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Ambient Earth noise and instrumental noise

The seismic frequency band can be defined from 0.3 mHz to tens or hundreds of Hz, in which the lower limit is defined by the period of the gravest observed free mode of the Earth (0S2).

Digital seismic recordings in this frequency band always contain noise, which essentially can be attributed to ambient Earth noise and instrumental noise, or self-noise, of the recording system. 

Figure 1. Seismic noise probability density functions at seismic stations Heimansgroeve (HGN), Witteveen (WIT) and Winterswijk (WTSB)
Figure 1. Seismic noise probability density functions at seismic stations Heimansgroeve (HGN), Witteveen (WIT) and Winterswijk (WTSB)

Instrumental noise of today's seismic sensors and high resolution digitizers is usually not considered during the interpretation of seismic data. However, this type of noise may dominate at lower frequencies (e.g. below 0.02 Hz) or at higher frequencies at sites with very low ambient Earth noise levels. In cooperation with Utrecht University (Faculty of Geosciences) KNMI developed a new method to measure instrumental noise in seismic recording systems using ambient Earth noise recordings1). This new method extracts self-noise and relative transfer functions of the recording systems from the measurements only, and does not require a priori information about the transfer function of each channel. As a consequence the method reveals under which conditions the interpretation of data may be biased by the recording system.

Ambient Earth noise in the Netherlands

Ambient Earth noise, or background noise, is defined as seismic signals in the absence of transient signals from earthquakes. The U.S. Geological Survey New Low Noise Model (NLNM)2) is often used as reference model for background noise. This model was constructed from a large number of vertical seismograms from many globally distributed seismic stations, and represents the lowermost envelope of a large set of power spectral densities of vertical true ground acceleration over the entire seismic frequency band. Essentially, this envelope reflects the minimum seismic noise level which is always expected in seismic recordings. The NLNM model is often used for the purpose of site selection or to compare the quality of seismic sites in terms of noise. Figure 1 displays the probability density functions of the background noise3) in The Netherlands, recorded at three seismic stations.

New Low Noise Model

Many of the large features of the NLNM are well understood, and the ambient Earth noise sources may roughly be classified in the frequency domain as follows:

  1. Between 1.10-6 and 1.10-3 Hz the Newtonian attraction of moving air masses in the local atmosphere above the seismic sensor is the principal source of noise4). Tidal frequencies, in particular the tidal constituent M2 due to the Earth rotation relative to the Moon with a period of more than 12 hour, can be measured in this range by very broad band seismic sensors. Also the theoretical, but never observed, Slichter normal mode has a period in this range.
  2. Between 0,3.10-3 and 30.10-3 the noise is not fully understood. In the range between 2 and 7 mHz the noise floor contains spectral peaks whose frequencies coincide with those of the fundamental spheroidal Earth modes. This structure, called ’hum’, is a global phenomenon and constitutes a lower bound for observable signals. The ’hum’, however, was revealed by stacking the spectra of many seismic recordings as it is slightly below or near the instrumental noise levels of today’s seismic sensors5). Figure 2 shows that the ’hum’ is detected in the Netherlands as well, both in stations HGN and WTSB, which confirms the high quality of these seismic stations in terms of the noise level. The quality has been achieved by careful site selection and installation of the sensors. The origin of the hum is debated but most studies direct towards atmospheric turbulence6) or ocean waves7). Between 7 and 30 mHz the background noise consists of Rayleigh waves, circling around the globe, for which the origin is also not fully understood.
  3. Marine microseisms due to interaction of ocean waves with the ocean floor dominate in the frequency range between 30 mHz and 1 Hz. The sources for these microseisms are recognized in storms at oceans, generating swell- and surf-induced pressure fluctuations at the bottom of the ocean.
  4. Noise at frequencies above 1 Hz is attributed to local random noise (cultural noise) and local atmospheric turbulences. In particular the cultural noise may show strong diurnal variations.
Figure 1. Seismic noise probability density functions at seismic stations Heimansgroeve (HGN), Witteveen (WIT) and Winterswijk (WTSB), measured in 2005.
Figure 1. Seismic noise probability density functions at seismic stations Heimansgroeve (HGN), Witteveen (WIT) and Winterswijk (WTSB), measured in 2005.
Figure 1. Seismic noise probability density functions at seismic stations Heimansgroeve (HGN), Witteveen (WIT) and Winterswijk (WTSB), measured in 2005.
Figure 1. Seismic noise probability density functions at seismic stations Heimansgroeve (HGN), Witteveen (WIT) and Winterswijk (WTSB), measured in 2005.
Figure 1. Seismic noise probability density functions at seismic stations Heimansgroeve (HGN), Witteveen (WIT) and Winterswijk (WTSB), measured in 2005.
Figure 1. Seismic noise probability density functions at seismic stations Heimansgroeve (HGN), Witteveen (WIT) and Winterswijk (WTSB), measured in 2005.

