I need a small clarification regarding finding out kappa parameter. From an engineering point of view, the value of kappa parameter can be calculated from the slope of Fourier amplitude spectrum (log Y scale), where the decay starts after fmax. But, fmax value changes for every Fourier amplitude spectrum obtained from ground motion. One needs to fix the frequencies to calculate slope of Fourier amplitude spectrum. I referred Anderson, 1984 paper on determination of kappa value for California region. They have considered 2-12 Hz as a range for slope, which is not valid for all cases. Is there any basis to fix this frequency range. I will be very much thankful if anyone suggest literature on it.
Hi
usually kappa is determined for each record, and then an average will state the final value. Slopes are manually picked with fmax visually estimated .
There are a number of paper that adresses this issue:
Analysis of the Origins of (Kappa) to Compute Hard Rock to Rock Adjustment Factors for GMPEs- Bssa, vol. 101, issue 6, pp. 2926-2941
A k Model for Mainland France, Pure Appl. Geophys. 167 (2010), 1303–1315
A Comparison of Spectral Parameter Kappa from Small and Moderate Earthquakes Using Southern California ANZA Seismic Network Data, BSSA, Vol. 102, No. 1, pp. 284–300, February 2012, doi: 10.1785/0120100309
and one of my paper:
Chapter A Finite–Fault Modeling of the 1755 Lisbon Earthquake Sources
This is a recent, good review paper on Kappa: http://srl.geoscienceworld.org/content/85/1/135.extract
Dr Chenna:
Apart from our review paper, you can also have a look at some considerations here: https://www.researchgate.net/publication/236462045_A_Study_on_the_Variability_of_Kappa_%28%29_in_a_Borehole_Implications_of_the_Computation_Process
Apart from the 'engineering' point of view in measuring kappa, there is also a 'seismological' point of view, related to the source corner frequency - and that is sometimes hard to distinguish from fmax.
Regards
Article A Study on the Variability of Kappa ( ) in a Borehole: Impli...
Rajaram Chenna 0.86
International Institute of Information Technology, Hyderabad
How can I fix the range of frequencies to determine kappa parameter from Fourier Amplitude Spectrum?
I need a small clarification regarding finding out kappa parameter. From an engineering point of view, the value of kappa parameter can be calculated from the slope of Fourier amplitude spectrum (log Y scale), where the decay starts after fmax. But, fmax value changes for every Fourier amplitude spectrum obtained from ground motion. One needs to fix the frequencies to calculate slope of Fourier amplitude spectrum. I referred Anderson, 1984 paper on determination of kappa value for California region. They have considered 2-12 Hz as a range for slope, which is not valid for all cases. Is there any basis to fix this frequency range. I will be very much thankful if anyone suggest literature on it.
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Dear Rajaram,
This is really not a simple question because kappa estimates may and often do depend on the following factors
- selected frequency band,
- non-linearity of log FS vs f trend in this band
- interfering site effects (resonance and like, not related to attenuation)
- event spectrum ("source-controlled fmax" and like).
This list is not complete; the listed ones seem to be the key ones.
I would recommend the following line: (1) select a trial fixed band sufficiently above second corner frequency, e.g. 3-10 or 7-15 or 10-20 Hz, and collect data that all have good S/N ratio over this entire band [therefore you must determine in advance S/N for each record]; (2) find kappas (checking absence of non-linearity), and (3) check distance dependence. If it is well seen, extrapolation to zero distance may result in a stable estimate (if you are lucky). However this estimate may be biased by site effects. If oppositely the distance dependence shows strong scatter, source spectral effects may be significant, and you are no so lucky.
Be ready to get another value of kappa for another selected band, this is normal. E.g. you can notice clear frequency-band dependence of FS(f) slope and thus kappa in data shown in figures 8 and 12 of Anderson&Hough 1984
The above "small clarification" reflects my personal experience, and I am responsible for this advice.
Best regards
A.Gusev
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