Voice of the Dolphin
 
Vol. 3 No. 5
20APR2001
 
 

POBox 1645 Pahoa, Hawai'I 96778 siriusinstitute@yahoo.com
Lee Tepley on LFAS Resonance
Voice of the Dolphin Vol. 3 No. 3 April 3, 2001


From Lee Tepley
 
PREFACE:
 
The primary purpose of this message is to supplement information recently submitted by Ken Balcomb to MARMAM and to the Navy (Reference 1). Balcomb's comments concern the importance of air-space resonance effects which intensify sound waves from mid and low frequency active sonars which may have already caused strandings and death of cetaceans in the Bahamas on March 15, 2000 and earlier in the Mediterranean sea.
 
This message also briefly considers two alternative mechanisms which may cause or contribute to the stranding of cetaceans. Finally, it points out what seems to be a serious misunderstanding on the part of NMFS personnel on the effective source level of LFAS. Air-space resonance effects will be considered first.
 
INTRODUCTION:
 
Since the Navy is anxious to deploy LFAS, it will probably minimize, ignore or try to debunk the importance of Balcomb's comments on air-space resonances (Reference 1). I hope that the following material will make the Navy's task more difficult.
 
Until the Final Environmental Impact Statement (FEIS) on SURTASS LFA Sonar, the Navy did not even acknowledge the possible existence of any resonance effects. However, in Comment 4-4.15 of the FEIS (in response to a question by Balcomb) the Navy acknowledged the effect while, at the same time, attempting to minimize it's importance. The navy's comment included a statement to the effect that the potential resonance frequency would last for only about 10 seconds which would not be a long enough time to cause any damage to marine mammals. Also, in a press release, Joe Johnson stated: "It takes a fairly steady tone to create resonance". These two comments seem to make no sense. As discussed in PART 6A below, it would take only a few milliseconds for the sound wave pressure to build up to a dangerously high level for both mid and LFAS sonar frequencies. In 10 seconds the marine mammal could be hit by several thousand cycles of the sound wave at a pressure at or near the resonance pressure.
 
After reading an earlier message by Balcomb and Claridge posted on MARMAM (Reference 2), I spent a great deal of time investigating the possibility of the Minneart resonance intensifying sound waves from mid-frequency sonars. I posted the results on my web site in a long technical paper (Reference 3). I did not otherwise publicize the results because I had some doubts as to whether the resonance would be strong enough to cause damage to cetaceans as suggested by Balcomb and Claridge. My paper also considered another possible mechanism about which I also had doubts and will not be considered here. However, in view of Balcomb's recent comments (Reference 1) and in view of the results presented below, it should be clear that a sonar sound level of 160 dB (or less) is enough to cause serious injury to cetaceans. Therefore, the Navy is clearly wrong in insisting that any sound level below 180 dB is relatively safe.
 
Balcomb demonstrated in Reference 1 that air space resonances could occur at reasonable depths at both mid and LFAS sonar frequencies. However, he did not estimate the actual pressure increases in the air spaces caused by the resonances. The following comments fill that gap.
 
In my posted paper, I pointed out that all parameters that I used were approximate and conservative. By slightly changing a single parameter, I obtain results which back-up and supplement Balcomb's ideas about the importance of air-space resonances.
 
PART 1. MATHEMATICAL FORMULATION:
 
The first mathematical formulation for the air-space resonance was done by Minneart in 1933 (Reference 4). He considered an air bubble oscillating (expanding and contracting) in open water. This effect was investigated in more detail by Devin in 1959 (Reference 5). Both investigations lead to the same equation which turned out to be identical in form to an equation which is considered in almost all college classes in physics and in electric circuit theory. Hence, the results are well known and can be easily applied. It is assumed that similar results would be obtained in the case of an air bubble restricted to an air space in a cetacean and separated from open water by the cetacean's bone and tissue. A related problem - the resonance of an air bubble in a fish bladder - was formulated and solved by Andreeva in 1964 (Reference 6). In deep water the Minneart and Andreeva resonances lead to almost identical results. In my posted paper I referred mostly to the Minneart resonance.
 
