Seismic array

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: :R_{n} = R_{min}\cdot 2.15^n (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 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. s. Weighted stack methods Schimmel and Paulssen introduced another non-linear stacking technique in 1997 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 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 velocity spectrum analysis. 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 well-known 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. Array transfer function The array transfer function describes sensitivity and resolution of an array for seismic signals with different frequency contents and slownesses. With an array, we are able to observe the wavenumber k=2\pi/\lambda=2\pi\cdot f\cdot s of this wave defined by its frequency f and its slowness s. While time-domain analog-to-digital conversion may give aliasing effects in the time domain, the spatial sampling may give aliasing effects in the wavenumber domain. Thus the wavelength range of seismic signals and the sensitivity at different wavelengths must be estimated. and further developed to include wide-band analysis, maximum-likelihood estimation techniques, and three-component data in the 1980s. 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. A monochromatic plane wave w(x,t) will propagate along the x direction according to equation :w(x,t)=Ae^{i2\pi(f_{0}t-k_{0}x)} It can be rewritten in frequency domain as :W(k_{x},f)=A\delta(f-f_{0})\delta(k_{x}-k_{0}) which suggests the possibility to map a monochromatic plane wave in the frequency-wavenumber domain to a point with coordinates (f, kx) = (f0, k0). Practically, f-k analysis is performed in the frequency domain and represents in principle beamforming in the frequency domain for a number of different slowness values. At NORSAR slowness values between -0.4 and 0.4 s/km are used equally spaced over 51 by 51 points. For every one of these points the beam power is evaluated, giving an equally spaced grid of 2601 points with power information. 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. == Applications ==

Current seismic arrays worldwide: Gräfenberg The Gräfenberg array is the first digital broadband array that has a continuous data history from 1976 until today. This array consists of 13 broadband stations in the Fränkische Alb. It extends approximately 100 kilometers north-south and approximately 40 kilometers east-west. 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 and small aperture array NORES. 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. 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 ==