An Analysis of Ground and Instrumental Short-Period Noise

An analysis of ground and instrumental short-period noise R . CONSOLE * - A. ROVELLI * Received on October 25th, 1978 ABSTRACT The main causes of b ackgrou nd noise on seismic recordings are considered. For this purpose, numerical spectral analysis techniques are applied to records obtained from an analogue-digital converter. Firstly, the causes of noise due to the data acquisition system itself, particu larly to the FM magnetic recording apparatus, are analysed. Subsequently, an analysis is made of seismic ground noise samples taken under various environmental conditions and recorded either in the field, or b y telemetry, or on magnetic tape. RIASSU NTO Vengono prese in esame le principali cause di ru more di fondo su registrazioni sismiche. A questo scopo vengono adoperate tecniche numeriche di analisi spettrale su registrazioni ottenute da un convertitore analogico-digitale. D apprima si analizzano le cause di ru more provenienti * Istitu to Nazionale di Geofisica, Roma. 318 R. C O N S O LE - A. RO V E LLI dal sistema di acquisizione stesso, ed in particolare dal complesso di registrazione magnetica FM. Successivamente vengono analizzati campioni di ru more di fondo sismico, prelevati in varie condizioni amb ientali e registrati direttamente sul posto, oppu re mediante telemetria, o anche su nastro magnetico. INTRODUCTION Anyone who has had anything to do with the installation of seismic recording instruments has had to face the prob lem of grou nd noise. This interference is the main cause which everywhere limits the effectice sensitivity of apparatus by reducing the distance at which an earthqu ake of a given magnitude may be u sefu lly recorded. Indeed, each site may be said to have its own peculiar behaviour as fa r as microtremors are concerned. Even though the latter varies as a fu nction of time in both amplitu de and spectral composition, there are also systematic differences as a result of which certain locations are to be preferred to others as sites for seismic stations. Microtremors are produ ced by pertu rb ation sources both in the vicinity of, and distant from, the recording site. Furthermore, the geological conditions peculiar to the site may cither damp or heighten the amplitu de. Examples of extremely local causes of microseismic agitation consist of the movements of persons or machines in the buildings housing the seismographs, or wind action on their structures. These causes may be removed fairly easily by setting up the seismic sensors in shallow holes or in rather low constructions separated from the buildings in which there are people. D epending on the nature of the ground, interference due to vehicle traffic on roads and to the motion of heavy factory machinery may be propagated over qu ite some distance. This interference appears as oscillation trains of rapidly varying amplitude and a frequ ency of a few hertz. The oscillations caused by gravel crushing and cement manu factu ring plant are parti- AN A N A L Y S IS OF G ROU ND AND IN S TR U M E N TA L ECC. 319 cularly annoying. Of interest in this connection is the work done by W alker et al. (1964), who detected clear-cut lines related to industrial machinery activity in recorded short- period noise spectra. Of course, all interference connected with human activities is characterized by a periodic variation peaking during the day and with minimu m intensity dLiring the night. Occasionally also a weekly periodicity corresponding to the Sunday holiday may be ob served. Some interference may originate fa r away from the recording site. This type of interference is connected mainly with sea conditions and is characterized by a quasi sinusoidal motion with a period of several seconds. Over a period of hours or days, this motion may increase by one order of magnitude with respect to the values ob served during calm periods. Generally speaking, these values are higher in winter months than during the summer, at least in Italy. Rob ertson (1965), for instance, has investigated the connection between short-period wind noise and geological and topographic factors, coming to the conclusion that short- period wind noise is more dependent on topography than on lithology. In view of the material and labour costs involved, a seismic station should be built in such a way that the maximu m amount of data may be obtained. This means that the records produ ced must have the highest possible signal-to-noise ratio. W ith this in mind it obviou sly becomes important to investigate backgrou nd noise, also by means of spectral analysis. Such an investigation may serve two different purposes: i) to check the suitability of a prospective site for a new seismic station; ii) to provide some information on which to base the design of filters to improve the signal-noise ratio during recording or electronic data processing. 