= Solution
At each source position, couple the vibrator to the ground, transmit a known <frequency> sweep $s(t)$ and record the ground response on synchronized <geophones>. Record a pilot or measured source-force reference and sufficient listening time for delayed arrivals. Repeat sweeps where beneficial and retain geometry and timing information.
If the Earth’s impulse response is $h(t)$, a linear model is $d=s*h+n$. <Vibroseis correlation> cross-correlates the record with the known sweep:
$$
c(\tau)=\int d(t)s(t-\tau)\,dt=(h*R_{ss})(\tau)+R_{ns}(\tau).
$$
The sweep’s <autocorrelation> $R_{ss}$ is a compact, approximately zero-phase wavelet, so the long chirp is compressed into identifiable delayed events. In the <frequency> domain this multiplies $D(\omega)$ by $\overline{S(\omega)}$, yielding $H(\omega)|S(\omega)|^2$ plus noise. It is \b[pulse compression, not an exact recovery of $h$ at <frequencies> never transmitted]. Spectral shaping or stabilized deconvolution can further compensate the finite source bandwidth and sidelobes.<Geophysical Survey Summary Report, Section 3: Geophysical Testing Methodology>[Vibratory sources: known input sweep correlated with geophone records]{ref}
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