Detection of atmospheric infrasound with a ring laser interferometer

After Macek et al.¹ demonstrated that a ring laser could detect rotation in the early1960s, the aerospace industry began developing and deploying small navigational ring lasers^2–4 as replacements for mechanical gyroscopes. More recently, large ring laser interferometers have been developed to explore numerous geophysical effects. A good review of the history, design, and use of large active ring lasers is contained in an invited review article by Schreiber and Wells.⁴ In the current paper, the results from using large active ring laser interferometers to detect infrasound are presented. Acoustic vibrations below the lower limit of human hearing of approximately 20 Hz are typically labeled as infrasound. An overview of atmospheric infrasound is contained in a paper⁵ by Bedard and Georges. In the 1970s, National Oceanic and Atmospheric Administration (NOAA) began a long term study to determine if infrasound could help to improve warnings of severe weather events. In a 2005 paper,⁶ Bedard examined the results from this and other studies that were devoted to measuring acoustic energy generated by severe weather and related tornadoes. He concluded the results were consistent with a model by Abdullah⁷ that suggested the radial vibration modes in tornado vortices were a source of infrasound and that the infrasound frequencies were inversely proportional to the vortex diameter. Bedard⁶ cited Doppler radar measurements of an evolving tornado; the maximum values of the circulation were observed to descend over a period of ∼30 min. A tornado funnel was sighted when the maximum circulation was near the surface of the Earth. During the 22nd American Meteorological Society Conference on Severe Local Storms in October of 2004, two sessions^8,9 were devoted to an infrasound network that was deployed in 2003. Several conclusions from this conference were based on the observations of numerous tornadoes: infrasound was usually observed well before the tornado funnel was reported on the ground; infrasound could travel long distances; vortex related signals usually last for 10 min or more; signals of 1 min or less were unlikely to be related to coherent vortex oscillations; and wind noise abatement systems improved tornado detection. During the first session,⁸ several ways a tornado could produce sound were discussed. Some of the possibilities include shear instabilities, boundary layer sound, fluid instabilities, and radial modes of vibration of the vortex core. Radial modes of vibrations of the vortex core were suggested as the most likely source. The focus⁶ of the NOAA studies was from 0.5 to 5 Hz. Although a ring laser interferometer is a totally different detection system, the results presented in this paper are in general agreement with the NOAA findings.

In an active ring laser interferometer, the excitation source is inside the cavity where it excites two counter-propagating waves. When the ring laser cavity is rotating, the two 632.8 nm He-Ne counter-propagating waves circulating in the cavity travel unequal path lengths.^2–4 Unequal path lengths produce frequency differences between the two counter-propagating waves that result in a beat note.

The square ring laser is 5.65 m on a side. The cavity is excited by a 75 cm plasma tube that is sealed on each end with a Brewster window. Ambient pressure dry nitrogen created by evaporating liquid nitrogen from a well insulated 20 l Dewar fills the remainder of the cavity. Outgassing from the unbaked aluminum beam lines is slowly flushed into an oil bath. The oil bath prevents atmospheric contamination of the cavity. However, it does not isolate the cavity from atmospheric pressure variations and infrasound. The flush is essentially constant; it takes up to a month to evaporate the liquid in the Dewar. Consequently, the effect of any bias introduced by the flush is considered to be negligible. To help isolate the cavity from temperature expansions and contractions of the beam lines, soft air tight couplings are used to connect the beam lines to the mirror boxes and the plasma tube container. The soft couplings are nearly transparent to atmospheric pressure variations. The laser cavity's stability is partially dictated by the basement slab on which the laser is rigidly attached. The Sagnac frequency or beat note induced by Earth's rotation is given by the following⁴ relation:

In this relation, Δf is the Sagnac frequency and A is the area of the cavity. The symbol p represents the perimeter of the cavity, λ is the laser's wavelength, Ω is the rotation rate of the Earth, and θ is the angle between the normal to the laser cavity and the Earth's axis of rotation. The relation 4A/λp is commonly referred to as the scale factor. Since the colatitude of the ring laser is ∼55° north and each side is 5.69 m, Earth's rotation produces a beat note of ∼375 Hz. The beat note serves as a carrier frequency. When the ring laser cavity is perturbed, the carrier frequency (beat note) is frequency modulated (FM). Numerous geophysical phenomena can perturb a ring laser cavity and modulate the carrier frequency. For example, phenomena such as the Chandler wobble, diurnal polar motion, tidal tilts, and solid earth tides produce variations⁴ in θ. Rotational ground motion, introduced by seismic shear waves that add to or subtract from Ω, has been detected by several research teams.^4,10–13 Variations in the cavity geometry can modulate the beat frequency.⁴ Also, infrasound can frequency modulate^14,15 the carrier frequency. A phase locked loop¹⁶ is often used as a FM demodulation technique to recover the modulation (perturbing) signals. If the perturbing signals are sufficiently coherent, Fast Fourier Transforms (FFTs) can reveal their frequency spectra. The results reported in this paper were obtained using an alternate FM demodulation scheme. An experimental comparison between the phase locked loops and the alternate scheme produced equivalent results.¹⁴ 

The demodulation system was built around a National Instruments Virtual Instrument (VI), “Extract Single Tone Information.” The VI takes a signal lasting for a certain interval of time and selects the single frequency in that interval with the highest amplitude. In this study, the digitized signal of 4000 samples/s was broken into 0.1 s intervals. The VI calculated the frequency with the highest amplitude in each 0.1 s interval. These results are initially stored in 10 min blocks. The stored data can then be used to show the variations of the carrier frequency with time. Typically, the ten minute data blocks are joined together creating extended data blocks. Each FFT measurement needs to include enough data to significantly exceed the Nyquist criteria. An FFT routine can then show the coherent modulation frequency spectrum in each data block.

Originally, the Arkansas ring laser was designed to be a relatively inexpensive seismic wave detector that did not require expensive turbomolecular vacuum pumps. To achieve this goal, a plasma tube and industrial grade dielectric mirrors were used. In Fig. 1, the dielectric mirror and its holder are shown in the mirror box. Figure 2 shows how the plasma tube is mounted. In addition, outgassing was flushed from the cavity using dry nitrogen. Initially, it was deployed to study shallow earthquakes associated with the underground disposal of waste water from hydraulic fracking operations in North Central Arkansas. When deployed, the interferometer not only detected regional earthquakes but also infrasound from hurricanes.

To verify that the ring laser was actually sensitive to infrasound, a controlled experiment using a portable Helmholtz acoustic resonator was set up in the basement containing the ring laser. As discussed by Kinsler,¹⁷ if the acoustic wavelength is greater than the dimensions of a Helmholtz acoustic resonator, the device behaves like a harmonic oscillator in one dimension. In this case, the Helmholtz resonator consists of a 55-gallon drum with a half-inch thick aluminum top that is connected to an aluminum duct 1-m long and 10.2 cm in diameter; the duct is open to the external environment. Air in the cavity (drum) acts as a spring, while the air in the duct acts as a mass; for a given geometry, a well-defined resonance frequency is created. An audio woofer between the volume and duct drives the combined system at resonance. The radiated infrasound from the duct opening was very small but sufficient for these tests. The resonator was located ∼3 m from the enclosed plasma tube. Care was taken to isolate the Helmholtz resonator from the floor by suspending it from the ceiling rafters so that the vibrations initially traveled through the air. At resonance, the Helmholtz acoustic generator emitted a very sharp frequency¹⁴ of 12.5 Hz. An FFT of the ring laser response¹⁴ agreed with the 12.5 Hz frequency generated by the Helmholtz acoustic resonator. Using FFTs, the coherent acoustic-gravity waves from hurricanes and explosive volcanic eruptions were subsequently detected. This paper reports the detection of tornadic infrasound as well as the acoustic-gravity waves from typhoons in the Pacific Ocean. FFTs are required to extract the comparative low level coherent acoustic responses from the more random higher intensity environmental noise.

