How deep the Challenger Abyss is: measuring depth

“We must understand the whole depth of our depths” (C) DMB

Greetings, dear ones!

I was always amazed that the distance to the moon is measured with millimeter accuracy. Even when exoplanets are discovered by the radial velocity method , stellar velocities are measured with an accuracy of 0.97 m / s . But, for example, the depth of the Challenger Abyss is determined with an accuracy of ± 10 meters .
Why is everything so complicated with water?



We deal with this issue under the cut. As a cherry on a cake: an application for visualizing the movement of sound through water with layers of different densities with source codes on a github and an online calculator.

Let me remind you that there are exactly two and a half fundamental ways of determining the depth:

• rope =)
• , . , . : , ( ) , .
• — .

Here with the last paragraph today, I propose to sort it out.

I like to always consider the situation to the limit. The Mariana Trench in general and the Challenger Abyss in particular - this is the limit of the situation with depth on our planet. Many effects become significant and are clearly visible only at great depths.

So, the story of measuring great depths originates from the very Challenger - HMS Challenger , whose name is the deepest depression of the ocean. Here, by the way, he is in the photo :



In the spring of 1875, the expedition measured the depth with a rope , no less than 8184 meters. By the way, the problems of measuring depth with a rope, in addition to such obvious ones as the drift of a vessel and currents, are described in Entertaining Physics by Perelman: the rope experiences friction against water, wriggles, twists like protein molecules and does not go down after a certain depth - it doesn’t accept water .

Since then, people have not been idle, and in 1952 the depths of the Mariana Trench were already measured by the HMS Challenger II:



With an explosive, a manual stopwatch, a wire with a load of 20 kg, crowbar and adhesive tape, as well as the first sonar, they measured 10,900 meters . After post-processing, the result was reduced to 10632 m with an ambiguity of ± 27 meters.

Digging out, or atmospheric, plunging into the history of exploring the oceans, in one of my previous articles I mentioned the legendary Soviet research vessel Vityaz - I used the image of a postage stamp with it as a KDPV:



In 1957, Vityaz measured the deepest depth of our depths - 11034 m . The measurements were made at the limit of the sonar range based on a constant speed of sound of 1,500 m / s, after which bottle water samples were taken to build a temperature and salinity profile, from which a value of 11034 meters was subsequently obtained . Although this result comes across wherever it comes to the Mariana Trench, modern experts are skeptical.

Further in 1960, aquanauts from Trieste reported measurements using an onboard pressure transducer of 10,911 meters , and the escort vessel, using explosives, measured a depth of 10,915 ± 20 meters. And already in 1976, with the help of an echo sounder, they received a value of 10933 ± 50 meters.

Where do all these ± 20 and 50 come from? A thoughtful reader most likely long ago realized what I was driving at - the speed of sound in water depends on temperature, salinity and pressure, i.e. from the density of the medium.

A temperature and salinity profile is a set of measurements with reference to depth.
And neither temperature, nor salinity can be measured remotely - you need to "put" a thermometer and conductivity meter at the right point in the ocean. It is advisable to make many measurements along the line as vertically as possible and through each meter.

Some profiles look like this:

Academician Ioffe , March 30, 2005.
Measurement site on Google maps.



American research vessel OCEANUS , April 10, 2010.
Measurement place on Google maps.
By the way, there is even a webcam on this oceanus . NOAA



vessel “RONALD H. BROWN” , October 20, 2001. Measurement place on Google maps

The history of measuring the deepest point is not poor and oddities

In 1992 (it would seem!), The participants of the Tokyo University expedition measured depths, like our compatriots in 1957, based on a constant speed of sound of 1,500 m / s, but for some reason did not collect temperature and salinity profiles. Instead, they corrected the data in the tables of 1980 (!) Year and got a value of 10933 m without indicating errors.

Already in 2002, an expedition aboard the Keirei vessel of the Japan Agency for Science and Technology for the Study of the Subsurface of the Sea (JAMSTEC) conducted research to search for the deepest depths using a rather advanced multi-beam echo sounder. They received a value of 10920 ± 5 m . They collected a large number of profiles, but the failure of the conductivity thermometer forced them to use profiles two years ago.
The Japanese were unlucky from time to time.

Later measurements

In 2008, researchers from the University of Hawaii on such a handsome Kilo-Moana



got a depth of 10903 meters using the multi-beam echo sounder EM 120 from Kongsberg Maritime.