PART 2. PRESSURE BUILD-UP AT RESONANCE:
 
The pressure build-up produced by the Minneart (air space) resonance is given by the ratio of the sound pressure at the resonance frequency to the sound pressure at a much lower frequency. This ratio turns out to be equal to a quantity usually referred to in electric circuit theory as "the Figure of Merit", "the Q factor" or as just plain "Q". The greater the value of Q, the sharper the resonance and the greater the increase in sound pressure. In an air space of a marine mammal, the value of Q is limited by sound absorption in adjacent tissues and can only be estimated. However, the (probable) maximum possible value of Q can be found by considering the case of resonance of an air bubble oscillating in water. It was calculated by Devin to be Q = 25 for frequencies in the range of mid-frequency sonar. In my posted paper, I used a very conservative estimate of Q = 5. To back up Balcomb's result, I need only to use a value of Q = 10 which is still conservative. This means that the sound pressure would be increased by the same factor of 10 which is equivalent to 20 dB. Although this is a relatively small increase, it means that the level of 180 dB - which even the Navy admits is on the verge of being dangerous - should be replaced by 160 dB. There is a great deal of data already available to the effect that 160 dB is dangerous but the Navy has made a great effort to minimize it's importance. The demonstrated importance of the Minneart (air-space) resonance should make it more difficult for the Navy to continue this charade. However, it will certainly try. Will it succeed in ignoring the facts??
 
PART 3. RESONANCE FREQUENCY:
 
The resonance frequency depends only on the ambient pressure and the mean radius of the air-space which decreases with increasing depth as the ambient pressure increases. This has to be taken into account using Boyle's law. Having no knowledge of the actual air-space volumes of any cetaceans, I calculated the depths at which the Minneart resonance occurs for a series of air-space volumes that seemed reasonable. Balcomb followed the same procedure in Reference 1. However, because of his knowledge of cetacean air-space volumes, his results are undoubtedly more reliable than mine. He found that resonances occurred at depths about 3 times greater than indicated in my posted paper.
 
PART 4. AMPLITUDE OF RESONANCE OSCILLATION IN AIR SPACE:
 
The amplitude of the resonance oscillation can be calculated from the equation of motion of an oscillating bubble. The applicable equation and results at various depths for a sound wave from mid-frequency sonar are given in Figures 1 and 2 of my posted paper. Amplitudes were found to be in the range 0.1 to 0.3 microns peak. I had expected to find much larger oscillations and was surprised to find that they were in the microscopic range. Initially, this caused me to question the importance of the Minneart resonance effect. The Navy could also use this fact to argue against it's importance. Therefore, I think it is crucial to demonstrate that a small oscillation is sufficient to cause a very large and dangerous effect.
 
A. First, it follows from basic physics that the amplitude of the oscillation will be small. This is because the pressure in the air-space is initially the same as the pressure of the surrounding water. Then the air-space bubble is caused to oscillate (expand and contract) by a sound wave which has propagated through the water by rapidly increasing and decreasing the ambient water pressure. The changing water pressure then penetrates the cetacean bone and tissue and causes the air-space bubble to oscillate. At the water's surface, the ambient water pressure is 1 atmosphere (the same as the air pressure at the surface). Perhaps surprisingly, this is equivalent to 220 dB. As we go deeper the water pressure increases. At 100 atmospheres (over 3,000 ft down), the ambient pressure has increased to 260 dB. But even just below the surface the ambient pressure is far greater than the sound wave pressure unless the air-space bubble is extremely close to the sonar source. Hence the bubble is being caused to oscillate by only a small perturbation in the ambient water pressure. For example, consider a 160 dB sound wave. This is a very intense sound wave but at 100 atmospheres the ambient water pressure is 100,000 times greater. Since the perturbation is small, the oscillation will also be small.
 
B. However, the oscillation amplitude is increased at resonance by the Q factor. But even considering the (probable) maximum value of Q = 25, the amplitude would still be small because the ambient pressure is almost always far greater than the sound wave pressure. As pointed out above, in my posted paper I used a conservative value Q = 5. Here I am assuming the still conservative value Q = 10. This increases the oscillation amplitude by a factor of 2.
 
C. My posted results considered peak oscillation amplitudes. From the standpoint of causing tissue damage, I should have considered peak-to peak amplitudes. This increases the oscillation amplitude by another factor of 2.
 
D. Although I don't have access to Balcomb's data, it appears that the mean radii of the air spaces that he used were about 3 times greater than the estimated values used in my posted paper. His values are undoubtedly far more reliable than mine. From the equation of motion for an oscillating bubble, it turns out that the oscillation amplitude will also increase by the same factor of 3.
 
Combining the three factors in B, C and D above leads to a typical resonance oscillation peak-to peak amplitude of slightly over 2 microns produced by a sound wave from mid-frequency sonar. This number would vary only slowly with depth.
 
