Vibroseis correlation

Let a linear Earth response $h$ be recorded using a known source sweep $s$, giving $d=s\ast h+n$. Cross-correlating the record with the sweep yieldsThus 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.^[ref]