= Vibroseis correlation
{c}
Let a linear Earth response $h$ be recorded using a known source sweep $s$, giving $d=s*h+n$. Cross-correlating the record with the sweep yields
$$
c(\tau)=\int d(t)s(t-\tau)\,dt=(h*R_{ss})(\tau)+R_{ns}(\tau).
$$
Thus a compact sweep <autocorrelation> $R_{ss}$ produces pulse-compressed arrival wavelets, while unrelated noise has a smaller coherent response. The <Fourier transform> of the result is $H(\omega)|S(\omega)|^2+N(\omega)\overline{S(\omega)}$. Correlation is a matched-filter operation, not an exact inversion of missing source <frequencies>. Spectral shaping or stabilized deconvolution can further adjust the wavelet within the measured bandwidth.<Geophysical Survey Summary Report, Section 3: Geophysical Testing Methodology>[Vibratory-source explanation: correlating the known sweep with geophone measurements]{ref}
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