In 2010, scientists from the University of New Hampshire on the USNS Sumner using the newer EM 122 model from the same Norwegians received a depth of 10,944 ± 40 m at a point (position on Google maps) .

In the end

The ambiguities in determining depths using echo sounders are consequences of the following factors:

• , , ( 1°1° 140 ), , , , . ..)
• — , — , , , , — .

Here I can want to touch only one of the factors - the profile of temperature and salinity, or, in our case is almost the same - the sound speed profile.
Just to visually evaluate: what is the effect?

We accept the assumption that our sound is almost like a ball from a ping-pong - it travels exclusively vertically, it bounces from the bottom entirely, the ship is motionless, the bottom is even. We measure time without errors. And the only thing that confuses us is the presence of a sound velocity profile.
How will it affect the measured depth?

In this case, our model can be described by a simple formula:

$$

$$s=\sum{v(t_i)\Delta t}$$

Where $$is the sound path$s$$$$v(t_i)$ is the speed of sound in the i-th time interval, the duration of which$$$\Delta t$ .

If we reduce$$$\Delta t$ (but we can’t) then it comes to the integral of school physics:

$$

$$s=\lim_{\Delta t\rightarrow 0}{\sum{v(t_i)\Delta t}}$$

$$

$$s=\int{v(t)dt}$$

Further, based on the measured propagation time of the sound (from the beginning of the radiation to the reception of the reflected signal) we need:

• at equal time intervals to approximately estimate the depth (to the nearest ten or two meters)
• interpolate (if necessary) from the existing profile the temperature and salinity for the estimated depth
• on it to calculate the speed of sound, and accordingly the path that the sound has traveled at this depth for a time interval.

For these (and other) purposes, I filmed the library , about which I spoke in the first part of the article . At the moment, it is implemented in C / C # / Rust / Matlab / Octave / JavaScript.

The speed of sound is calculated according to the formula of Chen and Millero . I like it because there the pressure goes, which is measured directly, and not the depth, as in other models. Plus, the range of parameters for this model covers almost all reasonable cases.

For example, for the second profile that is obtained at this pointApril 10, 2010, the difference between the depth obtained by the standard value of the speed of sound and the depth obtained by the above calculation with a propagation time of 5 seconds (round trip) is 18 meters: 3750 versus 3768.3 meters, and for 6 seconds the difference increases to 32 meters.
Unfortunately, I do not have a profile from the Mariana Trench, and in general I have not yet come across any profile deeper than 6000 meters. But if we assume that after 4-5 km of depth the parameters change slightly and the speed of sound mainly changes due to pressure, then it turns out that for the discussed depths the difference is about 420 meters, and the time from the moment the signal is emitted by the echo sounder to the reception of reflection is more 14 seconds

As demonstration materials are available:

an online calculator in which you can manually enter a profile or use one of the three, so to speak, hard-coded.

Since I really don’t understand anything in JavaScript, it was easier for me to do visualization in C # through the sleeves . I put the project on GitHub .
I know that everyone knows, but experience shows that it’s better to give a direct link to Release.

The application window looks like this:


By default, there is a propagation time of 5 seconds and some kind of profile from the North Pacific with only 13 points.

On the right there are 4 columns, in each of which (after pressing the ANIMATION button of course), the sound begins to travel at different speeds:

• in the first - 1500 m / s (standard value for fresh water),
• — , ,
• — ,
• —

The display is started on MMTimer with a period of 0.01 s, and the simulation works with the same period.

In the PROFILE menu, you can choose one of three demo profiles (there are few points in them), you can also download several profiles torn by me from the World Ocean Database which NOAA carefully collects .
These profiles are in the form of CSV and, among other things, contain information about the place of measurement, time, country, managing institute and the vessel on which it was made. I wrote in more detail about this in the article “Who and how explored the oceans: disassembling NOAA bases” .

Absolutely for the lazy (I repent, I am the same) I put together GIF animation, but GIF is displayed differently everywhere, and the “full presence effect” will not work:



When writing a historical review about the study of the Mariana Trench, I used the article by James Gardner and his associates. I highly recommend for those interested. There, difficulties are very well described when measuring, it would seem, such a "simple" thing as depth.

PS

I want to thank all those who voted in the previous article . For this one to appear, 109 votes were cast - guys, this is for you! Those two who were against - sorry, I listened to the majority opinion.

PPS

Traditionally, I will sincerely (for me this is not an empty word) I am grateful for the error messages, constructive criticism, interesting questions and discussions.