An examination of the path of the Mayflower-Vilonia tornado shown in Figure 3 provides the tornado's relation to the ring laser in Conway, Arkansas, and the Doppler radar in Little Rock, Arkansas. The tornado was on the ground from ∼7:06 p.m. to 8:02 p.m. CDT¹⁸ on April 27, 2014 (0006-0059 UTC on April 28). At ∼7:34 p.m. CDT on April 27, 2014, the tornado destroyed sections of Mayflower with damage rated at an EF4. At ∼7:50 p.m. CDT, it entered Vilonia, Arkansas, and destroyed large sections of the town with a damage rating of EF4. At ∼8:02 p.m. CDT, the parent storm lifted. At the closest approach, it came within ∼21 km of the ring laser. The location of the tornado was updated approximately every five minutes by radar scans. Descriptions of the tornado and the EF rating were supplied by the National Weather Service (NWS) in Little Rock, Arkansas,¹⁸ plus an after-the-fact damage survey¹⁹ that was provided by Marshall et al. An FFT of the infrasound detected by the ring laser over the 56 min life of the storm yielded a coherent frequency of ∼0.94 Hz. The 0.94 Hz frequency was detected 30 min before the funnel was reported on the ground; it continued until the funnel lifted. However, the long integration times required to develop FFT peaks from the incoherent noise may mask short term frequency variations.

The deployment location of the ring laser in the basement of a multistory building is not ideal. Wind loading of the building is a significant issue. Thunder easily couples into the ring laser, and frequency fluctuations are introduced by local noise. To remove outlying points due to building movement or large incoherent local noise, an upper and lower bound of 377–373 Hz was set up centered on the carrier (Sagnac) frequency in Figure 4. A program automatically eliminated points outside these bounds. The removed points were replaced by the average of the first valid points on either side of the removed entries.

Figure 5 shows the FFTs of four representative tornadoes, including the Mayflower-Vilonia storm. The tornadoes were identified by comparing their corrected arrival times with the tornadoes listed in the NOAA Storm Events Database and NWS weather reports. Since infrasound can travel long distances with limited attenuation, infrasound from numerous tornadoes can sometimes arrive at close to the same time. Consequently, there is a potential uncertainty in the identity of which storms actually created the infrasound response. This is particularly true for the infrasound peaks in Figure 5(d) created from the June 4, 2015, tornado outbreak in Colorado. The amplitudes of the FFT graphs provide no information about the intensity between storms.

Table I summarizes the results from the NOAA Storm Events Data Center and the Little Rock NWS that are pertinent to Figure 5. Comments on the tornados are provided after the table.

Long integration times were needed to allow the FFT routines time to extract clear coherent tornadic infrasound peaks. There were 21 tornadoes listed in the NOAA Storms Event Database for June 4, 2015, in Colorado, between 15:38 and 18:10 MST ranging in intensity from EF0 to EF3. The ring laser 2.41 Hz response in Figure 5(d) correlated best with the EF3 tornado that was located along the border of Boulder and Larimer counties in Colorado. Ten EF0 tornadoes were also listed during approximately the same time that the 2.41 Hz tornado was active. The 3.11 Hz response in Figure 5(d) is thought to have been generated by an EF0 tornado that was on the ground from 17:21 to 17:33 MST in Elbert County. Because of uncertainties in identifying the EF0 storm, it is not listed in Table I. The responses of 2.41 and 3.11 Hz in Figure 5(d) show the ability of the ring laser to distinguish between tornadoes with different funnel diameters that arrive at approximately the same time.