320 1. R. C O N S O LE - A. RO V E L L I RECORDING TECHNIQU ES Seismic b ackgrou nd noise must be recorded under the best possible conditions in order to facilitate subsequent processing. The signals are usually not recorded on paper but stored on magnetic tape aand subsequently reprodu ced in the lab oratory in the form in which it is intended to perform the analysis. Magnetic recording is always performed by means of the frequ ency modu lation of a carrier signal in the acoustic range. In simpler recording devices, the signals from variou s channels are mu ltiplexed by mixing different central frequ encies b efore the signals are sent to the recording heads. In more complex recorders, the central frequ ency is the same for all channels and numerous recording head are used to record parallel signals. B oth analogue and digital techniques may b e used for spectral analysis. In the former, the signal is transmitted to special bandpass filters which allow the amplitu de associated with each frequ ency range to be determined visually. In the latter, after the requ ired digitization of the signals has been carried out, the spectral transform of the signal is calculated numerically by the compu ter. The technical characteristics of the instruments used are described in the following (see Fig. 1). The sensors of the three components (two horizontal and one vertical) have a characteristic frequ ency of 1 Hz and are kept in a critical damping condition. Tey have a generator constant of about 600 V/m/s. The amplifiers allow a variab le gain of b etween 400 and 50.000, with a fla t characteristic b etween 0.1 Hz and 5 Hz. Outside this band the fall- off is 12 db/octave. The signals are fed into the input of a seven-track FM tape recorder with a tape speed of 15/16 inches per second with a fiat characteristic up to 150 Hz. The ratio of input to output signals amplitu de is 1:1. D igitization of the signals reprodu ced by the tape is performed on an instrument that can act on eight channels simul- AN A N A LYS IS OF G RO U N D AN D IN S TRU M E N TA L ECC. 321 taneously with a sampling rate of 100 per second for each one. The data are stored using 12 bit words on compu ter- compatib le magnetic tape. By means of this system, voltage differences of about one millivolt may be detected with a maximu m input of + 2 volts. D A TA SEISMOMETERS R / M TAPE RECORDER AMPUFUERS A/ D A/0 TO COMPUTER CONVERTER DIGITAL TAPE RECORDER F / M TAPE RECORDER FIG 2. A C Q U IS ITIO N S YS TE M 1 N U M E RIC AL DATA PROCESSING The advantage of the type of instrumentation described in § 1 ab ove is that it supplies data in digital form ready for direct use in computers. The values obtained from the digitizer are filtered to remove frequ encies lying outside the band to be analysed. Nu merical tests are then run to check for stationarity, a necessary condition for calculating the spectral density of background noise using standard stochastic process techniques (B endat, 1958). After the stationary conditions of the numerical sequences have been checked, the spectral contents may be calculated by the direct or indirect method (Bath, 1974). The former is used more frequ ently for processes of the deterministic R. C O N S O LE - A. 322 RO V E LLI type and consists in calculating the square-modulus of the Fourier transform of the record divided by the duration of the signal examined. For stochastic type processes, the results display considerable instabilities in certain cases. The indirect method is preferab le for seismic noise; the au tocorrelation fu nction of the sequence recorded is calculated first, and then the power spectrum is ob tained from the fast Fou rier transform of the au tocorrelation fu nction. This technique affords the advantage of a much higher stability (B endat- Piersol, 1971). More in detail, the operations to be performed after the record has been digitized are as follows : — Eliminate the continuous component (always present to some extent in FM records) from the initial data by transforming the starting series into a zero mean value series. — Filter out any trends, or even spectral contents in the high- frequency band, likely to produ ce aliasing errors. — Calculate the au tocorrelation fu nction on the pre-set intervalzyxwvutsrqponmlkihgfedcbaWVUTSRQPONMLIHGFEDCBA T from the digital data using the expression: f ( t ) f ( t + T) d i — Obtain the record power spectrum numerically from the expression: £r(w) = 2 CU) — Correct the record power e - iu td t spectrum using the seismo- graph response curve / / («) where the seismograph transfer fu nction H(w) takes into account frequ ency dependence due b oth to the seismometer and to the electronic components of the amplifier system. AN A N A L Y S IS OF GROU ND AN D IN S TR U M E N TA L ECC. 323 — Lastly, in order to avoid instability due to signal truncation effects, suitable smoothing operators are used. In recent years, in