Seismic array

A seismic array is a system of linked seismometers arranged in a regular geometric pattern (cross, circle, rectangular etc.)

[1] The data from a seismic array is obtained using special digital signal processing techniques such as beamforming, which suppress noises and thus enhance the signal-to-noise ratio (SNR).

The earliest seismic arrays were built in the 1950s in order to improve the detection of nuclear tests worldwide.

Seismic arrays are not only used to monitor earthquakes and nuclear tests but also used as a tool for investigating nature and source regions of microseisms as well as locating and tracking volcanic tremor and analyzing complex seismic wave-field properties in volcanic areas.

Modern seismic arrays such as NORES and ARCES are located on concentric rings spaced at log-periodic intervals.

The most important point during the beamforming process is to find the best delay times by which the single traces must be shifted before summation in order to get the largest amplitudes due to coherent interference of the signals.

For distances from the source much larger than about 10 wavelengths, a seismic wave approaches an array as a wavefront that is close to planar.

The directions of approach and propagation of the wavefront projected onto the horizontal plane are defined by the angles Φ and Θ.

The time delays τj also depends on the local crustal velocities (vc) below the given site j.

: Let wj(t) be the digital sample of the seismometer from site j at time t, then the beam of the whole array is defined as If seismic waves are harmonic waves S(t) without noise, with identical site responses, and without attenuation, then the above operation would reproduce the signal S(t) accurately.

After this summation, the beam has to be raised to the power of N The N-th root process was first proposed by K. J. Muirhead and Ram Dattin in 1976.

Schimmel and Paulssen introduced another non-linear stacking technique in 1997[3] to enhance signals through the reduction of incoherent noise, which shows a smaller waveform distortion than the N-th root process.

Kennett proposed the use of the semblance of the signal as a weighting function in 2000[4] and achieved a similar resolution.

All weighted stack methods can increase the slowness resolution of velocity spectrum analysis.

A cluster of earthquakes can be used as a source array to analyze coherent signals in the seismic coda.

This idea was consequently expanded by Krüger et al. in 1993 by analyzing seismic array data from well-known source locations with the so-called "double beam method".

being the Fourier transform of the seismogram w(t), using the definition of the wavenumber vector k = ω⋅ s This equation is called the transfer function of an array.

This method was proposed by Capon in 1969[6] and further developed to include wide-band analysis, maximum-likelihood estimation techniques, and three-component data in the 1980s.

[7] The methodology exploits the deterministic, non-periodic character of seismic wave propagation to calculate the frequency-wavenumber spectrum of the signals by applying the multidimensional Fourier transform.

[8] A beampacking scheme was developed at NORSAR to apply f-k analysis of regional phases to data of large array.

[8] This algorithm performs time-domain beamforming over a predefined grid of slowness points and measures the power of the beam.

In practice the beampacking process gives the same slowness estimate as for the f-k analysis in the frequency domain.

Another way of estimating slowness is to pick carefully times of the first onset or any other common distinguishable part of the same phase (same cycle) for all instruments in an array.

The horizontal components (sx, sy) of the slowness vector s can be estimated by Plane wave fitting requires interactive analyst's work.

[9] Because of the amount of required computations, plane wave fitting is most effective for arrays with a smaller number of sites or for subarray configurations.

YKA or Yellowknife Seismological Array is a medium size seismic array established near Yellowknife in the Northwest Territories, Canada, in 1962, in cooperative agreement between the Department of Mines and Technical Surveys (now Natural Resources Canada) and the United Kingdom Atomic Energy Authority (UKAEA), to investigate the feasibility of teleseismic detection and identification of nuclear explosions.

[11] NORSAR or Norwegian Seismic Array was established at Kjeller, Norway in 1968 as part of the Norwegian-US agreement for the detection of earthquakes and nuclear explosions.

[8] GERES is a small aperture array built in the Bavarian Forest near the border triangle of Germany, Austria and Czech, in 1988.