# Beamforming FK Analysis

Dear Obspy developer,

I am new using Obspy and I would like to ask something related with Beam Forming FK analysis.

I am trying to apply FK analysis to my data but unfortunately, I only have an array of three seismic sensors with a large aperture between them. I am trying to interpret the results but they change a lot depending on the window length and I do not know how to interpret well the resultant backazimuth. The backazimuth is calculated from the north to the direction of the epicenter. I have a question regarding to this angle:

• Does the direction of the epicenter is the direction between my source and the center of the seismic array? In my case the center of the seismic array there is not any seismic station.

Or does the direction from the epicenter to one of my seismic stations?

Thank you very much in advance.

Best Regards

Hi Cristina,

fk beamforming is subject to the far field approximation.
Hence the source of the signal of interest is far away so that the wavefront of the signal is approximately a straight line which propagates over the array.
Since one correlates a plane wave with the observed wavefield (fk beamforming) in the far field approximation, there is no such thing as an origin position of the beamformer, since a plane wave is characterized by frequency, velocity and azimuth only.

If you have only 3 stations with a large aperture, you need to make sure that your source fulfils the far field approximation other wise fk beamforming doesnâ€™t work!
But even then with 3 stations your resolution is going to be very limited.
Another thing to look out for; if your aperture is larger than a few hundred kilometers, path propagation effects are likely to distort your wave front and deviate from a plane wave model, which further reduces the chances of a successful fk beamforming application.
With only 3 stations this might not be the most useful approach I fear.

Cheers,
Martin

Thank you very much Martin for the explanation.

My source is close with respect to the aperture of the the array that is several kilometers. I can also have local site effects that I need first to evaluate. Thus, it is not a good application in this case.

Thank you again.

Best Regards