Under-Sampled Microphone Data as a Wind Measurement

It is common human experience that wind is associated with noise. Acoustic noise is generated by the turbulent pressure fluctuations  associated with the shearing flow near the ground. Sound levels recorded on the Venera 13/14 missions at Venus were used to estimate winds (Ksanfomality et al., 1983). More recently, measurements with the SuperCam microphone on the Mars 2020 Perseverance rover have found that the power spectral density at low frequencies correlates well with windspeed (e.g. Maurice et al., 2022; Stott et al., 2023). The rapid response of microphone sensors makes it possible to resolve rather rapid changes in wind conditions, e.g. during dust devil encounters (Murdoch et al., 2022).

Here we show that a simple, inexpensive microphone can yield quantitatively-useful measurements of wind speed in terrestrial field conditions, even when its output is very sparsely-sampled.  This is of practical utility in that passive acoustic measurements can be made with extremely low power requirements (unlike ultrasonic or hot film anemometers) and with no moving parts (as do cup or propeller anemometers) making them very useful for long-term field observations. These aspects, and their low geometric volume and cost, make them attractive for sensor networks.

The field measurements were conducted on a dry lake bed about 1 km southwest of the 70m radio telescope at the Goldstone Deep Space Communications Complex (35°25′36″ N, 116°53′24″ W) outside Barstow, California, operated by the Jet Propulsion Laboratory.  The measurement campaign was initiated by the InSight project, with the intent of acquiring representative seismic data from a shallowly-emplaced seismometer in desert field conditions.  In addition to the main equipment installation (seismometer and anemometer), we deployed loggers that recorded pressure and an analog voltage from a user-supplied sensor at 1 sample per second.   As an experiment, we connected this measurement channel to an amplified Micro ElectroMechanical System (MEMS) microphone (Analog Devices ADMP401).   We have previously shown (Lorenz et al., 2017) that the output from such a microphone can be related, as can that of other simple electret microphones (Chide et al., 2021) to windspeed and direction in a wind tunnel, even at Mars atmospheric density.

The microphone, datalogger, and 2 alkaline D-cell batteries permitting weeks of unattended operation, were mounted in a plastic box set on the playa floor, 60m to the west of the anemometer station.  The anemometer recorded at 1 minute intervals.  The instrumentation was deployed in May 2015 and retrieved in August. We concentrate our analysis on a 12-day period when good data were acquired.

The microphone record comprises individual instantaneous voltage samples at 1.5-s intervals. The samples are 12-bit integers (0-4095) mapping to the range 0-5 V; the amplifier shifts the zero level to half of the 3.3V supply, thus readings are symmetrically distributed about a base value of ~1667.   The signal of interest, then, is the absolute value of the difference between an individual sample and the base level  (the latter of which is readily obtained by taking a long-term average).

 

Figure 1.    Left panel is the 12 day period, with the maximum and 2x the mean signal value over 60s-intervals shown as grey lines and red points, respectively. In the lower panel is the 1-minute mean wind (red) and maximum ‘gust’ (grey) recorded by the anemometer.  The right panel is the same, but zoomed in on a 24-hr period in the middle of the record.

 

The dominant signals in the wind noise are at low audio frequencies, and at infrasound frequencies (where the microphone has poor response). But these are still high very frequencies compared with the sample rate of 0.67/s, and thus samples are at random phase.   Such ‘snapshots’ of a constant-amplitude monochromatic signal would yield a saddle-shaped histogram, since the system spends more time at the ends of the cycle than at the center. Thus, sparse sampling is quite effective at capturing the amplitude of a signal.

Figure 2.  Correlation of microphone signal fluctuation with mean wind speed. Above a speed of 20 m/s, the signal becomes saturated. 

 

It is seen in figure 2 that below a windspeed of ~4 m/s the microphone output is small. Between 4 and 20 m/s (10^0.6 and 10^1.3) there is an excellent correlation of the microphone output with wind speed, with the scatter being about +/- 10^0.1, or about 25% of the actual value.  The slope of the correlation in logarithmic space is ~1.6. This is close to the exponent of 2.0 that one would expect if pressure fluctuations were proportional to the dynamic pressure, i.e. mean velocity squared.

The microphone datasheet (Analog, 2012) indicates a -3dB low-pass sensitivity limit of 60 Hz and -10dB at 20 Hz. There is additional high-pass filtering (22 Hz corner frequency) in the amplifier. Thus in practical terms the wind sensitivity arises as a compromise between the larger pressure fluctuations at low frequencies, and the higher device sensitivity towards higher frequencies.  One could contemplate improving sensitivity by associating the device with a smaller structure (or even introducing specific resonant geometries, like an organ pipe) to develop higher-frequency pressure fluctuations for a given flow speed.  In any case, the ‘calibration’ of this type of measurement is rather device-dependent and mounting-dependent.

A simple microphone signal, even grossly undersampled, can yield a wind estimate over a useful range of speeds. It is easy to imagine that some simple analog signal-processing (e.g. a low-pass filter and envelope detector) could yield a better wind speed estimate than the statistics from random instantaneous voltage samples we have presented ; similarly, digital signal processing could be readily implemented. It seems likely that such an approach could yield wind estimation on sub-second timescales, without requiring large data volumes to be stored or telemetered : data volume is an important constraint on remote monitoring stations, especially those on planetary bodies.  This work will inform the sampling strategy to be used on the microphones on the Dragonfly mission (Lucas et al., 2024).