Applications of monitoring of seismic background noise

Not only for site selection purposes the NLNM model is important, but it also has been proven to be useful in seismic network monitoring purposes, e.g. for the Virtual European Broadband Seismograph Network (VEBSN)8), and in monitoring volcanic activity9). Such seismic networks continuously monitor the power spectral density of the background noise and compare these at specific frequencies with the NLNM to detect sudden changes or anomalies. These may, for example, indicate an increase of seismic activity, changes in site conditions or instrumental problems. KNMI seismic stations HGN, WIT and WTSB in The Netherlands, as well as the KNMI seismic stations on the Netherlands Antilles (Saba, St. Eustatius and St. Maarten) are continuously monitored in this way. Figure 3 is an example showing the ambient noise variation in time.

Figure 3. Variation of seismic background noise as function of time at a seismic station. This example illustrates the seasonal variation of the background noise for all frequencies, with lowest noise levels during the northern hemisphere summer.
Figure 3. Variation of seismic background noise as function of time at a seismic station. This example illustrates the seasonal variation of the background noise for all frequencies, with lowest noise levels during the northern hemisphere summer.

Below a few mHz the seismic noise correlates with local barometric pressure variations, mainly due to gravitational attraction by atmospheric masses above the seismic station. Correcting the vertical seismic recordings below a few mHz for atmospheric pressure changes permits the achievement of noise levels even below the NLNM4,10), which means that the NLNM may need some minor revision. Also a new analysis technique11) applied to recordings from the Global Seismographic Network (GSN) shows noise levels below the NLNM. The interpretation of such low noise data would only makes sense if the noise level of the data is above the noise levels of sensor and digitizer at these low frequencies. It is for these reasons that accurate knowledge or self-noise of the seismic equipment is crucial, and a new technique to estimate instrumental self-noise was developed.

Seismic instrumentation

Broadband and very broadband seismic sensors are used in global, regional and even local seismological studies, because of their wide frequency bandwidth, large dynamic range and low self-noise level. The bandwidth of the sensor specifies the frequency range in which the instrument has a more or less flat response to ground velocity, and may cover more than 4 logarithmic frequency decades. Today's broadband seismometers are of a force balance feedback system to provide a dynamic range up to about 160 dB, to capture signals from ambient Earth noise to earthquakes of magnitude 9.5 at 90 degrees epicentral distance. At low frequencies instrumental noise of today’s seismic sensors and dataloggers is of inherent 1/f type of noise, noise whose power spectral density is inversely proportional to frequency. The self-noise for present seismic systems is typically close to the NLNM over an extended bandwidth, from a few hundred seconds to a few Hz, and probably defines the NLNM at low frequencies.

Three-channel correlation analysis

In the conventional approach to estimate the self-noise of linear systems, two systems are used and fed by a common, coherent input signal. This technique has been used in many studies12), also to calibrate seismometers13), in which two seismometers are placed close together so that it can be assumed they record the same ground motion. The mathematical solution of such a system is very simple, but the practical application is limited because the method assumes that one of the pair of sensors has an accurately known frequency response. Small errors in the transfer functions (or gains) in the two linear systems will cause relatively large errors in the calculated noise levels14). Our approach1)uses three linear systems which are also fed by a common input signal. The mathematical solution for this system does not need a priori information about the frequency response of each system. The only assumptions are that (1) the self noise between each pair of 2 systems is uncorrelated and (2) the self noise and the input signal are uncorrelated. The mathematical description of the three-channel linear system model shows that we can estimate, solely from the output recordings, (1) the ratio of the transfer functions between the channels and (2) the noise spectrum for each channel. We do not need to know the transfer functions, or its accuracy as is required in the two-channel method.

