Application of “native" wavelet transform of gravity data for investigation of structure the sedimentary cover and crystalline basement

Authors: E.V. Utemov, D.K. Nurgaliev (Kazan (Volga Region) Federal University, RF, Kazan)
Key words: gravimetry, inverse problem, wavelet transform.
In this study authors have considered the basic theory and some real-world results of applying the technology of processing gravimetric data based on continuous and discrete wavelet transform with special "native" basic function. The most important result of this study is the technique for determining location and magnitude of the sources of the gravitational field in its wavelet domain for the two and three-dimensional cases.  Synthetic examples demonstrate that this problem can be successfully solved for a large number of sources even with significant noise present in the gravimetric data.

References

1. Audet P., Marescha J. C., Wavelet analysis of the coherence between

Bouguer gravity and topography: application to the elastic thickness

anisotropy in the Canadian Shield, Geophysical Journal International, 2007,

V. 168, pp. 287–298.

2. Boukerbout H., Gibert D., Identification of sources of potential fields with the

continuous wavelet transform: Two-dimensional ridgelet analysis, Journal of

Geophysical Research, 2006, V. 111, B071104, doi:10.1029/2005JB004078.

3. Cooper G.R.J., Cowan D.R., Comparing time series using wavelet-based

semblance analysis, Computers & Geosciences, 2008, V. 34, pp. 95–102.

4. Moreau F., Gibert D., Holschneider M., Saracco G., Identification of sources

of potential fields with the continuous wavelet transform: Basic theory, Journal

of Geophysics Research, 1999, V. 104(B3), pp. 5003-5013.

5. Panet I., Kuroishi Y., Holschneider M., Wavelet modeling of the gravity field

by domain decomposition methods: an example over Japan, Geophysical

Journal International, 2011, V. 184, pp. 203–219.

6. Sailhac P., Galdeano A., Identification of sources of potential fields with the

continuous wavelet transform: Complex wavelets and application to aeromagnetic

profiles in French Guiana, Journal of Geophysical Research, 2000,

V. 104 (B8), pp. 19455-19475.

7. Sailhac P., Gibert D., Boukerbout H., The theory of the continuous wavelet

transform in the interpretation of potential fields: a review, Geophysical

Prospecting, 2009, V. 57, pp. 517–525.

8. Utemov E.V., Nurgaliev D.K., Fizika Zemli – Izvestiya. Physics of the Solid Earth,

2005, no. 4, pp. 88-96.

9. Strakhov V.N., Doklady AN SSSR, 1977, V. 236, no. 3, pp. 571-574.

10. Tsirul'skiy A.V., Nikonova F.I., Fedorova N.V., Metod interpretatsii gravitatsionnykh

i magnitnykh anomaliy s postroeniem ekvivalentnykh semeystv resheniy

(The method of interpretation of gravity and magnetic anomalies with

the building of equivalent families of solutions), Sverdlovsk: Publ. of UNTs

AN SSSR, 1980, 136 p.

11. Paul T., Functions analytic on the half-plane as quantum mechanical

states, J. Math. Phys., 1984, V. 25(11), pp. 3252.

12. Novikov P.S., Doklady AN SSSR, 1938, V. 18, no. 3, pp. 165-168.

Key words: gravimetry, inverse problem, wavelet transform.
In this study authors have considered the basic theory and some real-world results of applying the technology of processing gravimetric data based on continuous and discrete wavelet transform with special "native" basic function. The most important result of this study is the technique for determining location and magnitude of the sources of the gravitational field in its wavelet domain for the two and three-dimensional cases.  Synthetic examples demonstrate that this problem can be successfully solved for a large number of sources even with significant noise present in the gravimetric data.

References

1. Audet P., Marescha J. C., Wavelet analysis of the coherence between

Bouguer gravity and topography: application to the elastic thickness

anisotropy in the Canadian Shield, Geophysical Journal International, 2007,

V. 168, pp. 287–298.

2. Boukerbout H., Gibert D., Identification of sources of potential fields with the

continuous wavelet transform: Two-dimensional ridgelet analysis, Journal of

Geophysical Research, 2006, V. 111, B071104, doi:10.1029/2005JB004078.

3. Cooper G.R.J., Cowan D.R., Comparing time series using wavelet-based

semblance analysis, Computers & Geosciences, 2008, V. 34, pp. 95–102.

4. Moreau F., Gibert D., Holschneider M., Saracco G., Identification of sources

of potential fields with the continuous wavelet transform: Basic theory, Journal

of Geophysics Research, 1999, V. 104(B3), pp. 5003-5013.

5. Panet I., Kuroishi Y., Holschneider M., Wavelet modeling of the gravity field

by domain decomposition methods: an example over Japan, Geophysical

Journal International, 2011, V. 184, pp. 203–219.

6. Sailhac P., Galdeano A., Identification of sources of potential fields with the

continuous wavelet transform: Complex wavelets and application to aeromagnetic

profiles in French Guiana, Journal of Geophysical Research, 2000,

V. 104 (B8), pp. 19455-19475.

7. Sailhac P., Gibert D., Boukerbout H., The theory of the continuous wavelet

transform in the interpretation of potential fields: a review, Geophysical

Prospecting, 2009, V. 57, pp. 517–525.

8. Utemov E.V., Nurgaliev D.K., Fizika Zemli – Izvestiya. Physics of the Solid Earth,

2005, no. 4, pp. 88-96.

9. Strakhov V.N., Doklady AN SSSR, 1977, V. 236, no. 3, pp. 571-574.

10. Tsirul'skiy A.V., Nikonova F.I., Fedorova N.V., Metod interpretatsii gravitatsionnykh

i magnitnykh anomaliy s postroeniem ekvivalentnykh semeystv resheniy

(The method of interpretation of gravity and magnetic anomalies with

the building of equivalent families of solutions), Sverdlovsk: Publ. of UNTs

AN SSSR, 1980, 136 p.

11. Paul T., Functions analytic on the half-plane as quantum mechanical

states, J. Math. Phys., 1984, V. 25(11), pp. 3252.

12. Novikov P.S., Doklady AN SSSR, 1938, V. 18, no. 3, pp. 165-168.



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