estimate of turbulent noise suppression efficiency in microbarometric measurements
Brednev S. P., Kudryavtsev V. I., Rybnov Yu. S., Kharlamov V. A.
ABSTRACT
Mathematical apparatus based on adopted assumptions is represented which describes operation of Wind-Noise-Reducing Filters (WNRF) used in recording of infrasound fluctuations from various geophysical sources. It is demonstrated that WNRF efficiency is determined above all by the spatial noise correlation as well as by the number of air pipes, their configuration and size. Data on spatial noise correlation was summarized based on the long-term observations that and used for WNRF efficiency estimates.
Spatial wind-noise-reducing filter is a system including Nreception air pipes connected with summing manifold (Fig.1). Air pipes are located on the ground surface in the form of a cross or a star. Distance “r“between open ends of air-pipe inlets is chosen under the condition of minimum spatial noise correlation. Pulsations of ambient pressure P which represents an additive signal-noise mixture affect the open air pipe inlets.
In addition, spatial filters in which air pipe is in the form of a ring (tore) with holes are often used in practice.
Linear noise reducing filter is an air pipe of length L which has “x”inlets made through certain interval “d”.
The principle of operation of any filter uses noise space averaging technique.
Let us consider an operation of WNRF realized in the form of a cross or a star. To describe the process let us apply some assumptions. When air pipe length to its diameter ratio is of great value air temperature becomes equal to the temperature of walls and remains practically constant along the full length. Therefore gas flow through a long air pipe of uniform cross-section can be assumed as isometric and one-dimensional. For small pressure falls gas can be considered as viscous fluid and its flow assumed as laminar [1].
Let ambient pressure pulsations in each time point come to summing manifold through mair pipes. Ambient pressure pulsations come to summing manifold through remaining lair pipes. In addition , where - pressure pulsations in summing manifold. This condition indicates that there is gas flow inside the WNRF with above stated limitations. Then gas flow rate via mair pipes will equal [2] to
,
where - air resistance of m-th air pipe.
Gas flow rate through lair pipes will be
,
where - air resistance of l-th air pipe.
Total gas discharge in stationary state will be equal to zero, i.e.
or
.
If all resistances and are equal to one another, then
.
Denoting ambient pressure pulsations as we shall obtain
.
This implies that summing of ambient pressure pulsations with scale parameter takes place within summing manifold. This property is posited as a principle of operation of wind-noise-reducing filters.
As before is assumed to be additive mixture of signal and noise
.
Let us also assume that input processes have zero average values and equal dispersions , and that they are statistically independent each one relatively to others. In addition we assume that signal is correlated and noise is not. Then average value of output process is [3]
,
and the dispersion of overall output process is equal to
.
Hence, ifWNRFinputSignal-NoiseRatio(SNR) isdefinedas
,
thenWNRFoutputsignalnoiseratiowillbeequalto
,
or in case of SNR representation in root-mean-square values
.
Thus, we get under applied assumptions that SNR increase at the WNRF output is proportional to .
However, wind noise correlation in real-life environment cannot be assumed as equal to 0. Spatial correlation measurements were carried out in IDG RAS during several years in various weather and climatic conditions and for different types of underlying surface [4, 5]. Statistically averaged measuring data for 0.5-3 m/s average wind speed are represented in Fig.2.
If noise spatial correlation coefficient has the same value for any pair of reception air pipes then according to [6] we have
,
where - noise spatial correlation coefficient. If noise suppression factor is defined as
,
then for WNRF in the form of a cross or a star WNR is within the range of 1.5–10. Graph of this dependency is represented in Fig.3. For real WNRFs WNR will be within the range of 2-3 when equals 0.1-02.
Output signal-noise ratio increase for linear wind-noise-reducing filters is proportional to a number of inlets. Provided spatial correlation coefficient is approximated by the expression [6]
,
where - is damping factor, and , then according to [6], we have for
,
and WNR will be within the range of 1.2 – 1.8 (see Fig.4). Here the WNR dependence on wind direction becomes obvious.
Noise suppression coefficient for toroidal WNRF is of intermediate value and is equal 1.5-2.
It should be emphasized that increase of WNRF efficiency by means of increase of their dimensions (up to hundreds of meters) aimed at the decrease of K(r) to the values close to zero will lead to infrasound signal common-mode disturbance at WRNF inlets, i.e. to its suppression (particularly for high-frequency infrasound signals).
Investigations carried out by IDG RAS on the efficiency of applying WNRF of different configurations confirmed represented estimates of their actual noise suppression.
At the same time, however, solution of WNRF dimensions and configuration optimization remains urgent task applying to measuring of infrasound signals of different nature. Special attention should be paid to the fact that signal spectra maximums fall at the frequencies from thousandth to few Hertz, and therefore differently approach is needed while choosing the appropriate WNRF.
Bibliography
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- Kharlamov V.A., Rybnov Yu.S. Research of Stochastic Infrasound Field Characteristics in Megalopolis. // In Publication «Dynamic Processes in Geospheres under the Influence of External and Internal Energy and Substance Flows ». M.: IDG RAS, 1998. P.313-320.
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Fig.1. Wind-Noise-Reducing Filters (WNRF)
Fig.2.Averaged values of noise spatial correlation coefficient
Fig.3.WNR dependency on the number of air pipes
Fig.4.WNR dependency on the number of inlets