b (source code)
= b
{scope}
For incidence from cap rock (1) into reservoir (2), use the conventional normal-incidence stress-amplitude <reflection coefficient>
$$
R_j=\frac{Z_{j2}-Z_{j1}}{Z_{j2}+Z_{j1}},\qquad Z_{pj}=\rho_jV_{pj},\quad Z_{sj}=\rho_jV_{sj}.
$$
Here <acoustic impedance> is the <P wave> impedance; $\rho V_s$ is the corresponding <shear-wave impedance>. Positive $R$ preserves the chosen stress-wave <seismic reflection polarity>; negative $R$ reverses it. These are amplitude coefficients, not reflected <energy> fractions. At normal incidence in the ideal isotropic model there is no P-to-S <mode conversion>. The cap-rock impedances are
$$
Z_{p1}=2.25\times10^6,\qquad Z_{s1}=0.900\times10^6\quad\mathrm{kg\,m^{-2}\,s^{-1}}.
$$
The following are \b[approximate readings of the supplied Figure 1 PNG], checked against the matching source PDF, rather than exact tabulated parameters. At zero gas, use $\rho\simeq1.75\ \mathrm{g\,cm^{-3}}$, $V_p\simeq1.75\ \mathrm{km\,s^{-1}}$, and $V_s\simeq0.60\ \mathrm{km\,s^{-1}}$; at full gas use $\rho\simeq1.25\ \mathrm{g\,cm^{-3}}$, $V_p\simeq1.15\ \mathrm{km\,s^{-1}}$, and $V_s\simeq0.65\ \mathrm{km\,s^{-1}}$. The left-hand $V_p$ endpoint is crowded against the axis and the <density> curve; readings differing by roughly $0.05$ in the plotted units are reasonable. The resulting coefficients deserve about two significant figures, not the apparent precision of the intermediate arithmetic.
Both end members change <seismic reflection polarity>, but the <P wave> change is much larger: approximately $+0.15$ to $-0.22$, compared with $+0.08$ to $-0.05$ for <S waves>. Thus a calibrated <P wave> survey is better for distinguishing these two saturation end members and should give a stronger reflection from the fully gas-filled reservoir. A negative <P wave> reflection relative to the water-filled prediction is a useful gas indicator in this stipulated model. In a real <seismic reflection survey>, lithology, <porosity>, effective <pressure>, and <seismic wavelet> phase also affect the response, so a bright or reversed reflection alone does not prove the presence of <gas>.
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