Although, a 2 micron oscillation is still in the microscopic range, it will be demonstrated below that it is large enough to cause serious injury to cetaceans. This is because we are dealing with the effects of damage to tissues and cells which are also microscopically small objects. It should also be pointed out that the air-space cavities which resonate at LFAS frequencies (lungs, etc.) will be larger than those that resonate at the higher frequencies of mid frequency sonar (sinus cavities, etc.). Again assuming Q = 10, the result at LFAS frequencies would be an increase in the amplitude of the resonance oscillation by an additional factor of about 10. However, Devin's calculations show that Q decreases slowly with decreasing frequency. Therefore, for LFAS the oscillation amplitude would probably be about 10 microns.
 
PART 5: RESONANCE OSCILLATIONS AND TISSUE DAMAGE: I can barely recall taking a biology course in high school so the Navy does not have to challenge my expertise in biology because I don't have any. Nevertheless, from a biology textbook (courtesy of Duane Erway) and from a quick search of the web, I obtained values of from 1 to 10 microns for the width of blood cells and 10 microns for the width of epithelial cells in the human intestine. The latter may be similar to the type of cell that make up the erectile tissue which contains blood and partially surrounds the air spaces in the heads of cetaceans. The function of this erectile tissue is discussed in Part 7 below.
 
So for the case of mid-frequency sonar we are dealing with a situation where cells of about 1- 10 microns across are being hit repetitively by sound waves of about 2 microns peak-to-peak amplitude. The potential for serious tissue damage should be obvious. How would you like to be hit thousands of times per second for many seconds with a very broad hammer that penetrates about one tenth of the way through your body?? This might be a good place for a microbiologist to weigh in but, to my simple mind, the result would be severe tissue damage. Air-space resonance oscillations must be taken very seriously. They explain why a 160 dB sound wave is more than adequate to injure and kill cetaceans.
 
At LFAS frequencies the oscillation amplitude will be about 5 times greater than for mid-sonar frequencies as discussed above. The potential for tissue damage may increase accordingly but may also depend on other characteristics of the larger resonant cavities. Again, this would be a good point for a microbiologist - or maybe Ken Balcomb might have some interesting ideas.
 
PART 6. CETACEAN EXPOSURE TIME:
 
As discussed in the Introduction above, the comments about resonance in the FEIS and by Joe Johnson might be interpreted as suggesting that the sound amplitude would not have time to build up to a dangerous value while the sound frequency was in the resonance range. This is incorrect as shown below.
 
A. BUILD-UP TIME:
 
From the electrical analogue of the Minneart resonance, I was able to derive the complete equation of motion at resonance - including the transient build-up time when the sound wave first strikes the air space. The build-up time depends only on the resonant frequency and the Q of the resonance circuit. I used the value of Q = 10 as discussed above. The equation was a bit complicated but Duane and Jennifer Erway were able to plot the results using computer programs. At 300 Hz - taken as the mid-frequency of LFAS - it took only about 5 cycles for the signal to build up to it's maximum value. This corresponds to about 17 milliseconds. At 3500 Hz. - taken as the frequency of mid-frequency sonar - it again took about 5 cycles. This corresponds to about 1.4 milliseconds. For practical purposes, both build-up times can be considered to be instantaneous.
 
B. SWEEP-THROUGH TIME:
 
I don't know if mid-frequency sonar sweeps at all. If it does not sweep, the cetacean could be exposed to the resonance frequency until it swims out of the resonance region. This could take many seconds. For LFAS I again assume a mid frequency of 300 Hz. Taking Q = 10 as before, leads to a bandwidth of 30 Hz. The signal would be 3 dB down at both 285 Hz. and 315 Hz. The Navy can vary the LFAS frequency in many different ways. However, it seems to prefer operating LFAS at a constant or slowly varying frequency for from 5 to 10 seconds (Reference 7, Page 34). Then LFAS is abruptly switched to another constant or slowly varying frequency. This means that if the LFAS frequency should coincide with an air-space resonance frequency, the cetacean will be subject to the same (or a nearby) frequency for from 5 to 10 seconds. The cetacean may be hit by about 2000 oscillations before the frequency is changed. I suspect that only a few oscillations would be enough to cause damage - but 2000 oscillations?? How can the FEIS and Joe Johnson imply "no problem!!"
 
