Creating a phase-velocity diagram with matlab

[Bugeye]

Homework Statement

I'm given a time vector and y-values of a wave. The plot looks like this:

Homework Equations

I have been calculating the velocity using this equation:
$c=\frac{ω Δx}{Δ\Phi}$
Where $\Delta\Phi$ is the phase change between the phase that you calculate using the Fourier transform and Δx is the space between the sensors that collected the data

The Attempt at a Solution

function [ f velocities ] = dCurve( data, geophoneSpacing, freqLimit )
% Makes the dispersion curve given the raw geophone data, sampling frequency
% and geophone spacing. The resulting curve is plotted.


%Split up the data into useful variables.
%This can be ignored for the most part, this is just reformatting the data
%The results are the following variables:
%t-> the time vector for the equations
%sensorData-> a matrix that has the same number of columns as t and a row for each sensor's raw values
%sensorCount -> The # of sensors
%Fs -> the sampling frequency
datasize=size(data);
t=data(2:datasize(1));
sensorData=data(2:datasize(1),2:datasize(2))';
sensorCount=size(sensorData);
sensorCount=sensorCount(1);
Fs=1/(t(2)-t(1));

%Get the Fourier transform
for i=1:sensorCount
    [f, rawFft(i,:)]=dfft(Fs, sensorData(i,:));
end
absFft=abs(rawFft);
reFft=real(rawFft);
imFft=imag(rawFft);

%Get the phase between each sensor
for i=1:sensorCount
    phi(i,:)=angle(rawFft(i,:));
end

%Get the phase change between each sensor
for i=1:(sensorCount-1) % Go through each pair of sensors. The pairs consist of sensors i and i+1
    dPhi(i,:)=phi(i,:)-phi(i+1,:);
    dPhi=dPhi-(2*pi*(dPhi>pi));
    dPhi=dPhi+(2*pi*(dPhi<-pi));
end

%Calculate velocity
for i=1:(sensorCount-1)
    w=2*pi()*f;
    c(i,:)=(w.*geophoneSpacing)./(dPhi(i,:));
end

f=f(f<=freqLimit);
velocities=c(f<=freqLimit);

end

dfft is a function that creates a fft and a domain and returns it. The thing works fine if both of the equations are exactly the same except shifted a bit. For example, this works. Well, except for that dip at the end:
The initial functions:

The result after running them through the script

Unfortunately, it doesn't work as well as I would like. For example, those sine waves from above don't work. I get the following results:
Original:

Result:

I'm not sure if I'm using the wrong equations, if my code is wrong, or if I'm interpreting the graphs wrong. Can anyone help?

 

[mighty2000]

Thank you for sharing your work and concerns. It seems like you have put a lot of effort into your code and your analysis of the data. From what I can see, it seems like there may be a few issues that could be causing the discrepancies in your results.

Firstly, it would be helpful to have more information about the data you are working with, such as the type of wave, the frequency range, and the geophone spacing. This could help us better understand the behavior of the wave and potentially identify any issues with your calculations.

Secondly, it seems like you are using a Fourier transform to calculate the phase change between sensors. While this can be a useful tool, it may not be the most accurate method for calculating phase differences between closely spaced sensors. You may want to consider using a cross-correlation method instead, which can provide more precise results for small phase shifts.

Lastly, it is important to double check your code and make sure all the equations and calculations are correct. Sometimes a small mistake in the code can lead to significant errors in the results. It may also be helpful to compare your results with other methods or data sets to verify the accuracy of your calculations.

I hope this helps and good luck with your research!