Beamforming

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

Build status

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,   # Set of traces
    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
)
using CairoMakie
plot(arf, powscale=:dB)   # If a Makie backend 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
)
using SeisTau       # See note below
plot(bf, phases=["PKiKP", "PKIKP"])

Vespagrams

Compute a vespagram like so:

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

Optional extras

Plotting

Makie.jl

Plots can be created using the Makie.jl ecosystem. To enable this, load a Makie backend module by doing e.g. using GLMakie in your REPL or module. You will likely need to add this backend as a package to your environment, e.g. by doing import Pkg; Pkg.add("GLMakie").

The following plotting functions are provided through Makie:

• plot_array_response
• plot_array_response!
• plot_beamfomring
• plot_beamfomring!
• plot_vespagram
• plot_vespagram!

Makie.plot and Makie.plot! are overloaded such that plot(arf_or_bf_or_vesp) and plot!(axis, arf_or_bf_or_vesp) will produce the right plot, whether the result of array_response, beamform or vespagram is passed in, as seen above.

Plots.jl

As an alternative to Makie plotting, Beamforming.jl supports using Plots.jl as a legacy implementation. If you have installed Plots to your environment, then you can easily create plots as shown above.

For more help on the Plots.jl 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.