Abstract
The possibility of applying the continuous wavelet analysis on the basis of a Poissonian core for the processing and interpretation of gravity and magnetic survey data is considered. Based on the wavelet spectrum, W(x,h), reconstruction of the initial signal, g(x), is possible. Additionally, based on this wavelet spectrum, the equivalent distributions of mass and magnetization that produce the initial field, g(x), can be reconstructed. These possibilities allow the wavelet transform to be used for solving such classical problems as the filtering of initial signals, continuation of the field, calculation of higher field derivatives in the upper and lower half-spaces, and reduction of magnetic anomalies to the pole.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Astaf’eva, N.M., Wavelet analysis: basic theory and some applications, Usp. Fiz. Nauk, 1996, vol. 166, no. 11, pp. 1145–1170.
Daubechies, I., Ten Lectures on Wavelets, Philadelphia (PA), SIAM, 1992
D’yakonov, V.P., Veivlety. Ot teorii k praktike (Wavelets: From Theory to Practice), Moscow: SOLON-R, 2002.
Kobrunov, A.I. and Varfolomeev, V.A., On one method of e-equivalent redistribution and its practical application in the interpretation of gravity fields, Izv. Akad. Nauk SSSR, Fiz. Zem., 1981, no. 10, pp. 25–44.
Koronovskii, A.A. and Khramov, A.E., Nepreryvnyi veivletanaliz i ego prilozheniya (Continuous Wavelet Analysis and its Applications), Moscow: Fizmatlit, 2003.
Moreau, F., Gibert, D., Holschneider, M., and Saracco, G., Wavelet analysis of potential fields, Inverse Probl., 1997, vol. 13, pp. 165–178.
Nikitin, A.A. and Petrov, A.V., Theoretical Teoreticheskie osnovy obrabotki geofizicheskoi informatsii. Uch. posobie (Theoretical Foundations of the Geophysical Data Processing. Textbook), Moscow: OOO “TsITvP”, 2010.
Obolenskii, I.V. and Bulychev, A.A., Continuous wavelet transformation of gravity and magnetic data, Rus. Geophys. J., 2011, no. 3, pp. 48–56.
Obolenskii, I.V. and Bulychev, A.A., Complex continuous Poisson wavelet transform for identifying the sources of the potential field anomalies, Geofiz. Issled., 2011, vol. 12, no. 3, pp. 5–21.
Utemov, E.V. and Nurgaliev, D.K., Natural wavelet transformations of gravity data: theory and applications, Izv., Phys. Solid Earth, 2005, vol. 41, no. 4, pp. 333–344.
Yudin, M.N., Farkov, Yu.A., and Filatov, D.M., Vvedenie v veivlet-analiz: Uch. prakt. posobie dlya sistemy distantsionnogo obrazovaniya (Introduction to the Wavelet Analysis. Handbook of Distance Education), Moscow: Moscow Gos. Razved. Akad., 2001.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © K.M. Kuznetsov, I.V. Obolenskii, A.A. Bulychev, 2015, published in Vestnik Moskovskogo Universiteta. Geologiya, 2015, No. 6, pp. 62–69.
About this article
Cite this article
Kuznetsov, K.M., Obolenskii, I.V. & Bulychev, A.A. Potential field transformation on the basis of a continuous wavelet transform. Moscow Univ. Geol. Bull. 71, 112–120 (2016). https://doi.org/10.3103/S0145875215060034
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S0145875215060034