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Beamforming

Beamforming is a Julia module for the array analysis of seismic data, using Seis.jl.

Build status

Build Status codecov

Installation

julia> ] # press ']' to enter pkg mode

(v1.7) pkg> add https://github.com/anowacki/Geodesics.jl https://github.com/anowacki/Seis.jl https://github.com/anowacki/Beamforming.jl

Beamforming.jl requires Julia v1.6 or above.

Usage overview

The main functions exported are:

  • For traditional beamforming:
    • array_response: Compute the array response function for a set of stations
    • beamform: Compute the beam power across a grid of slowness points (as in f–k analysis)
    • vespagram: Compute a slowness vespagram
  • For cross-correlation beamforming:
    • crosscorrelation_array_response
    • crosscorrelation_beamform

Docstrings are exhaustive, and can be consulted for usage of these functions. To bring up docstrings in the REPL, type ? followed by the name of the function and press return.

Array response

The array response for a set of stations can be computed like so:

using Beamforming, Seis
t = sample_data(:array); # 60 UK stations
# Array response parameters
arf = array_response(t,
                     5,   # Maximum slowness in s/°
                     0.1, # Slowness grid spacing
                     0.1, # Minimum frequency in Hz
                     1,   # Maximum frequency
                     0.1, # Frequency spacing
                     true # `true` for s/° slowness; `false` for s/km
                     )
plot(arf, powscale=:dB)   # If Plots is installed

Beamforming

Beamforming can be performed like so:

bf = beamform(t,
              1100, # Start time in s
              1160, # End time in s
              -1,   # Minimum east slowness in s/°
              0.5,  # Maximum east slowness
              0,    # Minimum north slowness
              4,    # Maximum north slowness
              0.01  # Slowness spacing
              )
plot(bf, phases=["PKiKP", "PKIKP"])

Vespagrams

Compute a vespagram like so:

vesp = vespagram(t,
                 1110, # Start time in s
                 1150, # End time
                 0,    # Minimum slowness in s/°
                 4,    # Maximum slowness
                 0.01, # Slowness spacing
                 )
plot(vesp, phases=["PKiKP", "PKIKP"], clim=(-1,1))

Optional extras

Plotting

If you have installed Plots to your environment, then you can easily create plots as shown above.

For more help on plotting commands provided in this package, call up the online help for Beamforming.plot:

help?> Beamforming.plot

Travel times

To plot the predicted location in slowness and time of arrivals, you can install SeisTau.jl. (See the installation notes for more.)

Simply do using SeisTau, then the phases option to plot will enable easy predicted phase arrival plotting for BeamformGrids and VespaGrids, produced respectively by beamform and vespagram.