Hi everyone,

I’m currently using the function obspy.signal.array_analysis.array_processing to perform beamforming.

Does anyone know what formula that the function used to compute the absolute power and the relative power? Is there any paper describing the algorithm?

The obspy website provides a reference paper:

Kværna, T. and Ringdal, F. (1986),

Stability of various f-k estimation techniques,

in *Scientific Report: Semiannual Technical Summary 1 - 1986/1987*, NORSAR, Kjeller, Norway.

But unfortunately, I cannot find it on internet…Anyone has a electronic version of the paper?

Thanks in advance!

Lili

Hi Lili,

that’s actually the wrong reference, the correct paper is by Kværna and Doornbos 1986 (attached), have a look from page 60 onwards.

As for the power question, it is quite likely (although I am not certain) that the power is not computed as in the attached paper, as many people do not have access to the NORSAR technical reports.

Instead they like to use it as a reference for the Bartlett beamformer (in seismology also known as f-k analysis).

In general the term absolute power refers to the total power contained in the seismogram, which in beamforming is computed as the trace of the cross spectral density matrix, i.e. sum of autocorrelations.

The normalized or relative power of a beamformer is generally the division of the beam map P(k) by P_max(k).

What is really implemented in obspy though, you might need to take a look at the code.

Cheers,

Martin

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Kværna, Doornbos - 1986 - An integrated approach to slowness analysis with array and three-component stations.pdf (2.89 MB)

ATT00001.htm (3.3 KB)