Frequency dependent quality factor

[anniejerk]

Hi,
I really like how easy this code is to use, great work! I have a quick question:
With the current version of the code, is it possible to include a frequency-dependent quality factor in my estimations?

Best wishes,
Annie

[claudiodsf]

Dear Annie,
Thank you for your positive feedback!

At the moment, it’s not possible to include a frequency-dependent quality factor directly.

Could you please specify your objective so I can better understand what you’d like to achieve?

Would you like to invert for a parametric form of a frequency-dependent quality factor, or would you prefer to fix this form so that the code does not invert for attenuation?

Cheers,
Claudio

[anniejerk]

You are right! The last one is what I want! Thanks again :)

[claudiodsf]

Ok, and, in your case, $f_0$ = 1 Hz, right?

[anniejerk]

yes. Thats correct!

[anniejerk]

[anniejerk]

[krisvanneste]

Claudio,

I haven't looked in detail, but I'm not sure this will be easy.
Of course a new configuration parameter can be added to define the frequency exponent (with default 0) related to Qo_min_max, but this is converted into tstar_min and tstar_max, defining the inversion bounds for tstar. I think it will be necessary to switch back from tstar to Q (including the frequency exponent) inside the inversion. Not easy because the entire inversion is centered around tstar...

I'm curious if you have an idea already how to solve this!

[claudiodsf]

You're right.

My idea was to modify both functions in ssp_spectral_model.py to take care of cases where t_star is fixed to a certain value or to a certain function. This will remove the need to use very close bounds to simulate a fixed t_star.

There are certainly modifications to do also in the ouput files and plots.

I'll try something, probably next week 😉

[krisvanneste]

OK, let me know if you need further input.

[claudiodsf]

@anniejerk @krisvanneste

I have a first implementation for this feature, currently in a separate branch (@krisvanneste, I'll make a PR later today).

@anniejerk : could you please test it and provide some feedback (e.g., before/after figures).

To install this version:

pip install git+https://github.com/SeismicSource/sourcespec.git@Q_model

Then, you should update your config file:

source_spec -u source_spec.conf

Finally, look at the following section in the config file:

# Prior knowledge of the attenuation model for your region can be specified
# through Q_model as either a fixed value or a frequency-dependent function.
# Use 'f' to represent frequency in the expression.
# The frequency dependence is commonly expressed as:
#   Q_model = Qo * (f/fo)**alpha
# where:
#   - Qo is the quality factor at the reference frequency fo
#   - fo is the reference frequency (typically 1 Hz), to keep Q_model unitless
#   - alpha is the frequency exponent
# Any functional form can be used, provided Q_model remains unitless.
# When Q_model is specified, t_star will not be inverted and all t_star-related
# inversion parameters above will be ignored.
# Examples:
#   Fixed value:
#       Q_model = 500
#   Frequency-dependent (assuming fo=1 Hz):
#       Q_model = 529 * f**0.42
Q_model = None

Let me know!

[anniejerk]

Thank you so much! I will run som tests.

[anniejerk]

@claudiodsf it is running smoothly and giving reasonable results. I will test more events on monday!

[claudiodsf]

Great! Don't forget to post some figure 😉