Seismic array

Last updated

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. [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).

Contents

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

Layout of Yellowknife Seismological Array (YKA) in Canada. Shortband seismometers are installed on blue and red sites, while broadband seismometers are installed on green sites. YKA.png
Layout of Yellowknife Seismological Array (YKA) in Canada. Shortband seismometers are installed on blue and red sites, while broadband seismometers are installed on green sites.

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. [1]

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

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.

A wavefront coming from north-east and crossing a seismic array Seismic array.png
A wavefront coming from north-east and crossing a seismic array

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.

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

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

In both the calculation can be written in vector syntax with position vector and slowness vector :

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. 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

Assuming that the noise nj(t) has a normal amplitude distribution with zero mean and variance σ2 at all sites, then the variance of the noise after summation is and the standard deviation is . That means the standard deviation of the noise is multiplied by while the coherent signal is multiplied by . The theoretical improvement of the SNR by beamforming (aka array gain) will be for an array containing M sites. [1]

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{wj(t)} is a function defined as -1 or +1, depending on the sign of the actual sample wj(t). N is an integer that has to be chosen by the analyst

Here the value of the function is defined as ±1 depending on the sign of the actual sample wj(t). 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. [2] With the N-th root process, the suppression of uncorrelated noise is better than with linear beamforming. However, it weighs 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 [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.

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". [5] 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 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. [1]

The difference between a signal w at the reference site A and the signal wn at any other sensor An is the travel time between the arrivals at the sensors. A plane wave is defined by its slowness vector so

, where is the position vector of site n

The best beam of an array with M sensors for a seismic signal for the slowness so is defined as

If we calculate all time shifts for a signal with the slowness so with respect to any other slowness s, the calculated beam becomes

The seismic energy of this beam can be calculated by integrating over the squared amplitudes

This equation can be written in the frequency domain with being the Fourier transform of the seismogram w(t), using the definition of the wavenumber vector k = ω⋅ s

, where

This equation is called the transfer function of an array. If the slowness difference is zero, the factor becomes 1.0 and the array is optimally tuned for this slowness. All other energy propagating with a different slowness will be suppressed. [1]

Slowness estimation

Slowness estimation is a matter of forming beams with different slowness vectors and comparing the amplitudes or the power of the beams, and finding out the best beam by looking for the vapp and backazimuth combination with the highest energy on the beam.

f-k analysis

Frequency-wavenumber analysis is used as a reference tool in array processing for estimating slowness. 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. A monochromatic plane wave w(x,t) will propagate along the x direction according to equation

It can be rewritten in frequency domain as

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. [8]

Beampacking

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. Compared to the f-k process, the beampacking process results in a slightly (about 10%) narrower peak for the maximum power.

Plane wave fitting

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. [1] Let ti be the arrival time picked at site i, and tref be the arrival time at the reference site, then τi = ti − tref is the observed time delay at site i. We observe the plane wave at M sites. With M ≥ 3. The horizontal components (sx, sy) of the slowness vector s can be estimated by

Plane wave fitting requires interactive analyst's work. However, to obtain automatic time picks and thereby provide a slowness estimate automatically, techniques like cross-correlation or just picking of peak amplitude within a time window may be used. [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.

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. [10]

LASA

Configuration of large aperture array NORSAR and small aperture array NORES. NORSAR.png
Configuration of large aperture array NORSAR and small aperture array NORES.

LASA or Large Aperture Seismic Array is the first large seismic array. It was built in Montana, USA, in 1965. [11]

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. [8]

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. [8]

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. [12]

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. [13]

See also

Related Research Articles

Signal-to-noise ratio is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. SNR is defined as the ratio of signal power to the noise power, often expressed in decibels. A ratio higher than 1:1 indicates more signal than noise.

Specific detectivity, or D*, for a photodetector is a figure of merit used to characterize performance, equal to the reciprocal of noise-equivalent power (NEP), normalized per square root of the sensor's area and frequency bandwidth.

<span class="mw-page-title-main">Synthetic-aperture radar</span> Form of radar used to create images of landscapes

Synthetic-aperture radar (SAR) is a form of radar that is used to create two-dimensional images or three-dimensional reconstructions of objects, such as landscapes. SAR uses the motion of the radar antenna over a target region to provide finer spatial resolution than conventional stationary beam-scanning radars. SAR is typically mounted on a moving platform, such as an aircraft or spacecraft, and has its origins in an advanced form of side looking airborne radar (SLAR). The distance the SAR device travels over a target during the period when the target scene is illuminated creates the large synthetic antenna aperture. Typically, the larger the aperture, the higher the image resolution will be, regardless of whether the aperture is physical or synthetic – this allows SAR to create high-resolution images with comparatively small physical antennas. For a fixed antenna size and orientation, objects which are further away remain illuminated longer - therefore SAR has the property of creating larger synthetic apertures for more distant objects, which results in a consistent spatial resolution over a range of viewing distances.

