Depth estimation of gravity anomalies by S-transform of analytic signal

نویسندگان

1 Ph.D. Candidate, Institute of Geophysics, University of Tehran, Tehran, Iran

2 Professor, Institute of Geophysics, University of Tehran, Tehran, Iran

چکیده

The S-transform has widely been used in the analysis of non-stationary time series. A simple method to obtain depth estimates of gravity field sources is introduced in this study. We have developed a new method based on the spectral characteristics of downward continuation to estimate depth of structures. This calculation procedure is based on replacement of the Fourier transform with the S-Transform in traditional downward formula. We expect the localized estimation of the depth of anomalies using the S-transform spectrum rather than FFT spectrum. Likewise in the wavelets which don’t have a direct relationship with wave numbers, the S-Transform corresponds to wave number instead of scale or pseudo wavenumber. This is the main advantage of using S-transform instead of wavelets. This advantage will lead to easier and more precise calculation of depth estimation. Synthetic examples indicate the usefulness of this method. The method was applied to field examples producing reasonable results comparable to some common methods such as wavelet-based source characterization and Euler deconvolution. It is possible to average the local spectra over the wavenumber axis that leads to the spectrum referenced to position axis. The depth of anomaly can be computed in any point of the profile by using localization of spectrum. Thereby, we can analyze distinguished traces of shallow and deep anomalies while the lateral effects are also considered.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Depth estimation of gravity anomalies by S-transform of analytic signal

نویسندگان [English]

  • Naeim Mousavi 1
  • Vahid Ebrahimzadeh Ardestani 2
1 Ph.D. Candidate, Institute of Geophysics, University of Tehran, Tehran, Iran
2 Professor, Institute of Geophysics, University of Tehran, Tehran, Iran
چکیده [English]

The S-transform has widely been used in the analysis of non-stationary time series. A simple method to obtain depth estimates of gravity field sources is introduced in this study. We have developed a new method based on the spectral characteristics of downward continuation to estimate depth of structures. This calculation procedure is based on replacement of the Fourier transform with the S-Transform in traditional downward formula. We expect the localized estimation of the depth of anomalies using the S-transform spectrum rather than FFT spectrum. Likewise in the wavelets which don’t have a direct relationship with wave numbers, the S-Transform corresponds to wave number instead of scale or pseudo wavenumber. This is the main advantage of using S-transform instead of wavelets. This advantage will lead to easier and more precise calculation of depth estimation. Synthetic examples indicate the usefulness of this method. The method was applied to field examples producing reasonable results comparable to some common methods such as wavelet-based source characterization and Euler deconvolution. It is possible to average the local spectra over the wavenumber axis that leads to the spectrum referenced to position axis. The depth of anomaly can be computed in any point of the profile by using localization of spectrum. Thereby, we can analyze distinguished traces of shallow and deep anomalies while the lateral effects are also considered.

کلیدواژه‌ها [English]

  • Analytic signal
  • depth estimation
  • Gravity data
  • S-Transform

مراجع

Ardestani, E. V., 2010, Delineating and modeling an underground water conduit by scattered micro-gravity data and electrical resistivity sounding, Exploration Geophysics, 41, 210-218.
Blakely, R. J., 1995, Potential theory in gravity and magnetic applications, Cambridge University Press.
Cooper, G., 2004, The stable downward continuation of potential field data, Exploration Geophysics, 35, 260-265.
Cooper, G., 2006, Interpreting potential field data using continuous wavelet transforms of their horizontalderivatives, Computers & Geosciences, 32, 984-992.
Fedi, M. and Florio, G., 2011, Normalized downward continuation of potential fields within the quasi-harmonic region, Geophysical Prospecting, 59(6), 1087-1100;
Fedi, M., Primiceri, R., Quarta, T. and Villani, A. V., 2004, Joint application of continuous and discrete wavelet transform on gravity data to identify shallow and deep sources, Geophysical Journal International, 156, 7-21.
Garcia-Abdeslem, J., 1995, Inversion of the power spectrum from gravity anomalies of prismatic bodies, Geophysics, 60(6), 1698-1703.
 
Goodyear, B. G., Zhu, H., Brown, R. A. and Ross Mitchell, J., 2004, Removal of phase artifacts from fMRI data using a Stockwell transform filter improves brain activity detection, Magnetic Resonance in Medicine, 51, 16-21.
Gupta, O. P., 1988, A Fourier transform minimization technique for interpreting magnetic anomalies of some two-dimensional bodies, Canadian Journal of Exploration Geophysics, 24(2), 179-184.
Kern, M., 2003, An analysis of the combination and downward continuation of satellite, airborne and terrestrial gravity data, PhD thesis, the university of Calgary, Alberta, Canada.
Li, Y., Braitenberg, C. and Yang, Y., 2013, Interpretation of gravity data by the continuous wavelet transform: The case of the Chad lineament (North-Central Africa), Journal of Applied Geophysics, 90, 62-70.
Mansinha, L., Stockwell, R., G., Lowe, R., P., Eramian, M. and Schincariol, R., A., 1997, Local S-spectrum analysis of 1-D and 2-D data, Physics of the Earth and Planetary Interiors, 103, 329-336.
Mareshal, J. C., 1985, Inversion of potential field data in Fourier transform domain, Geophysics, 50(4), 685-691.
Maus, S. and Dimiri, V., 1996, Depth estimation from the scaling power spectrum of potential fields, Geophysical Journal International, 123, 113-120.
Odegard, O. and Berg, J. W., 1965, Gravity interpretation using the Fourier integral,Geophysics, xxx, 3, 424-438.
Pinnegar, C. R. and Mansinha, L., 2003, The S-transform with windows of arbitrary and varying shape, Geophysics, 68(1), 381-385.
Nabighian, M. N., 1972, The analytic signal of two dimensional magnetic bodies with polygonal cross-section: its properties and use for automated anomaly interpretation, Geophysics, 37, 507-517.
Nabighian, M. N., Ander, M. E., Grauch, V. J. S., Hansen, R. O., LaFehr, T. R., Li, Y., Pearson, W. C., Peirce, J. W., Phillips, J. D. and Ruder, M. E., 2005, Historical development of the gravity method in exploration: Geophysics, 70(6), 63ND-89ND.
Senapati, K. and Routray, A., 2011, Comparison of ICA and WT with S-transform based method for removal of ocular artifact from EEG signals, Journal of Biomedical Science and Engineering, 4, 341-351.
Stockwell, R. G., Mansinha, L. and Lowe, R. P., 1996, Localization of the complex spectrum: the S-transform, IEEE Transactions on Signal Processing, 44, 998-1001.
Vatankhah, S., Ardestani, E. V. and Renaut, R. A., 2013, Automatic estimation of the regularization parameter in 2-Dfocusing gravity inversion: an application to the Safo manganesemine in northwest of Iran, Journal of Geophysics and Engineering (in press).

فایل ها

هم رسانی

ارجاع به این مقاله

آمار