This menu calls the following
PSD Linear scale :representation in linear scale of the square_root of PSD (Power Spectral Density). The unit is function of those of signal: if the signal is in velocity in µm.s, the unit will be : sqrt((µm/s)² .s² / s) = µm/sqrt(s) = µm .sqrt(Hz) ; if the signal is in displacement in µm, the unit will be : sqrt(µm² .s² / s) = µm.sqrt(s) = µm /sqrt(Hz)
PSD Log scale: the same, but in log-log scale.
FFT Linear scale: it is simply the modulus of the FFT; units are (SIGNAL_UNIT).s
FFT log scale: he same, but in log-log scale.
Dirac: just a non null value in an array composed of zeros ! Useful for testing the filters responses.
Constant: a simple constant value: it useful for testing the taper functions.
Sinusoid: a pure sinusoid of +100.0 units (0 to peak); . Useful also for testing the filters attenuation.
Hilbert: the envelop of a signal calculated with the Hilbert transform.
Time-Frequency: the name is explicit : a time-frequency representation (called also sonagram).
AutoCorr : the autocorrelation of a given signal: useful for computation of signal energy, and its dominant frequency.
Q_remove: the anelastic attenuation is a function of the Q factor (the amount of energy loss by a signal at each wave length). It is given in the frequency domain by:
Attenuation(f) = exp(- p f D / (Q U) ); where D is distance in km, U the group velocity in km/s, and f the frequency; the anelastic attenuation is simply obtained by the product of signal spectrum by the attenuation function: s(f).Attenuation(f); and to remove anelastic effect, one must divide by Attenuation(f) : s(f)/Attenuation(f)
Coef Fourier:: the Fourier coefficients series:
Every periodic signal can be decomposed in an orthogonal basis of sine and cosine function in function of the fundamental frequency F0:
s(t) = a0 + Σk=1,N ak cos(2πkF0 t) s(t) + bk sin( 2πkF0 t) s(t)
the coefficients themselves are defined by:
a0 = = <s(t)> = average, or : a0 = for discrete time series, with a sampling period of Dt .
ak = 2 / T Σi cos(2πkF0 t) s(i) Dt
bk = 2/ T Σi sin(2πkF0 t) s(i) Dt
In practice a P wave can be described with 250 coefficients of Fourier; example:
on left, P wave modelized with Fourier series of 200 coefficients; on right, the recorded P wave in COCO ( LHZ), for Sumatra 12 sept. 2007.
Special: FFT_NO_TAPER Linear scale: this menu computes the modulus of FFT without any taper function; it is useful for testing the response of some filters.
Special: FFT_NO_TAPER Log-log scale: the same in log-log
taper: Hanning : this submenu applies the Hanning taper function: g(t)=0.5 (1 – cos(2pit/T))
taper Hamming applies: g(t)=0.54 – 0.46 cos(2pit/T))
taper Blackman: g(t) = 0.42 -0.5 (cos(2pi t/ T) + 0.08 cos(4pi t/T)
Hanning 25%: this taper function gives a wider plateau equal to 1 than the previous ones : it equal to a cos function on 25% of the total leghth of the time window, on 25% at the end; it is equal to 1.0 between. It seems to give the best reliable spectral amplitude estimation.
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