<span class="mw-page-title-main">Sensor array</span>

A sensor array is a group of sensors, usually deployed in a certain geometry pattern, used for collecting and processing electromagnetic or acoustic signals. The advantage of using a sensor array over using a single sensor lies in the fact that an array adds new dimensions to the observation, helping to estimate more parameters and improve the estimation performance. For example an array of radio antenna elements used for beamforming can increase antenna gain in the direction of the signal while decreasing the gain in other directions, i.e., increasing signal-to-noise ratio (SNR) by amplifying the signal coherently. Another example of sensor array application is to estimate the direction of arrival of impinging electromagnetic waves. The related processing method is called array signal processing. A third examples includes chemical sensor arrays, which utilize multiple chemical sensors for fingerprint detection in complex mixtures or sensing environments. Application examples of array signal processing include radar/sonar, wireless communications, seismology, machine condition monitoring, astronomical observations fault diagnosis, etc.

<span class="mw-page-title-main">Array processing</span>

Array processing is a wide area of research in the field of signal processing that extends from the simplest form of 1 dimensional line arrays to 2 and 3 dimensional array geometries. Array structure can be defined as a set of sensors that are spatially separated, e.g. radio antenna and seismic arrays. The sensors used for a specific problem may vary widely, for example microphones, accelerometers and telescopes. However, many similarities exist, the most fundamental of which may be an assumption of wave propagation. Wave propagation means there is a systemic relationship between the signal received on spatially separated sensors. By creating a physical model of the wave propagation, or in machine learning applications a training data set, the relationships between the signals received on spatially separated sensors can be leveraged for many applications.

Beamforming or spatial filtering is a signal processing technique used in sensor arrays for directional signal transmission or reception. This is achieved by combining elements in an antenna array in such a way that signals at particular angles experience constructive interference while others experience destructive interference. Beamforming can be used at both the transmitting and receiving ends in order to achieve spatial selectivity. The improvement compared with omnidirectional reception/transmission is known as the directivity of the array.

<span class="mw-page-title-main">Ring laser</span>

Ring lasers are composed of two beams of light of the same polarization traveling in opposite directions ("counter-rotating") in a closed loop.

Phase-comparison monopulse is a technique used in radio frequency (RF) applications such as radar and direction finding to accurately estimate the direction of arrival of a signal from the phase difference of the signal measured on two separated antennas or more typically from displaced phase centers of an array antenna. Phase-comparison monopulse differs from amplitude-comparison monopulse in that the former uses displaced phase centers with a common beam pointing direction, while the latter uses a common phase center and displaced beam pointing directions.

Precoding is a generalization of beamforming to support multi-stream transmission in multi-antenna wireless communications. In conventional single-stream beamforming, the same signal is emitted from each of the transmit antennas with appropriate weighting such that the signal power is maximized at the receiver output. When the receiver has multiple antennas, single-stream beamforming cannot simultaneously maximize the signal level at all of the receive antennas. In order to maximize the throughput in multiple receive antenna systems, multi-stream transmission is generally required.

Radar engineering details are technical details pertaining to the components of a radar and their ability to detect the return energy from moving scatterers — determining an object's position or obstruction in the environment. This includes field of view in terms of solid angle and maximum unambiguous range and velocity, as well as angular, range and velocity resolution. Radar sensors are classified by application, architecture, radar mode, platform, and propagation window.

Time-domain thermoreflectance is a method by which the thermal properties of a material can be measured, most importantly thermal conductivity. This method can be applied most notably to thin film materials, which have properties that vary greatly when compared to the same materials in bulk. The idea behind this technique is that once a material is heated up, the change in the reflectance of the surface can be utilized to derive the thermal properties. The reflectivity is measured with respect to time, and the data received can be matched to a model with coefficients that correspond to thermal properties.

<span class="mw-page-title-main">Arcsine distribution</span> Type of probability distribution

In probability theory, the arcsine distribution is the probability distribution whose cumulative distribution function involves the arcsine and the square root:

In geophysics, geology, civil engineering, and related disciplines, seismic noise is a generic name for a relatively persistent vibration of the ground, due to a multitude of causes, that is often a non-interpretable or unwanted component of signals recorded by seismometers.