PART 7. AN ALTERNATIVE MECHANISM - PANIC AND EQUALIZATION:
 
In late February, I sent out several e-mails on an alternative mechanism which could have caused the Bahamas strandings. This was before I realized that a relatively small resonance oscillation could cause serious tissue damage as discussed above. Although it should now be clear that air-space resonances are extremely important, other mechanisms should not be ruled out. In fact, several mechanisms could work simultaneously to enhance tissue damage.
 
My alternative mechanism considered the possibility of tissue damage in the middle ear resulting indirectly from the loud sonar sounds which caused cetaceans to become frightened. It has been known for some time that loud sounds sometimes cause cetaceans to panic. In fact, (as pointed out by Duane Erway) "After WWII the Norwegians used sonar to hunt whales because they found the sonar frightened especially baleen whales and caused a predictable flight response making them easier to catch" (this may be a direct quote from Reference 8).
 
Furthermore, "panic" was the most common explanation offered for the strandings of the beaked whales in the Ionean sea. In that case, no necropsies were obtained so no ear damage was demonstrated. So how is panic connected to ear damage?? It comes down to the length of the time lag in the cetacean mechanism for "equalization".
 
As part of every day living, cetaceans dive deep and fast and also ascend rapidly from deep water. It is agreed by all experts that all cetaceans have air-filled sinus and middle ear cavities. To prevent serious ear damage, the inside air must rapidly achieve the same pressure as the outside water. This is called "equalization". Human free or scuba divers also must equalize as they descend and ascend. If they do not, the result is intense pain, bleeding around the ear, broken eardrums and, on rare occasions, death.
 
Most human divers are familiar with the mechanism for equalization. I won't go in to it here. What is important is that cetaceans use an entirely different mechanism because they have to cope with far greater and more rapid changes in water pressure than do human divers. The cetacean mechanism involves blood flowing rapidly in and out of porous tissues which partly surround and extend into the air-filled middle ear and sinus cavities. The porous tissue is thought to closely resemble the erectile tissue of the human male. As the cetacean descends, the tissue engorges with blood causing the cavities to become smaller and the air pressure to increase rapidly to that of the external water pressure. When the cetacean ascends the reverse process occurs.
 
The above is a pretty amazing mechanism but all the experts seem to agree that it really happens. But there has to be a limit as to how rapidly equalization can occur. If the cetacean should panic and descend or ascend too rapidly, equalization might not occur fast enough to totally prevent large differences between air and water pressure. This would cause pain, tissue damage and bleeding which could disorient the cetacean and lead to stranding and death. Under ordinary conditions cetaceans should know how rapidly they can safely descend and ascend. But being panicked by a high energy sound wave is not an ordinary condition.
 
There may be many other ways in which a malfunction in the equalization mechanism may be related to panic. Four examples follow.
 
a. Perhaps damage to the erectile tissues in the middle ear caused by an airspace resonance deactivates the equalization mechanism.
 
b. Perhaps panic effects the cetacean's nervous system is a manner that causes the equalization mechanism to malfunction - even if the cetacean is not ascending or descending extremely fast.
 
c. Perhaps the equalization mechanism may not work well in older or sickly cetaceans. Then panic- resulting in a rapid ascent or descent -could make the situation worse.
 
d. Perhaps ocean pollution has lead to toxins in the cetacean diet which has affected blood circulation of even young healthy cetaceans. This could cause or aggravate equalization problems.
 
The Navy and NMFS should not arbitrarily dismiss mechanisms involving equalization problems associated with panic because they have not been proven. The fact is that whales have been killed by mid-frequency sonar.
 
Panic might be more likely for the smaller cetaceans at higher frequencies - like those of mid frequency sonar - where they are likely to have higher hearing sensitivity - but it cannot be ruled out at LFAS frequencies - especially for the baleen whales who probably have high hearing sensitivity in the LFAS frequency range.
 
PART 6: ANOTHER ALTERNATIVE MECHANISM - BUBBLES IN THE BLOOD:
 
Crum and Mao (Reference 9) have investigated the problem of sound waves enhancing the growth of bubbles in blood for both humans and marine mammals under a number of conditions. They showed (as acknowledged by the Navy in the FEIS) that significant bubble growth may occurr at sound levels above 190 dB. This would ordinarily occur only if a cetacean was very close to the sonar source. However, in a private communication to me, Dr. Crum stated that, under conditions of extreme super-saturation, bubbles might possibly occur at substantially lower sound levels but this situation has not been investigated. Conditions of extreme super-saturation would occurr for cetaceans - such as sperm whales or beaked whales that can remain at great depths for long periods of time.
 
