When you use a "quite simple" DSP software in your computer audio adapter you can see clearly signals impossible, repeat, impossible to hear.
This is true, and quite amazing results have been produced. But... you cannot repeal the laws of physics.
DSP can improve the effective signal-to-noise ratio. For some kinds of signals (coherent ones), it can do this by a lot. The same principle that allows undersea submarines (shallow) to hear ELF radio waves is at work: integration of the signals over time. But... a submerged sub may have to integrate a (radio) signal for maybe one minute for every bit of information - a data rate of less than .1 bps! This same technique can be used in sonar - a maritime target like a sub hopefully has some relatively continuous signals (prop cavitation, or a pump resonance) which can be integrated for a long time.
However.... integration has the following limitation: signals decrease exponentially with distance, while integration only improves the SNR linearly.
This means that if the signal has gone down by 100 (which is only 20 decibels - dB), you have to integrate 100 times as long. With this signal going to 5dB per kilometer ( as opposed to low frequencies which go down at .001 dB per kilometer), it's clear that, while DSP can extend the range, it can only extend it by a few kliometers.
It helps if the signal is designed to be integrated, which these pingers are not.
There are other tricks in the DSP arsenal, but there are ultimate limits. I could see the "specified" range exceeded by a few to maybe 10 km.
A nice calculator for sound propagation attenuation is at
Calculation of absorption of sound in seawater.