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

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Discussion Overview

The discussion centers around the computation of travel-time for sound in a medium where the speed of sound varies significantly. Participants explore methods for calculating travel-time using a ray model, particularly in scenarios where the speed-of-sound distribution is known only at discrete points rather than as a continuous function.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions how to compute travel-time when the speed-of-sound varies significantly and is only known at discrete points.
  • Another participant suggests that if the speed of sound varies but is known as a function of position, it can be computed by solving a differential equation.
  • A later reply highlights the challenge of having large differences in sound speed between adjacent grid points and suggests using a finer grid for more accurate calculations.
  • Another suggestion is to consider linear interpolation between the known discrete points to estimate the speed of sound for travel-time calculations.

Areas of Agreement / Disagreement

Participants express differing views on the feasibility of calculating travel-time under the given conditions, with no consensus reached on the best approach. Some argue for numerical methods, while others propose interpolation techniques.

Contextual Notes

The discussion acknowledges limitations related to the lack of an analytical form for the speed-of-sound map and the potential impact of large variations in speed between grid points on the accuracy of travel-time calculations.

huangchao
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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!
 
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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.
 
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!
 
Last edited:
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?
 

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