4
$\begingroup$

i want to know how i get the wavelength/frequency of a seismic wave, if i only have a gaussian source and the velocity (c = 4000m/s) of a medium given.

e.g. for a ricker wavelet it would be easy to get the central frequency and max frequency of the source to compute the wavelength by c/f, but i have some issues with the gaussian and unfortunately only signals of a gaussian source.

Let's assume my source time function in time domain looks like this:

source = 1/(2* np.pi * 17.**2) * np.exp( - (t-100)**2 / (2* 17.**2))

So a gaussian with variance of 17 squared and shifted to the right. In the frequency domain it will be centered around zero and i dont really get a maximum frequency as well. Is there a way to find these?

$\endgroup$
  • $\begingroup$ It is correct that the Gaussian wavelet has its peak frequency at zero frequency (see in uhohs answer below, for f=0 you get the largest G). For the maximum frequency you'll have to come up with a criterion that defines it for you. For example, the point up to which you capture 95% of the spectrum. With uhohs answer and a wavelet of type source=[scaling_factor] * exp( - (t-100)^2/(2*17^2) ), I think you can find an analytical expression for this. ( >> sqrt( log(0.05) / (-2*pi^2*17^2 ) ) .) $\endgroup$ – Erik Jul 14 at 6:57
4
$\begingroup$

The Fourier transform of a Gaussian is a Gaussian.

If your signal is given by

$$g(t)=\frac{1}{\sqrt{2 \pi \sigma^2}} \exp\left( -\frac{(t-t_0)^2}{2 \sigma^2}\right)$$

then your frequency spectrum is

$$G(f) = \exp(-2 \pi^2 \sigma^2 f^2),$$

where f is the frequency ($2 \pi \omega).$

I'l let you do the substitution with your particular numbers. Enjoy!

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.