Assuming that R represents the funnel radius, Abdullah's theoretical model⁷ as simplified by Bedard⁶ suggests that the relation between the tornadic fundamental infrasound frequency and funnel radius is 207/R, and the relation between the first harmonic frequency and funnel radius is 371/R. Also, Abdullah's model suggests that there should be an inverse relation between the detected infrasound frequency and funnel diameter. Table II is arranged by increasing funnel diameter and shows the ring laser measured infrasound frequency versus Abdullah's theoretical values for the fundamental and first harmonic as a function of vortex radius.

Since there is a disagreement in the literature concerning the theoretical underpinning of Abdullah's formulation, some caution is needed in comparing the results in Table II. In a 2010 paper, Schmitter²⁰ presents results from using a model confined to the lower part of the tornado vortex to study sources and possible generating mechanisms of sound. His results suggest that significant differences occur in the relation between the emitted frequencies and vortex radius depending on the boundary conditions. Under certain boundary conditions and assumptions, his results are in agreement with Abdullah's analytically derived results. On the other hand, Schecter²¹ in a 2012 paper suggests there are mis-steps in Abdullah's derivations that cast doubt on its fundamental credibility. In addition, he states that the principal axisymmetric oscillations of a subsonic Rankine vortex (axisymmetric Kelvin modes) do not emit acoustic radiation. In 2005, Hurricane Wilma¹⁴ experienced an eyewall replacement. A satellite image clearly showed the inner eyewall and the outer eyewall in the hurricane. The acoustic-gravity wave frequencies measured by the ring laser were inversely related to the two radii.

Figure 6 shows the long distance over which the ring laser can detect the coherent acoustic-gravity waves.

The ∼7.1 mHz FFT peak is from the acoustic-gravity waves generated by Super Typhoon Haiyan as it made landfall in the Philippine Islands on November 7, 2013, at ∼20:40 UTC.²² Due to travel time, the acoustic-gravity waves were not received in Arkansas until November 8 between ∼0704 and 0834 UTC. Similar ∼7.1 mHz acoustic-gravity waves were detected by the ring laser in 2005 when Hurricanes Katrina and Wilma made landfall¹⁴ in the Gulf of Mexico. The hurricane acoustic-gravity waves were also detected in 2007 when Hurricane Dean passed between the islands of Martinique and St. Lucia in the Caribbean.¹⁴ Apparently, the peak at ∼4.2 mHz is from the explosive eruption of Volcano Shiveluch in eastern Russia. It arrived simultaneously with the waves from Super Typhoon Haiyan. The Smithsonian/USGS Global Volcanism Weekly Volcanic Activity Report for November 1–8, 2013, listed strong explosive eruptions from Sheveluch.²³ Using microbarographs, Tahira et al. recorded air waves in Japan of ∼4.4 mHz during the explosive eruption of Mount Pinatubo²⁴ in the Philippines on June 15, 1991. Volcanic infrasound peaks between 3.7 and 5.6 mHz were detected in Sweden when Mt. Saint Helens erupted in Washington State²⁵ on May 18, 1980. The cluster of frequencies between ∼3.0 and 3.3 mHz is in the buoyancy wave regime. Their source is unknown. Buoyancy wave periods range from 5 to 120 min. The restoring force is gravity; they have several sources such as cumulous convection, flow over topography, and fluid instabilities. Typical buoyancy waves have vertical wavelengths from 5 to 15 km, horizontal phase speeds of up to 80 m/s, and a horizontal wavelength from 10 to 200 km.²⁶ In a 1998 theoretical paper, Lognonne et al. developed a model²⁷ predicting that coupling between the ground and atmosphere occurs at a set of frequencies related to fundamental and harmonics of atmospheric normal modes. These modes were calculated as 3.681, 4.405, 4.696, 5.076, 6.104, 7.067, 8.118, and 9.171 mHz. Responses close to these atmospheric modes have been detected by the ring laser from volcanoes or hurricanes/typhoons. Specifically, the 7.067 mHz mode is very close to the response from Super Typhoon Haiyan and hurricanes in the Gulf of Mexico as they made landfall. Frequencies from explosive volcanic eruptions have been detected by the ring laser at 3.7, 4.4, 4.7, 5.0, and 6.2 mHz. Frequencies of 7.1, 8.1, and 9.2 mHz were detected in association with tropical and extratropical hurricanes.

