Seismic array

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 1950s in order to improve the detection of nuclear tests worldwide. Many of these deployed arrays were classified until 1990s. Today they become part of the 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 its aperture given by the largest distance between the single seismometers.

The sensors in a seismic array are arranged in different geometry pattern horizontally. The arrays built in early 1960s were either cross (orthogonal linear) or L-shaped. The aperture of these arrays ranges from 10 to 25km. 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.

Take the NORES design as an example, seismometers are placed on 4 concentric rings. The radii of the 4 rings are given by:

R_n = R_min * 2.15ⁿ (n = 0,1,2,3), 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 single array sites. The most important point during the beamforming process is to find the best delay times, with 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 on to the horizontal plane are defined by the angles Φ and Θ.

• d_j Horizontal distances between array site j and center site in [km].
• v_app Apparent velocity vector with the absolute value v_app = 1/s . v_app = (v_app,x ,v_app,y ,v_app,z) , where v_app,x ,v_app,y ,v_app,z are the single apparent velocity components in [km/s] of the wavefront crossing an array.
• v_app,h Absolute value of the horizontal component of the apparent velocity.
• s Slowness vector with absolute value s = 1/ v_app
• 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°.

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 τ_j between the center site 0 and site j with the relative coordinates (x_j, y_j) is

$\tau _{j}={\frac {d_{j}}{v_{app,h}}}={\frac {-x_{j}sin\Phi -y_{j}cos\Phi }{v_{app,h}}}$

In some cases, not all array sites are located on one horizontal plane. The time delays τ_j also depends on the local crustal velocities (v_c) below the given site j. The calculation of τ_j with coordinates (x_j, y_j, z_j) is

$\tau _{j}={\frac {-x_{j}sin\Phi -y_{j}cos\Phi }{v_{app,h}}}+{\frac {z_{j}cos\Phi }{v_{c}}}$

In both cases the time delays can be written in vector notation

$\tau _{j}=r_{j}\cdot s_{j}$

Let w_j(r_j ,t) be the digital sample of the seismometer from site j at time t, then the beam of the whole array is defined as

$b(t)={\frac {1}{M}}\sum _{j=1}^{M}w_{j}(t+\tau _{j})$

If seismic waves were 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

$B(t)=M\cdot S(t)+\sum _{j=1}^{M}n_{j}(t+\tau _{j})$

Assuming that the noise n_j(r_j ,t) has a normal amplitude distribution with zero mean and variance σ² at all sites. Then the variance of the noise after summation is σ_s² = M⋅σ². The theoretical improvement of the SNR by beamforming (aka array gain) will be $G={\sqrt {M}}$ for an array containing M sites.

The n-th root process

N-th root process is a non-linear method to enhance the SNR during beamforming. Before summing up the single seismic traces, the N-th root is calculated for each trace retaining the sign information. signum{w_j(t)} is a function defined as -1 or +1, depending on the sign of the actual sample w_j(t). N is an integer that has to be chosen by the analyst

$B_{N}(t)=M\cdot S(t)+\sum _{j=1}^{M}{\sqrt[{N}]{n_{j}(t+\tau _{j})}}\cdot signum\{w_{j}(t)\}$

After this summation, the beam has to be raised to the power of N

$b(t)=|B_{N}(t)|^{N}\cdot signum\{w_{j}(t)\}$

N-th root process is first proposed by K. J. Muirhead and Ram Dattin in 1976. With n-th root process, the suppression of uncorrelated noise is better than with linear beamforming. However, it weights the coherency of a signal higher than the amplitudes, which results in a distortion of the waveforms.

Weighted stack methods

Schimmel and Paulssen introduced another non-linear stacking technique in 1997 to enhance signals through 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 and achieved a similar resolution.

An easily implementable weighted stack method would be to weight the amplitudes of the single sites of an array with the SNR of the signal at this site before beamforming, but this does not directly exploit the coherency of the signals across the array. All weighted stack methods can increase the slowness resolution of vespagrams.

The double beam technique

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 wellknown source locations with the so-called "double beam method". The principle of reciprocity is used for source and receiver arrays to further increase the resolution and the SNR for small amplitude signals by combining both arrays in a single analysis.

Applications

Current seismic arrays worldwide:

YKA

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. YKA currently consists of 19 short period seismic sensors in the form of a cross with an aperture of 2.5 km, plus 4 broadband seismograph sites with instruments able to detect a wide range of seismic wave frequencies.

LASA

LASA or Large Aperture Seismic Array is the first large seismic array. It was built in Montana, USA, in 1965.

NORSAR

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. It has been an independent, not-for-profit, research foundation within the field of geo-science since 1999. NORSAR was constructed as a large aperture array with a diameter of 100 km. It is the largest stand-alone array in the world.

NORES and ARCES

NORES was the first regional seismic array constructed in southern Norway in 1984. A sister array ARCES was established in northern Norway in 1987. NORES and ARCES are small aperture arrays with a diameter of only 3 km.

GERES

GERES is a small aperture array built in the Bavarian Forest near the border triangle of Germany, Austria and Czech, in 1988. It consists of 25 individual seismic stations arranged in 4 concentric rings with radius of 200m, 430m, 925m and 1988m.

SPITS

SPITS is a very small aperture array at Spitsbergen, Norway. It was originally installed in 1992 and upgraded to IMS standard in 2007 by NORSAR.

See also

• Seismometer
• Array processing