addition to these conventional spectral analysis methods, «d a ta adaptive techniqu es » (Lacoss, 1971, U lrych-Bishop, 1975) have begun to be used on a increasing scale. One of these techniques, the maximu m entropy method, has been successfully applied in seismology (Slicther, 1967 and W iggins et al., 1972). Lacoss (1971), for instance, makes a comparison b etween long- period seismic noise spectra calculated by standard techniques and those using data adaptive methods. The maximu m entropy spectrum of a time sequence is calculated by the transfer fu nction of a linear operator wich filters a white noise in order to give the sequence as output. IfzyxwvutsrqponmlkihgfedcbaWVUTSRQPONMLIHGFEDCBA F( to) is the spectral amplitu de of the time series whitened by a filter with transfer fu nction T(w), it results | F ( w ) T (to) | = k where k is a constant (U lrych et al., 1973). Consequently FzwvtsrponljihgecaZXWVUTSRQPONMLKJIGFEDCBA (w) p = - = — M I F (col 2 I |l _ 2 Y i exp ( — 27if;wAO |2 ;= i M is the filter length, At is the sampling rate and y, are the filter coefficients, calculated using least squares criterion. Andersen (1974) furnishes a faster algorithm. A comparison between the two methods seems rather interesting (fig. 11). R. C O N S O LE - A. 324 3. RO V E LLI CHECKING OF ELECTRONIC NOISE INTRODUCED BY THE RECORDING CHAIN B efore starting on the actual analysis of the backgrou nd noise in seismic records, a check was carried out on the reliability of our data acquisition system. The intention was to check the possible existence and size of any output signals from the recording chain not produ ced by the motion of the grou nd on which the sensor was placed. These signals may originate in the electronic components of the amplifier, particu larly in the FM magnetic recording system. For the purpose of our investigation, an indirect method was chosen in which certain noise sources were deliberately excluded. The first test consiste of analysing the b ackgrou nd noise produ ced inside the analogue-digital converter. The test was run by simply sampling for a period of about 3 minutes with the digitizer input circuit open. As a result, the numerical values produ ced by the analoguedigital converter remained constant at a non-zero mean value (owing to amplifier polarization), displaying random shifting away from this value by a maximu m of plus or minus one digitation unit. The au tocorrelation fu nction of these signals (fig. 2a) is characterized by white noise, and the spectrum of the record ob tained is practically fiat over all frequ encies. The spectrum of the grou nd equivalent signal for this noise (fig. 2a') ob viou sly reproduces the inverse of the transfer fu nction of the system. In the second test, the noise introdu ced b y the grou p was examined by digitizing the output signal sensor mass had been stopped, thereby simulating the of actual zero grou nd motion as the seismometer longer provide any output signal. amplifier after the condition could no The amplitu de of the signals recorded was around 0.010 V. The spectrum of this record peaked at 50 Hz (fig. 2 b ') The presence of the 50 Hz frequ ency is noticeable also in the auto- > z zyxwvutsrqponmlkihgfedcbaWVU > z > r K! Ng O •H O - 3 ED fa o C z o > z o t» c g H z H > f W n o FIG. 2 - Autocorrelation functions (a, b, c, d) and power different recording techniques: directly from the electronic digital recording with stopped mass (case b and b ') by and by telephone cable, again with stopped mass (case (a', b', c', d') obtained from electronic noise produced by components of the digitizer (case a and a'), from direct frequency modulation with stopped mass (case c and c') d and d'). NJ 326 R. C O N S O LE - A. RO V E L L I correlation fu nction, fig. 2 b ) and a beat effect is set up with the Nyqu ist frequ ency of ~ 52 Hz, as can be seen even more clearly in fig. 3b. An analysis was then made of the noise produ ced b y the FM tape recorder. In this case, what was obtained from the reprodu ction of the tape was digitized using the normal amplification system and b locking the sensor masses. This test revealed the presence of signals of appreciab le amplitu de at the analoguedigital converter input. Ob served voltages flu ctu ated b etween plus or minus 0.030 V, while the FM tape recorder dynamics afforded a linear output up to values not exceeding + 2V. Nu merical analysis by compu ter revealed a high degree of au tocorrelation in these signals (2c). In fact, the power spectrum displays very distinct peaks that we b elieve to be related to the periodicity with which the motor and driving mechanism pivots revolve inside the FM tape recorder, or to over-shoots of the speed control system. The trend of the shift spectrum referring to the actual grou nd motion equivalent to the digitized signals is rather high at low frequ encies (fig. 2c'). This trend is the minimu m level for