Array Analysis

Array Response Function (ARF)

The Array Response Function (ARF) (Ruigrok et al., 2017) helps to evaluate the resolution of the array in a specific bandwidth.

First you need to create a coordinates files and then load it. To create the coordinate file go to “Files >>> Stations Coordinates” and fill the table with lat (o), lon (o) and depth (km).

Then you can compute the ARF and plot the map with the array stations.


Frequency-Wavenumber Analysis

The Frequency-Wavenumber (FK) is basically a method to compute the beamforming in the frequency domain (Capon, 1969).

To compute the FK you need follow this steps;

  • Files: Path where you have the seismograms
  • Dataless: path where you have the metadata (.dlsv or .xml)
  • Set temporal window of the analysis and check the box Trim
  • Plot the seismograms
  • Fill the parameters (Slowness Max, Time Window, overlap……)
  • Choose methods
  • Press Run F-K

Now, you will watch in the upper panels the Rel Power, Absolute Power, Back-Azimuth and Slowness results of your analysis.

Two more actions: Double pick in the upper panels will run the FK in that specific time window (starting in the point). Then, the slowness map and the stack corresponding to the delays of the maximum power in the slowness vector will show up.

The pick with the slowness vector corresponding to the phase you selected are automatically saved in the file “isp/arrayanalysis/dataframe.csv” and you can open the file just pressing “ctrl+o”



The vespagram is a visualization of the FK results for an specific backazimuth or slowness. So, once you have done the FK analysis, you can compute the vespagram (Rost and Thomas, 2002).

But before, you must select the time window. Go with the mouse to the any upper panel. Pick, hold and drag to the right direction to do the selection.  Now you can open the vespagram window.

In the vespagram window you can select the parameters (Win length, overlap, and frequency bandwidth of the analysis) and the backazimuth and slowness where you want to compute the vespagram.


Back Projection

The Back Projection is a relatively new technique (Kruger and Ohrnberger 2005) designed to quickly and effectively imaging rupture process of large earthquakes. Back-projecting seismic data can be done by big seismic arrays.

In ISP the user can process the seismograms and set the BackProjection parameters. It is shown a screenshot of the preparation of the data of Sumatra Earthquake using Earthquake Analysis module, and then using Back Projection tool.



First the user set the path to the seismograms, metadata and the output folder. Second, the seismograms can be chopped and a macro with some signal processing can be established. Then, the user must set the Back Projection parameters:

Warning. BackProjection is highly computing demanding, so we do not recomend using too high resolutions (dx = dy > 0.5), too long time window (time window < 800s) and too big grids (maxlat-minlat and maxlon - minlon < 15 degrees)

  • Grid: set the minimum longitude and latitude and the maximum latitude and longitude as well as dx and dy (resolution in longitude and latitude in degrees) where the Back projection is going to be calculated. Set the depth.

  • Time window is the whole period in which the BackProjection is going to be calculated. A small sliding window will be shifted forward in time in step by step.

  • Click on generate the Travel Time Grid. This action will create a travel time grid in wich your grid cells have the travel time from every station to every lat and lon cell.

  • Click on Run BackProjection. In every step will be calculated the Backprojcetion aligning the traces using the Multi Channel Cross Correlation technique (VanDecar and Crosson 1990) according to the Travel Time grid and estimating the power by a simple linear stack or using the Zero Lag Cross Correlation Technique (Almendros et al., 1999).

  • Finally, Load the result video and play it.

Multimedia Material (Array Analysis)

The following video shows a basic analysis of a nueclear explotion (Test from Nort Korea test 2017, Alaska Array ILAR)