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?

 

[sardar]

Hello,

Thank you for your question about travel-time and the use of the ray model in calculating it. The ray model is commonly used in geophysics and seismology to approximate the travel-time of seismic waves, so it is a valid approach to consider.

In order to calculate the travel-time using the ray model, you will need to know the velocity of sound at different points along the path from the source to the receiver. This information can be obtained from a sound speed profile, which is a map of the variation of sound velocity with depth or distance.

Since you mention that the variation of sound velocity is not small in your situation, it is important to consider the effects of refraction and reflection on the travel-time calculation. In areas with large variations in sound velocity, these effects can significantly impact the ray paths and travel-times. Therefore, it may be necessary to use more advanced methods, such as numerical modeling or ray tracing, to accurately calculate the travel-time in your specific scenario.

I recommend consulting with experts in geophysics or seismology to discuss your specific problem and determine the best approach for calculating travel-time in your situation. Additionally, further research and reading on ray tracing and its application to non-uniform velocity fields may also be helpful.

I hope this information helps. Best of luck with your research.