which any grou nd motion may be u sefu lly detected as a fu nction of frequ ency by the acquisition system being used. In this connection, the « seismic » backgrou nd noise is taken as the useful signal to be analysed. Obviously, it will also be a negative fa ctor tending to mask the true signals when the system is used to detect seismic events. In order to extend the investigation to other sources of electronic noise, tests were run on the cable transmission systems using frequ ency modu lation cu rrently being used b etween the Central Geophysical Ob servatory and several peripheral stations. Also in this case, care was taken to b lock the mass of the sensor (situated at the Aqu ila O b servatory) and the output signal fr om the electronic chain formed by the preamplifier, modu lator, telephone line and demodu lator, was digitized. In the record spectrum, and thus also in the grou nd displacement spectrum (fig. 2d'), a very conspicuous peak is visib le at a frequ ency of 17 Hz, in addition to the mains frequ ency. It is prob ab ly due to the modu lator- demodu lator couple. The autocorrelation fu nction is shown in fig. 2d. 1.00 1.00 ( a ) Q50 050 0.00 0.00 050 -0.50 i - 050 0.00 -i— 0.50 tlsecl . 100 1.00 1.00 (c) 0.50 050 0.00 050 - 050 - 050 000 050 tlsecl 100 -100 -0.50 000 050 100 150 tt?r=c) FIG. 3 - Autocorrelation functions of electronic noise for time lags not exceedng 1.5 sees. In case b, beat effect between the 50 Hz of the mains and the Nyqui st frequency of 52 Hz, superimposed on a long-period pattern, is shown. FIG. 4 - Power spectra of electronic noise in the 0 —10 Hz band. Only in case c sharp lines may be observed with a high spectral contents for frequencies lower than 10 Hz. AN A N A L YS IS OF GROU ND AND IN S TR U M E N TA L ECC. 329 It could be of interest to analyse the au tocorrelation function in fig. 2 in greater detail. If only time lags of less than 1 second are considered, the patterns for the various circumstances are those shown in fig. 3. The frequ encies discussed earlier are thus easier to discern. A more thorough analysis may be made also as fa r as frequencies are concerned (fig. 4) by examining the 0-10 Hz band, i.e. the one of greatest interest in seismology, using a higher resolution. W ithin this range, it may be observed that only in case 4c is there any interference with high frequ ency peaks that coLild be added to the seismic signals and alter things because of their high amplitude. 4. S E IS M IC BACKGROUND NOISE The subsequent tests were run on recordings of background noise samples taken in different places and under different environmental conditions. Some of these tests were run outside the Central Geophysical Ob servatory of Monte Porzio Catone, and requ ired the use of an FM magnetic tape recorder. Others were run by digitizing signals directly in real time using remote sensing by radio or telephone cable. Figs. 5ci, ci, C3 show the ground displacement spectra of tracks ai, a2, a3 recorded on seismograph S13 duringo a survey carried out in Calabria to ascertain the suitability of sites as locations for seismic stations. certain The signals were first recorded using the FM technique and then digitized. The auto- correlation functions are shoun in figs. 5bi, b 2, b3. Visib le in the first and second recording is a small seismic agitation (figs. 5ai and a 2) with fairly small amplitudes. The effects of meteorological interference (wind, rough seas, etc.) may be see in fig. 5a3. A fu rther example of recording by R. C O N S O LE - A. 330 RO V E LLI II vW ^Hty^' -05* 'V FIG. 5 - Seismic noise with related autocorrelation functions and ground motion spectra, recorded by the FM technique in different parts of Calabria, (a.) Martino; (a2) Pian della Corona; (aj) Monte Liccio. the FM technique was carried out inside the Central Geophysical Ob servatory (fig. 6). In this case, it was possible to compare three digital sequences directly recorded in real time (fig. 7). B oth in the FM recording (fig. 6) and in case ( 1) in fig. 7, the frequ ency peaks at 1.4 Hz, prob ab ly as a result of industrial machinery in operation. The noise level is, however, much higher in the FM recordings. In the case of track (1) and (2) in fig. 7 referring, respectively, to days with low and high meteorological interference, b oth the two au tocorrelation fu nctions and the energy distrib- FIG. 6 - Seismic noise, with related autocorrelation functions and ground motion spectra recorded by FM technique at the Central Geophysical Observatory of Monte Porzio Catone. FIG. 7 - Seismic noise of two recordings made at the Monte Porzio Catone station, near Rome: 1) "ca lm" situation with slight, industrial noise; 2) high meteorological noise. AN A N A L Y S IS OF G ROU ND AND IN S TR U M E N TA L ECC. 333 ution displayed by the two power spectra clearly reveal the presence of different frequ encies with different amplitudes. In case ( 1) the spectral contents are very high in the 3-5 Hz band, and there is a considerable noise level at 10 Hz. In case (2), the spectral contents all lie in the 0.5-10 Hz band with a very sharp spectral contenas show a very sharp drop after 1 Hz (fig. 7). The results concerning the background noise telemetered from the Montasola station are given in fig. 8. Tracks (1) and (2) in fig. 8 are contemporaneous respectvely with trains (1) and (2) in fig. 7. However, as the noise level at th eMontasola station is very low, there is not much observable difference between the two spectra and the two au tocorrelation functions. Also for the Duronia station two recordings were made, simultaneous at Roma Monte Porzio and Montasola. Ttrasmission was by telephone cable (fig. 9). For Duronia, track (1), which refers to a day with comparatively little interference, displays a considerably lower noise level (b y about a factor of ten) than track ( 2) in the low frequ ency band. In track (2), on the other hand, there is a rapid fall for frequ encies greater than 0.5-1 Hz. The spectral contents in the band around 5 Hz, so conspicuous in track (1), now disappear. The tracks in fig. 10 refer to recordings, again simultaneous with the others in figs. 7, 8 and 9, carried out in the Aquila station and also transmitted by telephone cable to the Central G eophysical Ob servatory. Both the noise level and the spectral pattern are virtually the same in case (1) and (2). -b. FIG. 8 - Seismic noise of two recordings made at Duronia station, near Rome: 1) "ca lm" situation with slight, industrial noise; 2) high meteorological noise. FIG. 9 - Seismic noise of two recordings made at Montasola station, near Rome: 1) "ca lm" situation with slight, industrial noise; 2) high meteorological noise. FIG. 10 - Seismic noise of two recordings made at Observatory of L'Aquila, near Rome: 1) "ca lm" situation with slight, industrial noise; 2) high meteorological noise. 338 5. R. C O N S O LE - A. RO V E LLI CONCLU SION It could be seen that, in a recording system wich included both a modu lator- demodu lator couple and a tape recorder, the main trou b le was due to the latter. The effect is mainly evidenced by noise, the spectrum of wich b rings out peculiar frequencies that do not exist when the recording is done withou t mechanical means. It is advisable that, putting into operation a seismic station working by means of such instrumentation, the level of the amplification given to the output signal of the seismometer be enough to overcome by at least an order of magnitude the instrumental nois (i.e. the noise present in the output when the mob ile coil of the transducer is stopped). Only if one operates the right way, it is possible to evidence the real featu res of the natural seismic noise. In the choice of a site to be used for a new seismic station, some preliminar tests concerning b ackgrou nd noise are necessary. W hen a spectral analysis is available, it can give information about the nature of the b ackgrou nd noise and the best design of electronic filters. Of course, b oth the amplitu de and the spectral composition of the noise can change. So, several test scarried out in different conditions and at different day times are advisable in order to get a fu ll knowledge of the microseismic noise of a site. AN A N A L YS IS OF G ROU ND AND IN S TR U M E N TA L ECC. 339 REFERENCES AND ERSEN mum H., entropy 1974 - zyxwvutsrqponmlkihgfedcbaWVUTSRQPONMLIHGFEDCBA On the calculation of filter coefficients for maxi- analysis. « Geophysics », 39, 1, pp. 69-72. BATH M., 1974 - Spectral analysis Publish. Company, N ew York. in geophysics. BENDAT J.S., 1958 - Principles and applications Elsevier Scient. Pubblish. Company, New York. Elsevier Scient. of randon noise theory. 1971 - Random data: analysis and measureInterscience, N ew York. B END AT J . S . , PIERSO L A . G . , ment procedures. Wiley LACOSS R.T., 1971 - Data adaptive spectral analysis methods. « Geophysics », 36, 4, pp. 661-675. H . , 1965 - Physical and topographic factors as related wind noise. « Bull. Seism. Soc. Am. », 55, 5, pp. 863-877. ROBERTSON short-period S LIC TH E R Journ. », 14, L.B ., 1, 1967 pp. - Spherical oscillations of the earth. to « Geophys. 171- 177. ULRYCH T.J., BISHOP T.N. - Maximum entropy spectral analysis and autoregressive decomposition. «Reviews of Geophysics and Space Physics», 13, 1, p p . 183- 200. U LRYC H T. J . , S M Y L E D zwvtsrponljihgecaZXWVUTSRQPONMLKJIGFEDCBA .E., JENSEN O . G . , CLARKE G . K . C . , 1973 - Predictive filtering and smoothing of short records by using maximum entropy. « Journ. of Geophysical Research », 78, 23, pp. 4959- 4964. WALKER R.A., MENARD J.Z., BOGERT B .P., 1964 - Real-time, spectroscopy of seismic 2, pp. 501-509. background high resolution noise. « Bull. Seism. Soc. Am. », 54, W IG G IN S R.A., M IL L E R S . 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