Abstract

The study area is focused on the Mariana Trench, west Pacific Ocean. The research aim is to investigate correlation between various factors, such as bathymetric depths, geomorphic shape, geographic location on four tectonic plates of the sampling points along the trench, and their influence on the geologic sediment thickness. Technically, the advantages of applying Python programming language for oceanographic data sets were tested. The methodological approaches include GIS data collecting, data analysis, statistical modelling, plotting and visualizing. Statistical methods include several algorithms that were tested: 1) weighted least square linear regression between geological variables, 2) autocorrelation; 3) design matrix, 4) ordinary least square regression, 5) quantile regression. The spatial and statistical analysis of the correlation of these factors aimed at the understanding, which geological and geodetic factors affect the distribution of the steepness and shape of the trench. Following factors were analysed: geology (sediment thickness), geographic location of the trench on four tectonics plates: Philippines, Pacific, Mariana and Caroline and bathymetry along the profiles: maximal and mean, minimal values, as well as the statistical calculations of the 1st and 3rd quantiles. The study revealed correlations between the sediment thickness and distinct variations of the trench geomorphology and sampling locations across various segments along the crescent of the trench.

Keywords

• Programming language,Python,Statistical analysis,Pacific Ocean,Hadal trenches,Mariana Trench,oceanology,marine geology

References

1. nsley, C. F. & R. J. Kohn. (1985). Estimation, filtering, and smoothing in state space models with incompletely specified initial conditions. Annals of Statistics 13, 1286–1316.
2. Bello-González, J. P., Contreras-Reyes, E. & Arriagada, C. (2018). Predicted path for hotspot tracks off South America since Paleocene times: Tectonic implications of ridge-trench collision along the Andean margin. Gondwana Research, 64, 216–234.
3. Boston, B., Moore, G. F., Nakamura, Y. & Kodaira, S. (2017). Forearc slope deformation above the Japan Trench megathrust: Implications for subduction erosion. Earth and Planetary Science Letters, 462, 26–34.
4. Björck, A. (1996). Numerical methods for least squares problems. SIAM, Philadelphia. ISBN 0-89871-360-9.
5. Box, G. E. P.; Tiao, G. C. (1992). Bayesian Inference in Statistical Analysis. New York: John Wiley and Sons. ISBN 0-471-57428-7. (Section 8.1.1).
6. Dierssen, H. M. & Theberge Jr. A. E. (2014). Bathymetry: History of Seafloor Mapping. Encyclopedia of Natural Resources, Taylor & Francis.
7. Fujie, G., Ito, A., Kodaira, S., Takahashi, N., & Kaneda, Y. (2006). Confirming sharp bending of the Pacific plate in the northern Japan trench subduction zone by applying a traveltime mapping method. Physics of the Earth and Planetary Interiors, 157, 72–85.
8. Grand, S. P., Hilst, R. D. van der, & Widiyantoro, S. (1997). Global Seismic Tomography: A Snapshot of Convection in the Earth. GSA Today, 7(4), 2–7.

9. Lemenkova, P. (2019). Processing Oceanographic Data by Python Libraries NumPy, SciPy And Pandas. Aquatic Research, 2(2), 73-91.
10. Ljung, G. M. & Box, G. E. P. (1978). On a Measure of a Lack of Fit in Time Series Models. Biometrika. 65 (2): 297–303.
11. Michibayashi, K., Tasaka, M., Ohara, Y., Ishii, T., Okamoto, A., & Fryer, P. (2007). Variable microstructure of peridotite samples from the southern Mariana Trench: Evidence of a complex tectonic evolution. Tectonophysics, 444, 111–118.
12. Millman, K. J. & Aivazis, M. (2011). Python for Scientists and Engineers, Computing in Science & Engineering, 13, 9-12.
13. Oliphant, T. (2015). Guide to NumPy (2 ed.). CreateSpace. ISBN 978-1517300074.
14. Oliphant, T. E. (2007). Python for scientific computing. Computing in Science & Engineering 9(3), 10-20.
15. Reid, W. D. K., Cuomo, N. J., & Jamieson, A. J. (2018). Geographic and bathymetric comparisons of trace metal concentrations (Cd, Cu, Fe, Mn, and Zn) in deep-sea lysianassoid amphipods from abyssal and hadal depths across the Pacific Ocean. Deep-Sea Research Part I, 138, 11–21.
16. Schellart, W. P. (2008). Subduction zone trench migration: Slab driven or overriding-plate-driven? Physics of the Earth and Planetary Interiors, 170, 73–88.
17. Seabold, S. & Perktold, J. (2010). Statsmodels: Econometric and statistical modeling with python. Proceedings of the 9th Python in Science Conference.
18. Smith, W. H. F., & Sandwell, D. T. (1997). Global Sea Floor Topography from Satellite Altimetry and Ship Depth Soundings. Science, 277, 1956–1962.
19. Strutz, T. (2016). Data Fitting and Uncertainty (A practical introduction to weighted least squares and beyond). Springer Vieweg. ISBN 978-3-658-11455-8.
20. Taira, K., Yanagimoto, D., & Kitagawa, S. (2005). Deep CTD Casts in the Challenger Deep, Mariana Trench. Journal of Oceanography, 61, 447–454.
21. Theberge, A. (2008). Thirty years of discovering the Mariana Trench. Hydro International, 12, 38–39.
22. Timm, N. H. (2007). Applied Multivariate Analysis. Springer Science & Business Media, 695 p. ISBN: 978-0-387-95347-2.