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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Seismic array | 1/3 | https://en.wikipedia.org/wiki/Seismic_array | reference | science, encyclopedia | 2026-05-05T09:43:55.448067+00:00 | kb-cron |
A seismic array is a system of linked seismometers arranged in a regular geometric pattern (cross, circle, rectangular etc.) to increase sensitivity to earthquake and explosion detection. A seismic array differs from a local network of seismic stations mainly by the techniques used for data analysis. 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. Many of these deployed arrays were classified until the 1990s. Today they have become part of the International Monitoring System (IMS) as primary or auxiliary stations. 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.
== Layout ==
Seismic arrays can be classified by size, which is defined by the array's aperture given by the largest distance between the single seismometers. The sensors in a seismic array are arranged in different geometric patterns horizontally. The arrays built in the early 1960s were either cross (orthogonal linear) or L-shaped. The aperture of these arrays ranged from 10 to 25 km. Modern seismic arrays such as NORES and ARCES are located on concentric rings spaced at log-periodic intervals. Each ring consists of an odd number of seismometer sites. The number of rings and aperture differ from array to array, determined by economy and purpose. Using the NORES design as an example, seismometers are placed on 4 concentric rings. The radii of the 4 rings are given by:
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{\displaystyle R_{n}=R_{min}\cdot 2.15^{n}(n=0,1,2,3),}
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{\displaystyle R_{min}=150m}
If the three sites in the inner ring are placed at 36, 156 and 276 degrees from due North, the five sites in the outer ring might be placed at 0, 72, 144, 216 and 288 degrees. This class of design is considered to provide the best overall array gain.
== Data processing ==
=== Array beamforming === With a seismic array, the signal-to-noise ratio (SNR) of a seismic signal can be improved by summing the coherent signals from the individual array sites. 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.
Φ Backazimuth (BAZ) = angle of wavefront approach, measured clockwise from the North to the direction towards the epicenter in degree. Θ Direction in which the wavefront propagates, measured in degree from the North, with Θ = Φ ±180°. dj Horizontal distances between array site j and center site in [km]. s Slowness vector with absolute value s = 1/ vapp vapp Apparent velocity vector with the absolute value vapp = 1/s . vapp = (vapp,x ,vapp,y ,vapp,z), where vapp,x ,vapp,y ,vapp,z are the single apparent velocity components in [km/s] of the wavefront crossing an array. vapp,h Absolute value of the horizontal component of the apparent velocity.
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{\displaystyle v_{app,h}={\sqrt {v_{app,x}^{2}+v_{app,y}^{2}}}}
In most cases, the elevation differences between single array sites are so small that travel-time differences due to elevation differences are negligible. In this case, we cannot measure the vertical component of the wavefront propagation. The time delay τj between the center site 0 and site j with the relative coordinates (xj, yj) is
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{\displaystyle \tau _{j}={\frac {d_{j}}{v_{app,h}}}={\frac {-x_{j}sin\Phi -y_{j}cos\Phi }{v_{app,h}}}}
In some cases, not all array sites are located on one horizontal plane. The time delays τj also depends on the local crustal velocities (vc) below the given site j. The calculation of τj with coordinates (xj, yj, zj) is
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{\displaystyle \tau _{j}={\frac {-x_{j}sin\Phi -y_{j}cos\Phi }{v_{app,h}}}+{\frac {z_{j}cos\Phi }{v_{c}}}}
In both the calculation can be written in vector syntax with position vector
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{\displaystyle r_{j}}
and slowness vector
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{\displaystyle s_{j}}
:
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{\displaystyle \tau _{j}=r_{j}\cdot s_{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
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{\displaystyle b(t)={\frac {1}{M}}\sum _{j=1}^{M}w_{j}(t+\tau _{j})}
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. Real data w(t) are the sum of background noise n(t) plus the signal of interest S(t), i.e. w(t) = S(t) + n(t). Assuming that the signal is coherent and not attenuated, calculating the sum of M observations and including noise we get
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{\displaystyle B(t)=M\cdot S(t)+\sum _{j=1}^{M}n_{j}(t+\tau _{j})}