# Beam forming FK analysis of a seismic wave

So after reading alot of literature on source localization, I found out that FK analysis is one of the most widely used methods to determine source location without explicitly calculating the difference in between the S and P phase arrivals. I had two questions regarding the same.

1. The output of the FK analysis algorithm is the Slowness,the back-azimuth and the corresponding power. This tells us the angle at which the source is present taking the center of the array geometry as the origin and the velocity of the wave which was received on site. My question is that, how to convert the Slowness vs Backazimuth plot to a X distance vs Y distance graph.

2. Where do we use the information that there are surface waves too since we only look at the vertical components and not the radial ones of the seismometer?

Any help, clarification or resource provision would be highly appreciated! Forgive me for my insufficient knowledge about the topic since this isn't my major.

Thank you :).

• I don't exactly follow what you want to see in the (X,Y) plot. The backazimuth and slowness tell you where the signal is coming from (or, identically, where the signal is going to) as a vector in (x,y,z) space. Is that what you want to know? How to go from slowness/backazimuth to a vector?
– Erik
Jul 28 '20 at 19:58
• @Erik like yeah..I mean we know the angle of the source and the velocity of the wave but we don't know the distance right? I want to calculate the distance. Jul 28 '20 at 20:01
• I don't think you can get the source-receiver distance, or source location, based on recordings at a single station/array. Do you have any material that claims otherwise?
– Erik
Jul 29 '20 at 11:43
• @Erik so what's you're saying is if I have 3 seismometers I can't determine the distance? Jul 29 '20 at 17:51
• Well, I would think that indeed it's not so simple. An array will tell you from which direction the energy comes, but it doesn't tell you where the energy originated. Typically, to my best knowledge, you need a number of stations located at many locations, to start to figure out the source location...
– Erik
Jul 29 '20 at 21:02