<p>If I understand correctly, you wanted to estimate a range where Pile driving energy attenuates to a threshold level.</p>
<p>As you did not give input values for your calculation, I assume next a typical scenario</p>
<ul>
<li><p>pile-diver Source energy level (1/3 octave at 125 Hz): SEL= 200 dB//<span class="math-container">$\mu$</span>Pa<span class="math-container">$^2$</span>s-1m</p>
</li>
<li><p>TTS threshold: <span class="math-container">$TTS_L$</span> = 180 dB//<span class="math-container">$\mu$</span>Pa<span class="math-container">$^2$</span>s</p>
</li>
</ul>
<p>then with cylindrical spreading (<span class="math-container">$10 log_{10}(R/R_0)$</span>) and no attenuation the TTS level will be reached at</p>
<p><span class="math-container">$R=10^{(SEL-TTS_L)/10}= 10^{(20/10)}=100$</span> m</p>
<p>I guess, your formula that is similar, has a typo in it, i.e. missing '()' before division by 10.</p>
<p>Obviously, the numbers I use are based on an educated guess and you should use the actual numbers that apply to your scenario.</p>
<p>As a side note: the formula you are using to accumulate multiple pulses is correctly accumulationg the energy, but may overestimate completely the effective sound exposure, especially as the disturbed animal has the possibility to move away from the source, so that the long term accumulated sound exposure must consider the actual distance from the source. Also the duty cycle of pulses should be factored in, but that is another story.</p>
<p><strong>Edit</strong>: a comment on spreading law and use of attenuation: For mitigation purpose, cylindical spreading and 0dB attenuation is very conservative (precautionary principle to its extrem) and should satisfy most authorities. Reducing the mitigation requirements will need careful modelling, which is not easy as @BrianMiller's answer indicates.</p>
<p>As modelling depends heavily on input data, they must be agreed on with permit authorities if modelling is used for mitigation purposes.
I know, this is also not an easy task.</p>

CC BY-SA 4.0
2023-11-28T16:14:18.390Z
2023-12-19T14:54:11.243Z
2023-12-19T14:54:11.243Z
WMXZ
<p>I wrote this as a comment to <a href="https://bioacoustics.stackexchange.com/a/1565/73">WMXZ's answer</a>, but it was too long, so I'll post it here as an 'answer' even though it doesn't really answer the question.</p>
<p>Since the parent question and WMXZ's correct and perfectly fine answer might be found and used by non-physicist/non-acoustician/environmental managers, I think it's important to at least mention all the assumptions here, and also perhaps to comment on how realistic/reasonable these assumptions are.</p>
<p>For example, it seems there's an unstated assumption that the SL for the pile/driver is that of an omnidirectional point source?  Or perhaps it's the level at some range after the source has 'filled' the cylindrical space in which it is spreading?</p>
<p>Choosing the right level of detail and realism for the model will depend on the application. For a homework assignment or reality-check maybe it's fine to assume a long cylindrical pile can be modelled as an omnidirectional point source in a homogenous, perfectly reverberant, constant-depth environment. However, it's not likely to be appropriate as part of an environmental impact assessment of a real-world site. In this case, there may be legal concerns about harming a critically endangered species or financial concerns about shutting down operations, so it may be much more appropriate to choose models of source, environment, and propagation that are much more realistic -- since these details may matter. This is why the complex models mentioned in the question are often used (though sadly seldom empirically validated).</p>

CC BY-SA 4.0
2023-12-05T07:09:22.883Z
A small comment: cylindrical spreading (as used in OP) results from a line source. A point source will result in spherical spreading (which at long distance may result in cylindical spreading)
WMXZ
CC BY-SA 4.0
2024-01-02T04:41:21.560Z
Thanks WMXZ, that's useful info and good to know. Just want to clarify that my comment would still be valid if one were to replace "point source" with "line source." In practice, there's still potentially going to be a large difference between such an idealised model and the real-world.
Brian Miller
CC BY-SA 4.0
2024-01-02T09:28:06.713Z
Correct, if one wanted to know the real exposure. The OP did not say the purpose of the estimation, but in most cases such estimates are made for permit (mitigation) purpose. So it depends on which side one is(applying, granting, or even challenging a permit) and as you know different nations have different standards.
WMXZ
CC BY-SA 4.0
2023-12-01T01:58:22.977Z
2023-12-19T16:27:15.973Z
2023-12-19T16:27:15.973Z
Brian Miller
<p>I was just wondering if anyone has any suggestions on how to find the auditory Permanent Threshold Shift (PTS) and Temporary Threshold Shift (TTS) ranges for Right whales.</p>
<p>I know the source level for the pile driving and the TTS and PTS onset thresholds, yet the math just is not working (I am getting numbers that are way too big or the PTS range is larger than the TTS range). The papers I am finding are not helpful as they say to do what I already did, or did some complex modeling and did not explain how they made the model.</p>
<p>I tried:
Solving for SELcumulative by doing the SELss + 10 log10(N), where N is the number of pulses and plugging that into rmax = 10^(SL-TL/10)<br />
Note: I am assuming cylindrical spreading and no absorption, SL = dB of Pile Driving, RL = dB PTS or TTS and I am using the same reference for both.</p>
<p>I tried the above rmax equation but with peak SPL instead, it did not work</p>
<p>I tried the above but with
BW (Hz) = 1 / T, where T is the pulse length in seconds (the bandwidth was quite large, but I was not given an exact bandwidth).</p>

CC BY-SA 4.0
2023-11-28T12:18:23.273Z
Hi Karianney, welcome to Bioacoustics SE! Could you give more background for your question by editing it please: which software are you referring to? What do PTS and TTS stand for?
Noil
CC BY-SA 4.0
2023-11-28T15:31:26.347Z
added full wordings for PTS and TTS
WMXZ
<analysis><exposure>
Modeling PTS and TTS Distances for Pile Driving?
# Modeling PTS and TTS Distances for Pile Driving?

