= Solution
Let a positive incident stress wavelet be $w(t)$ and measure return times relative to a receiver just above the reservoir. The top interface gives a negative P return of amplitude $-3/19$ and no basal P return. For a separately generated and measured S wave, the top return is also negative, $-3/19$, while the basal return is positive, $1/9$ at the lower interface.
If $h$ is reservoir thickness, the basal return arrives $2h/V_{P2}$ or $2h/V_{S2}$ after the top return; no numerical $h$ is supplied. Including downward and upward transmission through the top boundary, but ignoring <seismic attenuation>, spreading and <seismic multiples>, its observed S-wave amplitude is
$$
T_{12}R_{23}T_{21}=(1-R_{12}^2)R_{23}=\frac{352}{361}\frac19\simeq+0.10834.
$$
Thus \b[the synthetic S trace has an earlier negative wavelet and a later, smaller positive wavelet; the synthetic P trace has only the earlier negative wavelet]. The figure chooses $h=250\ \mathrm m$ solely to separate the pulses visually. Receiver electronics or a displacement convention can reverse the displayed trace polarity, so the convention must accompany the sketch.
A marine <hydrophone> streamer with a purely normal-incidence P source does not directly record the hypothetical S trace. A seabed multicomponent receiver and suitable S excitation or oblique-incidence <seismic mode conversion> are required. This distinguishes the calculated solid-layer response from what a particular acquisition system can measure.
\Image[/past-exam-of-the-year-2-of-the-earth-sciences-geology-course-of-the-university-of-oxford/2023/paper-1-reflection-signals.png]
{title=Idealized normal-incidence P and S reflection wavelets, including transmission through the reservoir top}
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