1 De Bilt Infrasound Workshop – 10/2002Noise reducers frequency response Date : 28/10/02DASE / Alcoverro & Le Pichon Frequency response of of Infrasonic

Date : 28/10/02DASE / Alcoverro & Le Pichon 1

De Bilt De Bilt Infrasound Infrasound Workshop – 10/2002Workshop – 10/2002 Noise reducers frequency responseNoise reducers frequency response

Frequency responseFrequency response ofof

Infrasonic Noise ReducersInfrasonic Noise Reducers

B. ALCOVERRO & A. LE PICHONB. ALCOVERRO & A. LE PICHON



Infrasonic measurements need wind noise reduction. This noise reduction is performed by the mean of mechanic noise reducer before sensor measurement. The performance in term of noise reduction is dependant to to size of the used device.

Large sizes are well designed for high wind speeds. But a large size introduce resonance in the upper frequency band that perturb the analysis. Impedance matching of acoustical circuit reduce them but introduce time lag.

Poles & zeroes of noise reducers are calculated. They are used to estimate the effects of noise reducer on detected events.

IntroductionIntroduction



Infrasonic measurement chain characterizationInfrasonic measurement chain characterization

Noise reducer Sensor Digitizer AnalysisAtmospheric

pressure

Filters coefficients

Theoretical Poles and zeroes


Spectrumanalyzer

Infrasoundcalibrator

Spectrumanalyzer

Measured Frequency &

Amplitude & Phase

Measured Poles and zeroes

?actually


Mean of measurement

Characteristic used

Design Characteristics

Use of noise spectra:Sufficient to validate theory



Examples of improved noise reducer designExamples of improved noise reducer designBy PTS (DBy PTS (Drr Douglas Christies) Douglas Christies)

• Equal response of each inlets

• Number of inlets is large to improve the maximal noise reduction (96 or 144 inlets).

• Designs with large diameters improve noise reduction under high wind speeds.



Geometrical parameters:Number of inlets,Kind of geometry

Construction parameters:Length of pipes,Diameter of pipes,Volumes of manifolds,Model of sensor used,

Checking geometry

ElectroacousticalModel

Frequency responses

Poles & zeros calculation

Wind speed: WindModel

DelayedImpulses

responses

FFT -1 Convolution

Inlets position Stimulus

Sum

FFT FFT

Time Domain

Frequency Domain

Noise reduction Potential

Design principleDesign principle



• The calculation is easy: only pipes, cavities, and simple acoustic elements.

• Use an accurate electro acoustical model of the entire array including the sensor.

Calculation of frequency responses: HCalculation of frequency responses: Hii(j(j))

Pi

Psum

Calculation of transfer function for each inlet between Psum and Pi by the mean of a matrix method:

iin PZPZ With:

• [Z] the matrix impedance of the circuit,

•{Pn} the pressure at each node,

• {Zi} the input impedance of each inlet,

• {Pi} the stimulus pressure at each inlet,



Models used for acoustic elements :Models used for acoustic elements :

• Cavity (Vb) Acoustic compliance :

• Short pipe (lp, rp) Acoustic mass :

+ Acoustic resistance :

• Long pipe (l,S) Dissipative Transmission Line :

2c

VsCavs

2rp

lpMap

4

8

rp

lpRap

2

2

1

1

)()(1

)()(

u

plchlsh

Z

lshZlch

u

p

c

c

2

Γtanh1

lZcZatli

lΓ

Zc2Zatli

Zc and are the characteristic impedance of the medium and the constant of propagation in this medium, respectively. Benade (Benade, 1968) gives the expressions for Zc and in the case of fine tubes and wide tubes, as well as for a non-dimensional parameter rv. The approximation for the broad tubes is valid if:

11 045.11045.1Γ rvjrvk

11 369.0369.01 rvjrvRoZc

12

Sfrv

(m3/Pa)

(kg/m4)

()

Zatli1 Zatli1

Zatli2 = 18.6 10-6 Pa.s



Frequency response of large noise reducersFrequency response of large noise reducersExample of 144 ports PTS NExample of 144 ports PTS Noise oise RReducereducer..

• Verified on IS57 noise reducers (Hedlin & Alcoverro 2002 JASA Publication)

• 70 m system has wide resonance around 2.6 Hz that amplify the signal & noise in the upper frequency band.

• Above 3 Hz, 180° phase differences between 18 m system & 70 m system.

This may introduce differences in analysis of signals issued from various noise reducers.

Introduce theoretical responses of large noise reducers during analysis.

Reduce or shift these resonance.

Example of frequency responses of 18 m & 70 m N.R.

18 m

70 m



Reducing the resonance by…Reducing the resonance by…Using shorter pipes by introducing multiple sensor in noise reducer.

SensorsSensors

The longer pipe is less than the half length of « single sensor » noise reducer resonant frequency is shifted toward high frequencies.

Requires stable & precise sensors for perfect electrical summing

Adapting impedance with capillaries at the end of longer pipes.

Longer pipe(Section S)

Capillary(fine pipe of radius rp)

Low impedance device.

The longer pipe is terminated by a fine pipe that act as an acoustic resistance:

the resistance must equal the characteristic impedance of the concerned pipe.

