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Application of the polynomial adjustment to the aeromagnetic survey of the Spanish Mainland; Requirements and shortcomings

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Abstract

Polynomial surfaces are a very useful tool in order to represent the geomagnetic field over small area of the Earth’s surface. Nevertheless, the method has not always been applied with enough precision, nor its limitations are considered in detail. This work analyses the conditions of applicability of this method to data from the aeromagnetic survey of the Spanish mainland accomplished in 1986, and the fulfilment of the necessary conditions to enhance a merely descriptive model to produce another of inferential character. The best statistical adjustment with only descriptive character, valid for the whole Spanish mainland, is a third degree model. The study proves that the conditions of validity for inferential models are met using polynomials of second and third degree in restrictive areas, but not over the whole Iberian Peninsula. In this case, the model of second degree is proposed as the best option because of its simplicity and the extension of its region of validity. To a great extent, the restrictions to enhance the descriptive models are due to the own nature, specially to their geographical dependence, and can also affect the analysis of other kinds of geophysical data.

References

  1. Afifi, A. A. and S. P. Azen, Statistical Analysis. A Computer Oriented Approach, 442 pp., Academic Press, London, 1977.

  2. Ardizone, J. A., Análisis de datos aeromagnéticos. Metodologías y aplicación al levantamiento aeromagnético de Espa ña Peninsular, Ph.D. Thesis, 225 pp., Facultad de Ciencias Físicas, Universidad Complutense de Madrid, 1996 (in Spanish).

  3. Ardizone, J. A., J. Mezcua, and I. Socias, Mapa Aeromagnético de España Peninsular, 29 pp. and 3 maps, Instituto Geográfico Nacional, Madrid, 1989 (in Spanish).

  4. Belsley, D. A., A. Khu, and R. E. Welsch, Regression Diagnostics, 292 pp., John Wiley & Sons, New York, 1980.

  5. Galdeano, A. and J. C. Rossignol, Assemblage à altitude constante des cartes d’anomalies magnétiques couvrant l’ensemble du bassin occidental de la Mediterranée, Bull. Soc. Géol. France., XIX(3), 461–468, 1977 (in French with English abstract).

  6. Haines, G. V., A Taylor expansion of the geomagnetic field in the Canadian Artic, Publications of the Dominion Observatory, XXXV, 115–140, 1967.

  7. Haines, G. V., Polinomial estimation of certain geomagnetic quantities, applied to a survey of Scandinavia, Publications of the Dominion Observatory. XXXVII, 79–112, 1968.

  8. Haines, G. V., Regional magnetic field modelling: A review, J. Geomag. Geoelectr, 42(9), 1001–1018, 1990.

  9. Haines, G. V. and W. Hannaford, Magnetic anomaly maps of British Columbia and the adjacent Pacific Ocean, Publications of the Earth Physics Branch, Department of Energy, Mines and Resources, Otawa, 42(8), 215–228, 1972.

  10. Haines, G. V. and W. Hannaford, A three component aeromagnetic survey of the Canadian Artic, Publications of the Earth Physics Branch, Department of Energy, Mines and Resources, Otawa, 44(8), 213–234, 1974.

  11. Haines, G. V., W. Hannaford, and P. H. Serson, Magnetic anomaly maps of the Nordic Countries and the Greenland and Norwegian seas, Publications of the Dominion Observatory, 39(5), 1970.

  12. Huber, P. J., Robust Statistics, 308 pp., John Wiley & Sons, New York, 1981.

  13. Jobson, J. D., Applied Multivariate Data Analysis, Vol. I, Regression and Experimental Design, 621 pp., Springer-Verlag, 1991.

  14. Morrison, D. F., Applied Linear Statistical Methods, 562 pp., Prentice-Hall Inc., New Jersey, 1983.

  15. Peña, D., Estadística Modelos y Métodos, V. 1 Fundamentos, 402 pp., Edit. Alianza Universidad Textos, Madrid, 1989a (in Spanish).

  16. Peña, D., Estad ística Modelos y Métodos, V. 2 Modelos Lineales y Series Temporales, 745 pp., Edit. Alianza Universidad Textos, Madrid, 1989b (in Spanish).

  17. Siegel, S., Estad ística no Paramétrica, 562 pp., Trillas, Méjico, 1986 (in Spanish).

  18. Socías, I., J. Lynam, and R. del Potro, Interpretation of an Aeromagnetic Survey of the Spanish Mainland, Earth Planet. Sci. Lett., 105, 55–64, 1991.

  19. Tanaka, M., K. Hiroishi, S. Ando, and S. Matsumura, Aeromagnetic surveys in the Geographical Survey Institute and the magnetic anomalies in and around Japan, Bull. of the Geological Survey of Japan, XXX, 1–14, 1986.

  20. Torta, J. M., Modelización regional del campo geomagnético sobre España: Campo anómalo, variación secular y campo de referencia, 139 pp., Publicaciones del Observatorio del Ebro, 15, Tortosa, 1992 (in Spanish with English abstract).

  21. Weisberg, S., Applied Linear Regression, 324 pp., John Wiley & Sons, New York, 1985.

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Correspondence to J. Ardizone.

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Ardizone, J., Herraiz, M. Application of the polynomial adjustment to the aeromagnetic survey of the Spanish Mainland; Requirements and shortcomings. Earth Planet Sp 52, 183–196 (2000) doi:10.1186/BF03351627

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Keywords

  • Polynomial Model
  • Contour Interval
  • Degree Model
  • Inferential Model
  • Polynomial Surface