Viscoelastic wave test function

[barnhillec]

Hello,

I am writing up (for some other students) our lab's inversion method for viscoelastic media. I want to use some test functions for simple illustrations, side by side with the actual inverted images.

I can write simple test functions for elastic waves that come out perfectly -- all storage no loss -- along the lines of v(i,j) = cos(i+j). I can't figure out a good test function for something viscoelastic however.

Can anyone suggest a test function that would produce a result with storage and loss. Or if this is not so simple to do, can anyone say anything about why? Obviously I've got a gap here.

Many thanks,
Eric

 

[Achy47]

Hello Eric,

Thank you for reaching out to our scientific community for help with your lab's inversion method for viscoelastic media. I can understand your struggle in finding a suitable test function for this type of media. Viscoelastic materials are unique in that they exhibit both elastic and viscous behavior, which can make it challenging to find a simple test function that accurately captures these properties.

One approach you can take is to use a combination of sine and cosine functions in your test function. For example, you can try v(i,j) = sin(i) + cos(j) to simulate both storage and loss components. Another option is to use a Gaussian function, which can also represent both elastic and viscous behavior.

However, it is important to note that these test functions may not fully capture the complexity of viscoelastic media. The behavior of these materials is highly dependent on the frequency and amplitude of the input signal, as well as the material properties such as viscosity and elasticity. Therefore, it is important to use a range of test functions and carefully analyze the inverted images to ensure they are accurately representing the viscoelastic properties.

I hope this helps you in your research and good luck with your lab's inversion method.



Scientist in Viscoelastic Materials