Past exam of the year 2 of the earth sciences (geology) course of the University of Oxford / 2025 / Paper 3 / 1 / c

The P wave source is normally the more useful depth source for the end members and for the stated approximately 50% gas case, because the predicted $|R_p|$ exceeds $|R_s|$, making the reservoir-top arrival easier to identify, assuming comparable source and recording quality. For a horizontal reflector and vertical two-way travel time $t$ entirely through the homogeneous cap rock,or $h=V_{s1}{t}_s/2=300t_s\mathrm{m}$ for an identified S wave arrival, with times in seconds. The reservoir's own wave speed is not the overburden wave speed used in this conversion. Nonzero-offset data require moveout correction and an appropriate overburden velocity model; no numerical depth can be obtained without a measured time.

At approximately 50% gas, Figure 1 gives $\rho \simeq 1.5\mathrm{g}\mathrm{c}{\mathrm{m}}^{-3}$, $V_p\simeq 1.05\mathrm{km}{\mathrm{s}}^{-1}$, and $V_s\simeq 0.62$–$0.63\mathrm{km}{\mathrm{s}}^{-1}$. ThusThe S wave reflector is then weak because its impedance is nearly matched to the cap rock. An exact impedance match, ${\rho }_2{V}_{s2}={\rho }_1{V}_{s1}$, gives $R_s=0$: a reservoir top can exist without producing an observable normal-incidence S wave reflection. Rounding the 50% $V_s$ to $0.60$ would suggest exactly that cancellation, but the plotted line sits slightly higher. The continuous $Z_s$ curve crosses the cap-rock value at a somewhat greater saturation; the coarse figure does not justify a precise percentage.

There is also a smaller-saturation P wave impedance match: $R_p$ changes sign between zero and modest gas saturation, so it must pass through zero. Thus neither source guarantees a detectable reflector at every saturation. Joint P wave and S wave observations help distinguish a weak impedance contrast from an absent reservoir; a slower S wave speed alone is no reason to prefer it when its reflected amplitude is near zero.