Sunday, September 04, 2016

Acoustic Signature of a Submarine.

After the Scorpene leak there is a lot of talk about acoustic signature of a submarine. I hope this helps people understand where that noise comes from.

When I create mechanical motion (using for example an engine), I couple energy from the engine into the mounts (on which the engine sits), the shafts (which are connected to the engine) and to the chamber (i.e. the walls of the room) in which the engine sits.

For a submarine, the chamber walls are the walls of the submarine itself. And once I have ordered the submarine, I can't really change its shape. So if any energy from my engine couples into the walls of the submarine, I can't really prevent it from driving the mechanical vibrations of the walls themselves.

I can theoretically improve the quality of noise suppression in the mounts, use "active feedback" to try and cancel out the inside noise coupling to the walls, but I have no control over the noise that couples via the propeller to the water and then back to the walls. So this noise is basically impossible to mask. Ideas like anechoic tiles etc... have been proposed, but I wonder how successful they are.

Now a submarine is a very complicated shape, and since I am a physicist who likes using the "Spherical Cow" approximation, I reduce the shape of the submarine to a simple beam. Now I can use standard equations for the vibrations of a mechanical beam to determine what the likely resonance frequencies will be [see here].

If I take the numbers from the internet for the length and breadth of the Arihant (which may or may not be accurate) I can crude estimate from the above reference that the the resonance frequencies of a beam of steel of the same length and cross sectional area as the Arihant will be about 4-5 Hz.

Again I am not saying that this is what the frequency of the Arihant's acoustic signature is - because I don't know what it is, but it is not that hard to come up with a ball park figure of where the frequencies are.

What is much harder is determining what the amount of power coupled to this "wall mode" will be. That is where a leak like the Scorpene data dump can be very damaging.

Let's assume for a moment I am trying to detect where the Arihant is in the waters off the Bay of Bengal. I have at my disposal a microphone that works under water, an amplifier, a filter and a computer to analyze the signal.

I know that the Arihant will have mechanical noise in the 4-5 Hz range. So I tune my filter to cut out all noise above and below that frequency band. An ideal notch filter exists [Wikipedia], but actually building one that works reliably in the range I want is a major pain but since I have no choice - I do it anyway. Once I have the notch filter I still need to know how low the signal strength is going to be, if I don't I can't reliably set the gain of my amplifier. If I set the gain too low, I will miss the Arihant's signature, if I set it too high I will see every whale noise amplified - so again the noise will overwhelm the signal.

In order to set the amplifier gain in a Goldilocks Zone, I need to have a rough sense of what the signal magnitude is. And that is what I get from a leak like the Scorpene data dump. Once I know the gain setting - I can then collect data from the microphone for months on end - and then use my computer to search for repeating patterns in the data (a relatively simple autocorrelation function [see here]).

If I find a pattern at one such sound surveillance station, I can look for similar sound patterns in data collected at other sound surveillance stations and that will allow me to triangulate the position of the Arihant.

I do this a few dozen times, I can get a rough sense of the patrol path of the Arihant. Now I can go back and look at weather reports of the area and see what kind of weather conditions the Arihant is happy working in.

I can also go back and see when the patrols began and ended, and I can conclude how far along the platform testing is.

So basically the acoustic signal magnitude is like a spherical kamadhenu that keeps on giving!


At 1:46 PM, Blogger Ralphy said...

when a submarine leaves port it has to follow certain protocols. it must always assume an attempt is being made to track it. it can't hide the fact that it is leaving so it must take certain measures to insure that potential enemy subs and/or underwater monitors are interfered with. I don't wish to discuss these measures but suffice it to say it is like a spicy hot sauce.......everybody's got their favorites....grin.

At 11:17 PM, Blogger Nanana said...

Won't the salinity gradients + warm waters provide enough cover in BoB and AS?

At 3:30 AM, Blogger Ralphy said...

no. not if you are successfully tagged upon leaving port.

At 3:47 AM, Blogger Ralphy said...

a few months ago, the Russians who have a naval base in the eastern Med, were in the news for harassing a US naval destroyer that was clearly in international waters in the eastern Med. the US media was appropriately indignent at such outrageous behavior of the Russians. No further explanation was given. After a few days the US destroyer finally moved away from its location after some close call manuevers by the Russians.

very mysterious......LoL.

At 5:12 AM, Blogger maverick said...

@ Ralphy,

Oh I am sure each submariner has tricks up their sleeve to escape detection, I just wrote that post to help ordinary people understand what is so damaging about the Scorpene dump.


I actually don't know where exactly those gradients are in the BoB or AS, but you are correct in principle those should help reduce detection.

The thing is that a ELF signature is difficult to hide because there is not much attenuation simply because nothing absorbs it.

The only thing that hides your ELF is noise in the same spectral range. So I think your best bet it to keep the ELF signature hidden.

As long as your signature is hidden, the enemy has to put their back into the data analysis and spend the better part of a decade mining randomly pieces of data. It becomes an exercise in spotting ghosts.

I have completely trivialized the shape resonances of a submarine hull, I think one could use a FEM of a submarine to calculate these modes in detail, but I don't want to do all the work that entails and I could speak for hours on the issue of reliable FEM codes.

At 5:17 AM, Blogger maverick said...


Did the boys from Commander Wiley's place in Penghu do something recently?

Just asking 'cause the Chinese don't look too happy.

At 6:26 AM, Blogger Ralphy said...

have not been following the Taiwan strait lately.....what's up?

At 7:03 AM, Blogger maverick said...

Dunno either - look at all the footage from the G-20. The Chinese don't look happy.

At 7:19 AM, Blogger maverick said...

Is there anything active at Pratas? I ask because the GE shots are all blurry and I can't find recent imagery of the TA of the airport. That to me is a flag that someone is hiding something in plain sight.

Also for some reason the Chinese seem convinced that positions in the Paracels and the Spratlys will be sufficient to act as a choke point on ONG traffic to ROC and Japan - I don't get the "why" of this but then I am not Chinese.

And while I am on the topic of not being Chinese, can someone from Beijing please explain to me why neither the bases in the Paracels nor the bases in the Spratlys look like they could survive an air attack?

Also do any of these places have native fresh water sources?

Just asking because - as you know I am not Chinese, and I don't get things that PLAN folks find obvious.

At 11:29 PM, Blogger Ralphy said...

it's all about Han territorial imperative.

At 5:59 AM, Blogger maverick said...

Yeah which is why I am asking if someone went and trampled on their roses.

At 6:56 AM, Blogger Ralphy said...

they don't like the recent international court decision. they blame the US for it. they also don't like the regional Asian meeting that is happening in Laos right now and which Obama is attending. they see the US and its neighbors conspiring together in order to oppose the imperial Han imperative. they cite the US past history in its territorial aggrandizement as their perogative too and how unfair it is for the US and China's diminutive neighbors to oppose them in regional and international disputes. Can't a Han get some respect?

At 5:17 AM, Blogger maverick said...

I think their minds are much further along than their actual capabilities are.

They don't have the ability to really support or protect those island airbases they are constructing.

There is very little fresh water on those islands. And they don't have ships that can act as a screening force around the islands.

Given that background - they are going to feel threatened by the slightest thing. This is just a recipe for getting perpetually harassed.

I don't know why they indulge in these bizarre displays of national stamina. There are better ways to express your national interests on the high seas.

At 5:22 AM, Blogger maverick said...

Actually I am wondering if I should do a post about the importance of freshwater lenses in choosing an "unsinkable" aircraft carrier.

Very few people realize how the unsinkability of an island airbase depends delicately on saltwater intrusion into Ghyben-Herzberg lens.


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