Data analysis of the unsteadily accelerating GPS and seismic records at Campi Flegrei caldera from 2000 to 2020.

Since the annual rate F' displays an increasing trend (Fig. 4 a,b) we consider the rate change F"(t) instead, and by ∀k in N we define the Fourier coefficients: Φ k , F ′ = [ φ 1 k 2 + φ 2 k 2 ] 1 / 2 / k , φ 1 k = sin k · F ′′ , φ 2 k = cos k F ′′ , where · is the integral product over the interval [t 0 , t 0 + Δt], and ∀t in the interval we have: sin k t = sin 2 π kt / Δ t , cos k t = cos 2 π kt / Δ t .

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Since the GPS rate changes lack of a significant trend, we build the Fourier analysis on these functions, as described in “ Fourier spectrum of the GPS data in 2000 – 2020 ”.

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