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Instantaneous frequency law.
We further consider that the b-value of the Gutenberg-Richter's magnitude frequency law is location dependent.
The modulation features are extracted from the instantaneous phase and instantaneous frequency law (IFL) curve which is calculated according to (14) and (17).
Moreover, a time-frequency tracking algorithm based on the high-order ambiguity function (HAF) is employed to reconstruct the instantaneous frequency law of the micro-Doppler [16, 17].
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Signals characterized with multiple components having different frequency laws leave distinct features when examined in the time-frequency domain [5].
Various time-frequency distributions have been used for the analysis of noisy nonstationary signals with different instantaneous frequency laws [11, 12].
On the other hand, the phase-analysis method needs neither iterative algorithm in each window nor filtering for estimated instantaneous frequency laws.
After the initial reconstruction, the instantaneous frequency laws must be filtered in order to mitigate the possible gaps that may appear at the transitions between estimation windows [17].
The HAF-based method tracks the instantaneous frequency laws by dividing the range line of the vibrating target in nonoverlapping windows and locally approximating the phase with a polynomial expression.
Together with the Gutenberg-Richter's magnitude-frequency law with location-dependent b-values, the elaborated model is applied for short-term, intermediate-term and long-term forecasting of baseline seismic activity.
The bottom panel shows the frequency modulation law of this signal.
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