PART 7: THE "240 dB" NUMBER:
 
In a phone conversation between Mark Palmer of the Earth Island Institute and Dr. Roger Gentry of NMFS, Dr. Gentry apparently stated that the proposed LFA level was 215 dB. The exact quote from Mark's message is "The Navy is also claiming that the Bahamas sonar was used at 230 dB, higher than the LFA level of 215 dB."
 
It is discouraging that the 215 dB number keeps coming up over and over again. It is incorrect and Dr. Gentry should know better. 215 dB refers to the output of a single element of the LFA array. Since there are 18 elements, the effective output is about 240 dB.
 
The concept of an "effective output" or "an effective source level" is important when comparing outputs and distant sound levels from different sources. This is exactly what Dr. Gentry did above and, because he does not understand the concept of "effective source level", he did it wrong - or, perhaps, he was mislead by the Navy.
 
I spent some time trying to explain the concept of effective source level in earlier e-mails but it is difficult to understand for anyone without a technical background and my efforts never seem to take hold. I won't make another effort here because this message is already quite long. However, I will again point out that the 25 dB difference between 215 dB and 240 dB is given by the formula 25 dB = 20 log (18 squared). This is even admitted by the Navy (but very quietly) on Page B-3 of the appendix of the draft DEIS.
 
Also, in my comments on the DEIS I brought this point up again. In reply the Navy briefly mentioned the term "effective source level" but it dodged my question by not specifically stating it was 240 dB. It appears that the Navy's policy is to be deliberately misleading -perhaps to prevent people like Dr. Gentry from becoming overly concerned. This is upsetting because NMFS will determine if and when LFAS goes operational. Therefore NMFS personnel should be required to understand the technicalities about LFAS but apparently they do not. Hence, NMFS will probably go along with the Navy's propaganda.
 
One final comment on the effective source level: It is probably correct that the actual sound level close to the LFAS cable does not exceed 215 dB but this is of little importance because, as pointed out in Part 6 above, if a cetacean is close enough to the cable so that it encounters a sound level of greater than 190 dB, it is likely to be seriously injured because bubbles will have formed in it's blood vessels. Therefore, it may not make much difference if a cetacean comes any closer. What is far more important is that the effective source level be used when considering and comparing the effects of LFAS and other sonars in the so-called "far field" - that is, at distances greater than 1 kilometer from the source. The LFAS sound level can sometimes be at a dangerous level of 150 - 160 dB out to several hundred kilometers from the source and therefore, can cause injury or death to very large numbers of cetaceans - even at great distances. In contrast, the Navy's so-called "mitigation measures" (even if they work) would prevent serious injury to an almost negligibly small number of cetaceans which happen to be very near the source. As the saying goes: "Out of sight, out of mind".
 
REFERENCES:
 
1. K. Balcomb -Message to MARMAM "Cetaceans & Sonar - Bahamas Strandings", March 2, 2001
 
2. Draft Report For MARMAM distribution and comment. "Report on the whale and dolphin strandings around March 15, 2000 on Abaco, Grand Bahama and North Eleuthera, Bahama Island" By Ken Balcomb & Diane Claridge, June 26, 2000.
 
3. L Tepley, "Possible mechanisms for strandings of beaked whales", http://home1.gte.net/leetpley/lfassummary.html, Sept. 2000
 
4. M. Minnaert, Phil. Mag. XVI, 235 (1933)
 
5. C. Devin, "Survey of thermal, radiation, and viscous damping of pulsating air bubbles in water". J. Acoust. Soc. Am. 31, 1654-1667 (1959)
 
6. I. Andreeva, "Scattering of sound by air bladders of fish in deep sound-scattering ocean layers". Soviet Physics-Acoustics 10, 17-20 (1964)
 
7. C. Clark, Application for SRP for LFS Scientific Research Pogram, June 25, 1997.
 
8. E. Mitchell, G. Blaylock, and V.M Kozicki , "Modifers of effort in whaling operations: with a survey of anecdotal sources on searching tactics and the use of asdic in the chase". Center for Environmental Education Monograph Series (1981)
 
9. L. Crum & Y. Mao, "Acoustically enhanced bubble growth at low freuencies and its implications for human diver and marine mammal safety". J. Acoust. Soc. Am. 99, 2898-2907 (1996)
 
ACKNOWLEDGEMENT: Thanks to Duane Erway for many suggestions and informal discussions about this issue and for his computer calculation of sound wave rise time which he did with the help of Jennifer Erway.
 


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