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:

s(t) = a

_{0}+ Σ_{k=1,N}a_{k}cos(2πkF_{0}t) s(t) + b_{k}sin( 2πkF_{0 }t) s(t)the coefficients themselves are defined by:

a

_{0}= = <s(t)> = average, or : a_{0}= for discrete time series, with a sampling period of Dt .a

_{k}= 2 / T Σ_{i}cos(2πkF_{0}t) s(i) Dtb

_{k}= 2/ T Σ_{i}sin(2πkF_{0}t) s(i) DtIn practice a P wave can be described with 250 coefficients of Fourier; example:

Every periodic signal can be decomposed in an orthogonal basis of sine and cosine function in function of the fundamental frequency F0:

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.