Question about travel-time (or time-of-flight)

[huangchao]

Hi, everyone,

I have a question about the travel-time of sound: If the distribution of speed-of-sound is known (the variation of the speed-of-sound map is NOT small), how can I compute the travel-time from a source to a receiver? Here I want to use the ray model instead of the wave model.

I've read some papers about this, but they all require small variation of speed-of-sound, which is not my situation. So I am wondering if someone can give me some suggestions. Thanks in advance!

 

[HallsofIvy]

If speed of sound is varying, and you do NOT know how it is varying, then you cannot calculuate that.

If you do know the speed of sound as a function of x, say v= f(x), perhaps because the speed of sound varies with air pressure and you know how the pressure varies with x, then you need to solve the differential equation, dx/dt= v= f(x) which you can convert to dx/f(x)= dt and integrate.

 

[huangchao]

Hi, HallsofIvy,

This is the exact bottleneck. I only know the speed-of-sound on discrete points or grids, but the analytical form of the speed-of-sound map is not available, so do you think if the travel-time can be computed numerically in this case? Thanks!

 

[Redbelly98]

If immediately adjacent grid points have a large difference in the sound speed, perhaps you need to use a finer grid.

Otherwise, why not linearly interpolate the speed?