Difference between revisions of "Array signal processing"
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| − | == | + | == Basic principle of array processing - [[Wikipedia:Delay_and_sum|''delay and sum'' (or ''shift and sum'')]] == |
| − | == | + | == Array response function == |
| − | + | some books and papers for reference | |
| − | === | + | * Johnson and Dudgeon (1993) <ref name="Johnson and Dudgeon (1993)">D.H.Johnson & D.E.Dudgeon, Array Signal Processing - concepts and techniques, Prentice Hall Signal Processing Series, Alan v. Oppenheim, Series Editor, 1993.</ref> |
| + | * Mykkelveit et al. (1983) <ref name="Mykkelveit et al. (1983)">Mykkeltveit, S., Astebol, K., Doornbos, D.J., and Husebye, E.S. (1983). Seismic Array configuration Optimization, BSSA, 73(1), pp. 173-186.</ref> | ||
| + | * Rost and Thomas (2002) <ref name="Rost and Thomas (2002)">Rost, S. and Ch. Thomas, Array Seismology, Reviews of Geophysics, 2002.</ref> | ||
| + | * Schweitzer et al. (2002) <ref name="Schweitzer et al. (2002)">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.</ref> | ||
| + | * Van Trees (2002) <ref name="Van Trees (2002)">H.L. Van Trees, Optimum Array Processing, Part IV of 'Detection, Estimation, and Modulation Theory, John Wiley | ||
| + | and Sons, Inc., New York, 2002.</ref> | ||
| − | |||
| − | |||
| − | + | '''[[Warangps|warangps]]''' is a graphical interface for simple visualization | |
| + | of the array response function for a specific array geometry. | ||
| + | The array reponse function is computed on a regular cartesian grid | ||
| + | in the wavenumber domain <math>\vec{k}</math> by evaluating: | ||
| − | + | <math>AR(\vec{k}-\vec{k}_0) = \| \frac{1}{N} \sum_{i=1}^{N} \exp(-j\vec{r}_i(\vec{k}-\vec{k}_0)) \|</math> | |
| + | |||
| + | Here, <math>\vec{r}_i</math> is the position vector of sensor i in | ||
| + | a cartesian coordinate system, <math>j</math> the imaginary unit and | ||
| + | <math>\vec{k}_0</math> the ''true'' wavenumber vector of a single | ||
| + | plane wave. | ||
| + | |||
| + | As most seismological array applications are restricted to the | ||
| + | deployment of sensors on the earth's surface, the above equation | ||
| + | is evaluated in the horizontal plane, i.e. <math>\vec{r}_i = (r_{ix}, r_{iy})</math> | ||
| + | and <math>\vec{k} = (k_x, k_y)</math> (horizontal wavenumber vector). | ||
| + | |||
| + | The evaluation of the array reponse function is simple, | ||
| + | still the limits of the wavenumber range as well as the desired | ||
| + | resolution for the grid computation <math>(\delta k_x, \delta k_y)</math> | ||
| + | needs to be specified. The resolution needs to be sufficiently high in | ||
| + | order not to miss small details of the peaked surface and the | ||
| + | size of the grid should allow to determine the position of | ||
| + | grating lobes or strong secondary side lobes in the 2D surface. | ||
| + | |||
| + | '''[[Gpfksimulator|gpfksimulator]]''' is another tool for ... | ||
| + | |||
| + | == Frequency wavenumber power spectrum == | ||
| + | |||
| + | |||
| + | |||
| + | == References == | ||
| + | <references/> | ||
Latest revision as of 09:42, 11 March 2010
Contents
Basic principle of array processing - delay and sum (or 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]
warangps is a graphical interface for simple visualization of the array response function for a specific array geometry.
The array reponse function is computed on a regular cartesian grid in the wavenumber domain by evaluating:
Here, is the position vector of sensor i in a cartesian coordinate system, the imaginary unit and the true wavenumber vector of a single plane wave.
As most seismological array applications are restricted to the deployment of sensors on the earth's surface, the above equation is evaluated in the horizontal plane, i.e. and (horizontal wavenumber vector).
The evaluation of the array reponse function is simple, still the limits of the wavenumber range as well as the desired resolution for the grid computation needs to be specified. The resolution needs to be sufficiently high in order not to miss small details of the peaked surface and the size of the grid should allow to determine the position of grating lobes or strong secondary side lobes in the 2D surface.
gpfksimulator is another tool for ...
Frequency wavenumber power spectrum
References
- ↑ D.H.Johnson & D.E.Dudgeon, Array Signal Processing - concepts and techniques, Prentice Hall Signal Processing Series, Alan v. Oppenheim, Series Editor, 1993.
- ↑ Mykkeltveit, S., Astebol, K., Doornbos, D.J., and Husebye, E.S. (1983). Seismic Array configuration Optimization, BSSA, 73(1), pp. 173-186.
- ↑ Rost, S. and Ch. Thomas, Array Seismology, Reviews of Geophysics, 2002.
- ↑ 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.
- ↑ H.L. Van Trees, Optimum Array Processing, Part IV of 'Detection, Estimation, and Modulation Theory, John Wiley and Sons, Inc., New York, 2002.