3D sound localization refers to an acoustic technology that is used to locate the source of a sound in a three-dimensional space. The source location is usually determined by the direction of the incoming sound waves and the distance between the source and sensors. It involves the structure arrangement design of the sensors and signal processing techniques.

<span class="mw-page-title-main">Sonar signal processing</span> Underwater acoustic signal processing

Sonar systems are generally used underwater for range finding and detection. Active sonar emits an acoustic signal, or pulse of sound, into the water. The sound bounces off the target object and returns an “echo” to the sonar transducer. Unlike active sonar, passive sonar does not emit its own signal, which is an advantage for military vessels. But passive sonar cannot measure the range of an object unless it is used in conjunction with other passive listening devices. Multiple passive sonar devices must be used for triangulation of a sound source. No matter whether active sonar or passive sonar, the information included in the reflected signal can not be used without technical signal processing. To extract the useful information from the mixed signal, some steps are taken to transfer the raw acoustic data.

Multidimension spectral estimation is a generalization of spectral estimation, normally formulated for one-dimensional signals, to multidimensional signals or multivariate data, such as wave vectors.

Synthetic Aperture Ultrasound (SAU) Imaging is an advanced form of imaging technology used to form high-resolution images in biomedical ultrasound systems. Ultrasound Imaging has become an important and popular medical imaging method, as it is safer and more economical than computer tomography (CT) and magnetic resonance imaging (MRI).

Beamforming is a signal processing technique used to spatially select propagating waves. In order to implement beamforming on digital hardware the received signals need to be discretized. This introduces quantization error, perturbing the array pattern. For this reason, the sample rate must be generally much greater than the Nyquist rate.

Multidimensional seismic data processing forms a major component of seismic profiling, a technique used in geophysical exploration. The technique itself has various applications, including mapping ocean floors, determining the structure of sediments, mapping subsurface currents and hydrocarbon exploration. Since geophysical data obtained in such techniques is a function of both space and time, multidimensional signal processing techniques may be better suited for processing such data.

<span class="mw-page-title-main">Digital antenna array</span>

Digital antenna array(DAA) is a smart antenna with multi channels digital beamforming, usually by using fast Fourier transform (FFT). The development and practical realization of digital antenna arrays theory started in 1962 under the guidance of Vladimir Varyukhin (USSR).

References

  1. 1 2 3 4 5 6 7 8 Bormann, P (2012). New Manual of Seismological Observatory Practice (NMSOP-2). IASPEI. p. Chapter 9.
  2. Muirhead, K. J., and Ram Datt (1976). The N-th root process applied to seismic array data. Geophysical Journal International, 47(1), 197-210.
  3. Schimmel, M., and Paulssen, H. (1997). Noise reduction and detection of weak, coherent signals through phase-weighted stacks. Geophysical Journal International, 130(2), 497-505.
  4. Kennett, B. L. N. (2000). Stacking three-component seismograms. Geophysical Journal International, 141(1), 263-269.
  5. Krüger, F., Weber, M., Scherbaum, F., and Schlittenhardt, J. (1993). Double beam analysis of anomalies in the core-mantle boundary region. Geophysical Research Letters, 20(14), 1475-1478.
  6. Capon, J. (1969). High-resolution frequency-wavenumber spectrum analysis. Proceedings of the IEEE, 57(8), 1408-1418.
  7. Kværna, T., and Doornbos, D. J. (1986). An integrated approach to slowness analysis with arrays and three-component stations. NORSAR Semiannual Technucal Summary, 1, 2-85.
  8. 1 2 3 4 5 "NORSAR". Norsar.no. Retrieved 2015-11-17.
  9. Del Pezzo, E., and Giudicepietro, F. (2002). Plane wave fitting method for a plane, small aperture, short period seismic array: a MATHCAD program. Computers and Geosciences, 28(1), 59-64.
  10. "The Yellowknife Seismological Array". Can-ndc.nrcan.gc.ca. 2015-10-20. Retrieved 2015-11-17.
  11. Frosch, R. A., and Green, P. E., Jr. (1966). The concept of a large aperture seismic array. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences (Vol. 290, No. 1422, pp. 368-384). The Royal Society.
  12. "GERES - Deutsche IMS-Station: Seismische Primärstation GERES (PS19)" (in German). BGR. 2000-08-12. Retrieved 2015-11-17.
  13. "AS072, Spitsbergen, Norway: CTBTO Preparatory Commission". Ctbto.org. 2007-04-27. Retrieved 2015-11-17.