Difference between revisions of "Array signal processing"

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The co-array is defined as the set of all possible combinations of two array sensors (Haubrich, 1968 <ref name="Haubrich (1968)"> Haubrich, R.A., 1968. Array Design, Bull. seism. Soc. Am., 58(3), 977–991. </ref>): the array can thus be divided into several semicircular sub-arrays (hereafter called rings) as described in Bettig et al. (2001) <ref name="Bettig et al. (2001)"> Bettig B., P.-Y. Bard, F. Scherbaum, J. Riepl, F. Cotton, C. Cornou, D. Hatzfeld, 2001. Analysis of dense array measurements using the modified spatial auto-correlation method (SPAC). Application to Grenoble area., Boletin de Geofisica Teoria e Applicata, 42, 3-4, 281-304.</ref>. Since, for each ring, an azimuthal and radial integration is performed when computing spatial autocorrelation values, the design of rings results from a compromise between a number of sensors pair per  ring as large as possible and a ring thickness as small as possible.
 
The co-array is defined as the set of all possible combinations of two array sensors (Haubrich, 1968 <ref name="Haubrich (1968)"> Haubrich, R.A., 1968. Array Design, Bull. seism. Soc. Am., 58(3), 977–991. </ref>): the array can thus be divided into several semicircular sub-arrays (hereafter called rings) as described in Bettig et al. (2001) <ref name="Bettig et al. (2001)"> Bettig B., P.-Y. Bard, F. Scherbaum, J. Riepl, F. Cotton, C. Cornou, D. Hatzfeld, 2001. Analysis of dense array measurements using the modified spatial auto-correlation method (SPAC). Application to Grenoble area., Boletin de Geofisica Teoria e Applicata, 42, 3-4, 281-304.</ref>. Since, for each ring, an azimuthal and radial integration is performed when computing spatial autocorrelation values, the design of rings results from a compromise between a number of sensors pair per  ring as large as possible and a ring thickness as small as possible.
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== References ==
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Revision as of 08:47, 10 March 2010

Basic principle of array processing - delay and sum / shift and sum

Array response function

some books and papers for reference

  • Johnson and Dudgeon (1993) [1]
  • Mykkelveit et al. (1983) [2]
  • Rost and Thomas (2002) [3]
  • Schweitzer et al. (2002) [4]
  • Van Trees (2002) [5]

Frequency wavenumber power spectrum

Modified Spatial Autocorrelation method (MSPAC)

The Modified Spatial Autocorrelation (MSPAC) was introduced by Bettig et al. (2001) [6] after pioneer paper of Aki (1957)[7]. This method allows computing spatial autocorrelation coefficients for any arbitary array configurations.

BLA BLA BLA


The co-array is defined as the set of all possible combinations of two array sensors (Haubrich, 1968 [8]): the array can thus be divided into several semicircular sub-arrays (hereafter called rings) as described in Bettig et al. (2001) [6]. Since, for each ring, an azimuthal and radial integration is performed when computing spatial autocorrelation values, the design of rings results from a compromise between a number of sensors pair per ring as large as possible and a ring thickness as small as possible.

References

  1. ↑ D.H.Johnson & D.E.Dudgeon, Array Signal Processing - concepts and techniques, Prentice Hall Signal Processing Series, Alan v. Oppenheim, Series Editor, 1993.
  2. ↑ Mykkeltveit, S., Astebol, K., Doornbos, D.J., and Husebye, E.S. (1983). Seismic Array configuration Optimization, BSSA, 73(1), pp. 173-186.
  3. ↑ Rost, S. and Ch. Thomas, Array Seismology, Reviews of Geophysics, 2002.
  4. ↑ Schweitzer, J., Fyen, J., Mykkeltveit, S. and Kvaerna, T. (2002). Chapter 9: Seismic Arrays, In: Bormann, P. (Ed.), IASPEI New Manual of Seismological Observatory Practice, GeoForschungsZentrum Potsdam, Vol. 1, 51pp.
  5. ↑ H.L. Van Trees, Optimum Array Processing, Part IV of 'Detection, Estimation, and Modulation Theory, John Wiley and Sons, Inc., New York, 2002.
  6. ↑ 6.0 6.1 Bettig B., P.-Y. Bard, F. Scherbaum, J. Riepl, F. Cotton, C. Cornou, D. Hatzfeld, 2001. Analysis of dense array measurements using the modified spatial auto-correlation method (SPAC). Application to Grenoble area., Boletin de Geofisica Teoria e Applicata, 42, 3-4, 281-304.
  7. ↑ Aki, K., 1957. Space and Time Spectra of Stationary Stochastic Waves, with Special Reference to Microtremors, Bull. Earthq. Res. Inst. Tokyo, 35, 415-457.
  8. ↑ Haubrich, R.A., 1968. Array Design, Bull. seism. Soc. Am., 58(3), 977–991.
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