Digitizer noise level

Figure 4 shows the self-noise of two modern dataloggers, the Quanterra Q4120 and the NARS datalogger. The self-noise was determined with the new technique, using the vertical output of an STS-2 sensor as common input, and compared to the noise level which was measured with closed digitizer inputs. Both digitizers produce some additional noise during the digitizing process of a real input signal, and this disturbance is more pronounced in the NARS datalogger. Both digitizers have a flat noise level at higher frequencies but show a large difference in the dynamic range of about 16 dB. The self-noise levels are above the reference ambient Earth noise level, for frequencies above 1 and 8 Hz respectively, which is too high to record true seismic background noise at the quietest places in the world at high frequencies. Also the frequency at which the 1/f type of noise becomes dominant is different (0.1 Hz for NARS, 0.4 Hz for Q4120), as well as the slope of the 1/f noise. The slope for the Q4120 is modelled with 1/f 1.55 and for the NARS datalogger with 1/f 1.0.

Impact

The new 3-channel correlation technique is a novel, robust and reliable analysis technique to estimate instrumental self-noise, without a priori knowledge of the properties of the instrument. The technique is becoming the standard for manufacturers of seismic equipment and major sensor testing projects to provide accurate estimates of instrumental self-noise. From a scientific point of view the new method is important as it reveals under which conditions the interpretation of seismic data may be biased by the recording system. It is expected that this technique has to be used in studies towards a revised NLNM as to identify the contribution of instrumental noise to the NLNM.

Figure 4. Instrumental noise levels of the NARS datalogger (top) and the Quanterra Q410 datalogger (bottom).
Figure 4. Instrumental noise levels of the NARS datalogger (top) and the Quanterra Q410 datalogger (bottom).
  1. Sleeman, R., A. van Wettum and J. Trampert, 2006. Three-channel correlation analysis: a new technique to measure instrumental noise of digitizers and seismic sensors. Bulletin of the Seismological Society of America, 96, 1, 258-271.
  2. Peterson, J., 1993. Observations and modeling of seismic background noise. U.S. Geological Survey, Open-File report 93-322, 95 pp.
  3. McNamara, D.E. and R.P. Buland, 2004. Ambient noise levels in the continental United States. Bulletin of the Seismological Society of America, 94, 4, 1517-1527.
  4. Zürn, W. and R. Widmer, 1995. On noise reduction in vertical seismic records below 2 mHz using local barometric pressure. Geophys. Res. Lett., 22, 3537-3540.
  5. Widmer-Schnidrig, R., 2003. What can superconducting gravimeters contribute to normal-mode seismology ? Bulletin of the Seismological Society of America, 93, 3, 1370-1380.
  6. Rhie, J. and B. Romanowicz, 2004. Excitation of Earth’s continuous free oscillations by atmosphere-ocean-seafloor coupling. Nature, 431, 552-555.
  7. Webb, S. C., 2007. The Earth’s ‘hum’ is driven by ocean waves over the continental shelves. Nature, 445, 754-756.
  8. Sleeman, R and J. Vila, 2007. Towards an automated quality control manager for the Virtual European Broadband Seismograph Network (VEBSN). ORFEUS Newsletter, 1. (http://www.orfeus-eu.org/newsletter/vol7no1/ index.htm)
  9. Garcia, A., J. Vila, R. Ortiz, R. Macia, R. Sleeman, J.M. Marrero, N. Sanchez, M. Tarraga and A.M. Correig, 2006. Monitoring the reawakening of Canary Islands' Teide volcano. EOS, 87, 6, 61- 65.
  10. Beauduin, R, P. Lognonne, J.P. Montagnier, S. Cacho, J.F. Karczewski and M. Morand, 1996. The effects of the atmospheric pressure changes on seismic signals or how to improve the quality of a station. Bulletin of the Seismological Society of America, 86, 6, 1760-1769.
  11. Berger, J., P. Davis and G. Ekström, 2004. Ambient Earth noise: a survey of the global seismographic network. J. Geophys. Res., 109, B11307.
  12. Holcomb, L. G., 1989. A direct method for calculating instrument noise levels in side-by-side seismometer evaluations. U.S. Geological Survey, Open-File report 89-214, 35 pp.
  13. Pavlis, G.L. and F.L. Vernon, 1994. Calibration of seismometers using ground noise. Bulletin of the Seismological Society of America, 84, 4, 1243-1255.
  14. Holcomb, L.G., 1990. A numerical study of some potential sources of error in side-by-side seismometer evaluations. U.S. Geological Survey, Open-File report 90-406, 41 pp.
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