4

8

rp

lpRap

S

cZc

lp

Example: 15 mm pipe Zc = 2.37 MCapillary : Ø2 mm & 50 mm long

These atractive solution must be validated over the time: Hedlin & Alcoverro 2002 JASA Publication

is air viscosity coefficient



Capillaries use: effects on frequency responseCapillaries use: effects on frequency response

• 70 m system with adapted impedance has a flat amplitude response over [0.02 – 4] Hz band.

• The amplitude response is similar to the 18 m system.

• The phase response increase slowly from low frequencies to reach –90° at 2.6 Hz.

• This phase behaviour could introduce problems in analysis.

Example of frequency responses of 18 m & 70 m PTS noise reducers



Example of time lag of 18 m & 70 m PTS noise reducers System DASEPTS

18 m

PTS

70 mPTS 70 m(Z adapted)

t (s) < 0.002 < 0.003 < 0.02 0.1

d (m) < 0.68 < 1.1 < 6.8 34

Time lag introduced by noise reducersTime lag introduced by noise reducers

• If two different noise reducers are used in a station, the relative position accuracy is > 1 m. (Specs CTBTO : < 1m).

• for example, if 18m & ‘70m adapted’ noise reducers are used simultaneously, an uncertainty of 33 m is added on the relative position accuracy.

Solution is to introduce theoretical responses of adapted large noise reducers for analysis.

d

dtpg

)(



Example of poles and zeroes for noise reducersExample of poles and zeroes for noise reducers

PTS 18 m 96 p PTS 70 m 144 p PTS 70 m ‘A’ 144 p DASE 18 m 32 p

Scale factor:

0.070786

poles:

-3.63056+154.902i

-3.63056-154.902i

-4.11616+85.6769i

-4.11616-85.6769i

zeros:

-422.6108

192.7827+71.5062i

192.7827-71.5062i

-139.6601

Scale factor:

0.26383

poles:

-4.12035+65.6014i

-4.12035-65.6014i

-2.62171+51.8546i

-2.62171-51.8546i

-1.3849+17.4936i

-1.3849-17.4936i

zeros:

-34.1562+48.6299i

-34.1562-48.6299i

35.8154+43.7417i

35.8154-43.7417i

39.8276

-30.2416

Scale factor:

1.5457

poles:

-9.99267+56.1659i

-9.99267-56.1659i

-31.332

-0.26827

zeros:

24.7659+40.2482i

24.7659-40.2482i

29.2354

-0.27105

Scale factor:

0.11007

poles:

-5.831733+139.8788i

-5.831733-139.8788i

-4.87981+85.8315i

-4.87981-85.8315i

zeros:

163.1681+83.64683i

163.1681-83.64683i

-239.1636

-163.6828

• Calculated from simulation frequency responses and regression analysis.

• Poles & zeroes values are mainly length pipes dependant.



Perturbations introduced by noise reducers on the Perturbations introduced by noise reducers on the detectiondetection

Example of array used for simulations

Synthetic signal

generator

Impulses responses

ConvolutionConvolution

PMCCDetector

• AzimuthAzimuth• Horizontal trace velocityHorizontal trace velocity

•Azimuth•Frequency

•Noise

Poles & zeroes of Noise Reduc.

Process used for simulations

• Analyze for various frequencies & various azimuths with a plane wave crossing the array at 345 m/s.



IIIIII

18 m

70 m

18 m

70 m adapted

18 m

5.6° - 346 m/s 5.7° - 347 m/s 5.9° - 360 m/s

Analyse at 2 Hz, 5° & 245°Analyse at 2 Hz, 5° & 245°



Frequency

configuration I II III I II III I II III

5,6 5,6 5,8 5,6 5,7 5,9 5,7 5,8 5,8

345 346 362 346 347 360 345 356 358

244,5 244 241,5 244,5 244,5 241,5 244,5 242 241,5

347 347 339 347 347 339 347 340 339

Azimuth uncertainty < 0,5° < 0,5° < 4° < 1° < 1° < 4° < 1° < 4° < 4°

Wave speed uncertainty < 2 m/s < 2 m/s < 20 m/s < 2 m/s < 2 m/s < 20 m/s < 2 m/s < 20 m/s < 20 m/s

245°

0,2 Hz 2 Hz 4 Hz

5°

Effect on detection resultsEffect on detection results

Configurations: I : 4 x 18m noise reducerII : 3 x 18m + 1 x 70m noise reducerII : 3 x 18m + 1 x 70m ‘capillary’ noise reducer

• The use of large noise reducer adapted in impedance introduces errors in azimuth and wave speed detection over the entire bandwidth.

• The introduction of the frequency response during analysis will correct these effects.



SummarySummary

• The use of large noise reducers (Diameter > 70 m) is a necessity in windy conditions to maximize the signal to noise ratio.

• They introduce resonance around 2 Hz that could be reduced by using matched impedance systems.

• These noise reducers have non negligible response and particularly in phase response (tpg = 0.1 s).

• Detected events uncertainty increase (~5° in azimuth and ~20 m/s in wave speed).

• To prevent errors in detection, the filters responses could be introduced in the measurement chain characteristics as a part of sensor.

Documents

1 De Bilt Infrasound Workshop – 10/2002Noise reducers frequency response Date : 28/10/02DASE / Alcoverro & Le Pichon Frequency response of of Infrasonic