Frequency response of Infrasonic Noise Reducers B. ALCOVERRO & A. LE PICHON

Frequency response of Infrasonic Noise Reducers B. ALCOVERRO & A. LE PICHON DASE / Alcoverro & Le Pichon

Introduction 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. DASE / Alcoverro & Le Pichon

? actually Infrasonic measurement chain characterization Design Characteristics Theoretical Poles and zeroes Theoretical Poles and zeroes Filters coefficients Atmospheric pressure Noise reducer Sensor Digitizer Analysis Mean of measurement Infrasound calibrator Spectrum analyzer Use of noise spectra: Sufficient to validate theory Spectrum analyzer Measured Frequency & Amplitude & Phase Characteristic used Theoretical Poles and zeroes Measured Poles and zeroes DASE / Alcoverro & Le Pichon

Examples of improved noise reducer design By PTS (Dr 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. DASE / Alcoverro & Le Pichon

Time Domain Design principle Wind Model Wind speed: Frequency Domain Checking geometry Delayed Impulses responses Inlets position Stimulus • Geometrical parameters: • Number of inlets, • Kind of geometry FFT -1 Convolution Electroacoustical Model Sum Frequency responses • Construction parameters: • Length of pipes, • Diameter of pipes, • Volumes of manifolds, • Model of sensor used, FFT FFT Noise reduction Potential Poles & zeros calculation DASE / Alcoverro & Le Pichon

Calculation of frequency responses: Hi(j) • 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 transfer function for each inlet between Psum and Pi by the mean of a matrix method: Pi Psum • 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, DASE / Alcoverro & Le Pichon

Models used for acoustic elements : • Cavity (Vb)  Acoustic compliance : • Short pipe (lp, rp) Acoustic mass : • + Acoustic resistance : • Long pipe (l,S)  Dissipative Transmission Line : (m3/Pa) (kg/m4) () 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: Zatli1 Zatli1 Zatli2 = 18.6 10-6 Pa.s DASE / Alcoverro & Le Pichon

Frequency response of large noise reducers Example of 144 ports PTS Noise Reducer. Example of frequency responses of 18 m & 70 m N.R. • 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. 18 m 70 m DASE / Alcoverro & Le Pichon

Sensors Reducing the resonance by… Using shorter pipes by introducing multiple sensor in noise reducer. Adapting impedance with capillaries at the end of longer pipes. lp • 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 Low impedance device. Longer pipe (Section S) Capillary (fine pipe of radius rp) • 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.  is air viscosity coefficient Example: 15 mm pipe  Zc = 2.37 M Capillary : Ø2 mm & 50 mm long • These atractive solution must be validated over the time: Hedlin & Alcoverro 2002 JASA Publication DASE / Alcoverro & Le Pichon

Capillaries use: effects on frequency response Example of frequency responses of 18 m & 70 m PTS noise reducers • 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. DASE / Alcoverro & Le Pichon

Time lag introduced by noise reducers Example of time lag of 18 m & 70 m PTS 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. DASE / Alcoverro & Le Pichon

Example of poles and zeroes for noise reducers • Calculated from simulation frequency responses and regression analysis. • Poles & zeroes values are mainly length pipes dependant. DASE / Alcoverro & Le Pichon

Process used for simulations Synthetic signal generator PMCC Detector • Azimuth • Frequency • Noise Poles & zeroes of Noise Reduc. Impulses responses Convolution • Azimuth • Horizontal trace velocity Perturbations introduced by noise reducers on the detection Example of array used for simulations • Analyze for various frequencies & various azimuths with a plane wave crossing the array at 345 m/s. DASE / Alcoverro & Le Pichon

Analyse at 2 Hz, 5° & 245° II III I 70 m adapted 70 m 18 m 18 m 18 m 5.6° - 346 m/s 5.7° - 347 m/s 5.9° - 360 m/s DASE / Alcoverro & Le Pichon

Effect on detection results Configurations:I : 4 x 18m noise reducer II : 3 x 18m + 1 x 70m noise reducer II : 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. DASE / Alcoverro & Le Pichon

Summary • 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. DASE / Alcoverro & Le Pichon

Frequency response of Infrasonic Noise Reducers B. ALCOVERRO & A. LE PICHON