(Asked by: username_0 on 2023-11-28)

I was just wondering if anyone has any suggestions on how to find the auditory Permanent Threshold Shift (PTS) and Temporary Threshold Shift (TTS) ranges for Right whales.

I know the source level for the pile driving and the TTS and PTS onset thresholds, yet the math just is not working (I am getting numbers that are way too big or the PTS range is larger than the TTS range). The papers I am finding are not helpful as they say to do what I already did, or did some complex modeling and did not explain how they made the model.

I tried:
Solving for SELcumulative by doing the SELss + 10 log10(N), where N is the number of pulses and plugging that into rmax = 10^(SL-TL/10)  
Note: I am assuming cylindrical spreading and no absorption, SL = dB of Pile Driving, RL = dB PTS or TTS and I am using the same reference for both.

I tried the above rmax equation but with peak SPL instead, it did not work

I tried the above but with
BW (Hz) = 1 / T, where T is the pulse length in seconds (the bandwidth was quite large, but I was not given an exact bandwidth).

**Tags:** analysis, exposure

> **Comments:**
> **username_1**: Hi username_0, welcome to Bioacoustics SE! Could you give more background for your question by editing it please: which software are you referring to? What do PTS and TTS stand for?  
> **username_2**: added full wordings for PTS and TTS  

---

## 2 answers

### Answer by username_2 on 2023-11-28. Score: 2

If I understand correctly, you wanted to estimate a range where Pile driving energy attenuates to a threshold level.

As you did not give input values for your calculation, I assume next a typical scenario

* pile-diver Source energy level (1/3 octave at 125 Hz): SEL= 200 dB//$\mu$Pa$^2$s-1m
* TTS threshold: $TTS\_L$ = 180 dB//$\mu$Pa$^2$s

then with cylindrical spreading ($10 log\_{10}(R/R\_0)$) and no attenuation the TTS level will be reached at

$R=10^{(SEL-TTS\_L)/10}= 10^{(20/10)}=100$ m

I guess, your formula that is similar, has a typo in it, i.e. missing '()' before division by 10.

Obviously, the numbers I use are based on an educated guess and you should use the actual numbers that apply to your scenario.

As a side note: the formula you are using to accumulate multiple pulses is correctly accumulationg the energy, but may overestimate completely the effective sound exposure, especially as the disturbed animal has the possibility to move away from the source, so that the long term accumulated sound exposure must consider the actual distance from the source. Also the duty cycle of pulses should be factored in, but that is another story.

**Edit**: a comment on spreading law and use of attenuation: For mitigation purpose, cylindical spreading and 0dB attenuation is very conservative (precautionary principle to its extrem) and should satisfy most authorities. Reducing the mitigation requirements will need careful modelling, which is not easy as @username_3's answer indicates.

As modelling depends heavily on input data, they must be agreed on with permit authorities if modelling is used for mitigation purposes.
I know, this is also not an easy task.


---

### Answer by username_3 on 2023-12-01. Score: 1

I wrote this as a comment to [username_2's answer](https://bioacoustics.stackexchange.com/a/1565/73), but it was too long, so I'll post it here as an 'answer' even though it doesn't really answer the question.

Since the parent question and username_2's correct and perfectly fine answer might be found and used by non-physicist/non-acoustician/environmental managers, I think it's important to at least mention all the assumptions here, and also perhaps to comment on how realistic/reasonable these assumptions are.

For example, it seems there's an unstated assumption that the SL for the pile/driver is that of an omnidirectional point source? Or perhaps it's the level at some range after the source has 'filled' the cylindrical space in which it is spreading?

Choosing the right level of detail and realism for the model will depend on the application. For a homework assignment or reality-check maybe it's fine to assume a long cylindrical pile can be modelled as an omnidirectional point source in a homogenous, perfectly reverberant, constant-depth environment. However, it's not likely to be appropriate as part of an environmental impact assessment of a real-world site. In this case, there may be legal concerns about harming a critically endangered species or financial concerns about shutting down operations, so it may be much more appropriate to choose models of source, environment, and propagation that are much more realistic -- since these details may matter. This is why the complex models mentioned in the question are often used (though sadly seldom empirically validated).

> **Comments:**
> **username_2**: A small comment: cylindrical spreading (as used in OP) results from a line source. A point source will result in spherical spreading (which at long distance may result in cylindical spreading)  
> **username_3**: Thanks username_2, that's useful info and good to know. Just want to clarify that my comment would still be valid if one were to replace "point source" with "line source." In practice, there's still potentially going to be a large difference between such an idealised model and the real-world.  
> **username_2**: Correct, if one wanted to know the real exposure. The OP did not say the purpose of the estimation, but in most cases such estimates are made for permit (mitigation) purpose. So it depends on which side one is(applying, granting, or even challenging a permit) and as you know different nations have different standards.  

---