The ring laser interferometer is a very broad band instrument. Assuming sufficient coherence, FFTs can be used to reveal the frequency signatures from multiple sources that arrive simultaneously. The book²⁸ by Gossard and Hooke provides a good reference and a comprehensive review of the generation and propagation of atmospheric waves including a chapter devoted to infrasound. Various types of waves can exist in the atmosphere. The acoustic-gravity waves travel at the speed of sound and their restoring force is compression. When the wavelengths of acoustic waves become long enough, gravity becomes a factor in the restoring force.⁵ Lamb waves²⁹ are compressional atmospheric free oscillations that can be excited by impulsive forces such as volcanic eruptions; they propagate horizontally along the surface of the earth at the speed of sound. Their energy is mostly in the troposphere.

Laser interferometers have numerous configurations and uses. For example, in a relatively early paper, Herskovitz³⁰ describes the use of a Michelson interferometer as an interferometric manometer. Michelson interferometers use a beam splitter to produce two laser beams that can be recombined to create an interference pattern. Gas pressure changes in one of the beams change its optical path length. Consequently, the fringes in the interference pattern shift and allow pressure changes to be measured. An active cavity such as the one used in the ring laser interferometer presented in the current paper has the excitation source (plasma tube) inside the cavity. It produces a frequency change due to pressure induced perturbations inside the cavity. It is much easier to measure small frequency changes as opposed to fringe shifts.

Ideally, the counter-propagating waves in a ring laser rotation detector are independent oscillations; however, in practice, there is cross coupling introduced by optical back scatter^2–4 from one counter-propagating wave into the other. If the cross coupling is sufficiently strong, the two counter-propagating waves are injection-locked to the same frequency, which causes the beat note to disappear. Lock-in^2–4 is a ubiquitous characteristic of all coupled oscillators, including ring lasers. Apparently, lock-in was first observed by Christiaan Huygens³¹ in 1665, when swings of the pendulums in two clocks mounted on the same wall became perfectly synchronized. Siegman³² devotes a chapter of his book in a very lucid discussion of injection locking in general and how it leads to ring laser lock-in. The cavity perimeter of 22.6 m in the Arkansas laser is large enough to allow Earth's rotation to bias the ring laser out of lock-in. However, some residual coupling remains. Back scatter induced residual coupling can create frequency pulling^2–4 between the counter propagating waves. If the backscatter increases, the frequency pulling between the counter-propagating waves slightly increases. Therefore, the carrier (beat) frequency will slightly decrease. If the scatter decreases, the carrier frequency will slightly increase. Consequently, the 375 Hz carrier frequency is frequency modulated. Optical elements such as plasma tubes are not generally used in ring lasers. A plasma tube in the beam line increases backscatter and can introduce stress birefringence.² Since acoustic waves tend to be more coherent than non-acoustic vibrations,⁶ FFTs can be used to extract the frequency spectrum of the coherent signals.

To our knowledge, the 16 m² ring laser⁴ at the Fundamental Station in Wettzell, (Bavaria) Germany, is the most sensitive and stable ring laser currently in operation. Its lock-in threshold is cited as 0.010 Hz.⁴ This incredibly low value can be attributed to superb vault and cavity engineering plus improvements in laser mirror technology resulting in the so-called “super mirrors.” Variations in the scale factor (4A/λP), in the sensor orientation, and in Earth's rotation influence the frequency in Sagnac interferometers. Even in the best designs like the ring laser⁴ in Germany, atmospheric pressure loading of the deployment site, microseismic activity, and solid Earth tides can affect the Sagnac frequency. In the Arkansas interferometer, variations in Earth's rotation are too small to be detected; however, variations in the scale factor can result from changes in the laser cavity geometry and backscatter coupling. The changes in the cavity geometry and sensor orientation can result from distortions of the basement slab in our three story science building. The basement slab distortions can result from atmospheric pressure loading of the deployment site, wind loading of the building, and uneven solar heating. In addition to these effects, in the Arkansas laser, pressure variations can couple into the nitrogen filled cavity and introduce minute perturbations in the 22.6 m cavity. These pressure variations can slightly perturb the cavity mirrors, cause minute changes in the effective cavity length, and slightly perturb the plasma tube. All these effects can vary the backscatter which in turn modulates the carrier frequency by small amounts.

