 Solution

For a wide horizontal Bouguer slab replacing surrounding basement, use the density contrast $\Delta \rho ={\rho }_{\mathrm{sed}}-{\rho }_{\mathrm{base}}$, not the absolute sediment density:Take downward attraction as positive. The negative anomaly therefore requires $\Delta \rho <0$. With $\Delta g=-40\mathrm{mGal}=-4.0\times 10^{-4}\mathrm{m}{\mathrm{s}}^{-2}$, $h=3000\mathrm{m}$, and $G=6.67430\times 10^{-11}{\mathrm{m}}^3\mathrm{k}{\mathrm{g}}^{-1}{\mathrm{s}}^{-2}$,soThis is the requested Bouguer slab approximation: a flat observation surface, laterally infinite constant-thickness material, uniform average geophysical density contrast, and a regional anomaly already removed. The actual basin in Figure 1 narrows downwards and is finite. For a fixed maximum thickness, finite width reduces the central anomaly magnitude, so this calculation can underestimate the true magnitude of the average geophysical density contrast. It does not establish a unique basement density without the geometrical assumption.