A number of years ago the corresponding author conducted a series of experiments examining lock-in thresholds. An equilateral triangular ring laser with a perimeter of 150 cm was placed on a turntable. The laser employed a plasma tube, industrial quality dielectric mirrors, and a cavity filled with air. Distortion of the sine wave from the ring laser due to frequency pulling became clearly observable in an oscilloscope below approximately 1.5 kHz. The frequency pulling became increasingly nonlinear as the lock-in threshold was approached. In a commercial navigational ring laser with a perimeter of 40 cm, using 1970 vintage mirror technology, without a plasma tube, and sealed from the atmosphere, Aronowitz² cited the lock-in threshold as approximately 300 Hz. High levels of back scatter create significant coupling between the counter-propagating waves; however, the size of the Arkansas ring laser provides enough bias to keep it out of lock-in. In summary, our results suggest that one source of backscatter modulation is infrasound introduced perturbations of the laser cavity. In turn, frequency pulling due to backscatter changes can modulate the 375 Hz carrier frequency. FFTs can then extract the coherent infrasound and acoustic-gravity wave signatures from the non-coherent pressure and noise perturbations.

Although the coupling mechanism between coherent atmospheric infrasound and the ring laser is somewhat complex, the validity of using the ring laser as a coherent infrasound detector was verified in a controlled experiment. An FFT of the ring laser output agreed with the driving frequency of a collocated Helmholtz acoustic generator.¹⁴ Comparison with results from various NOAA studies^6–9 also suggest that the ring laser has the potential to serve as an infrasound detector. Although four tornadoes are too few to draw many conclusions, the inverse relation between tornadic infrasound frequencies and tornado funnel diameters is supported by the Mayflower-Vilonia, Arkansas (Faulkner County), tornado when compared to the other three storms in Table II. In all four tornadoes, infrasound was consistently detected before the funnel was reported on the ground as was also observed by NOAA.^6,8,9

A single instrument is of limited value as a tornado detector. To be of practical value, it would require an array of ring lasers and/or companion instruments such as Doppler radars. In areas where Doppler radar coverage is limited, the detection of tornadic generated infrasound is a candidate to supplement radar coverage. As large hurricanes¹⁴ move ashore, they emit infrasound. This suggests that ring laser interferometers may have the potential to supplement Doppler radar and satellites in the study of large convective storms. For example, the ring laser's ability to detect eye wall replacements¹⁴ in hurricanes may be useful in determining if this or related mechanisms are associated with hurricane intensification. Jet engines can be destroyed by volcanic ash. The extremely long distances over which an array of ring laser interferometers could detect explosive volcanic eruptions might be useful in locating eruptions in remote regions such as the Aleutian Islands. The ring laser's sensitivity to frequencies as low as 0.1 mHz allows it to detect responses in the buoyancy wave spectrum.²⁶ It has been suggested that buoyancy waves may play a role in the intensification of tornadoes.³³ The ability to show characteristic frequency spectra may help in identifying infrasound sources. Since the ring laser can detect both seismic waves and infrasound, ring lasers may have the potential for studying ground-atmospheric coupling.

This material was based in part upon work supported by the National Science Foundation under Grant No. 1147919 RUI: Geophysical Measurements Using Ring Laser sand Arrays. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. We also acknowledge the support of the NASA Arkansas Space Grant Consortium. A note of appreciation is due the reviewers whose comments were very helpful and significantly improved the paper.