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The gravity anomaly section distinguishes free-air correction, simple Bouguer slab correction and complete terrain reduction.

A geophysical gravitational acceleration unit: $1\mathrm{mGal}=10^{-5}\mathrm{m}{\mathrm{s}}^{-2}$. It is used for small gravity anomalies and should be converted before substitution into SI forms of the Bouguer slab formula.

The positive centers in the supplied maps are examples of lunar mascons, especially associated with large impact basins. An empty excavation by itself removes mass and would not explain a positive central anomaly. Basin formation can thin the low-density lunar crust and raise denser lunar mantle beneath the floor; impact melting, collapse and later cooling can also create dense material and lock in a mass excess. Where a basin was later flooded, dense mare basalt adds another contribution. Mare infill is therefore one possible contributor, not a necessary explanation of every mascon.^[ref]

The difference between the maps is the modeled topographic contribution. On a common reference surface, write schematicallyThe free-air gravity anomaly retains relief-related attraction. Rims, excavated floors and central peaks therefore contribute fine structure. The Bouguer gravity anomaly removes the attraction predicted from the measured topography at an assumed crustal density, making internal density and interface structure more apparent. A low basin floor has a negative topographic contribution; subtracting it can enhance an underlying positive central anomaly. Removing a positive rim contribution can weaken a rim high. The supplied lower map is correspondingly smoother at short wavelengths and shows prominent residual basin centers and surrounding rings. This is a change of gravity reduction, not a physical change of the craters.^[ref]

For scale, a Bouguer slab approximation gives $\Delta g\simeq 2\pi G\Delta \rho d$. A $5$ km layer with geophysical density contrast $300\mathrm{kg}{\mathrm{m}}^{-3}$ produces about $63$ mGal above an ideal infinite slab. Actual basin geometry, burial, porosity and mantle uplift require a finite three-dimensional model. Smaller craters can have central lows, damaged porous interiors or more complex rings; the maps do not imply that every crater has a positive anomaly or that positive anomalies measure basalt thickness uniquely.

A gravity anomaly is measured gravity minus a specified reference gravity after the stated reductions. A Bouguer gravity anomaly aims to remove the predictable effects of latitude, observation elevation and surrounding topographic mass, so residual variations can be related to subsurface geophysical density contrasts.

Measure relative gravity with a calibrated gravimeter at stations across and beyond the crater, and survey station positions and elevations accurately, preferably with GNSS tied to a reference datum. Repeat a base station through the day to estimate instrument drift and tie the traverse to a gravity datum. Record station times, because tidal and drift corrections are time dependent.

Apply instrument scale and drift corrections, solid-Earth and relevant ocean-loading tidal corrections, latitude/reference-ellipsoid gravity subtraction, the free-air correction, the Bouguer slab correction for material between station and datum, and a terrain correction for departures from a flat slab. The crater’s strong relief makes the last correction important. A local regional-field/background estimate is also needed if the target is the crater’s residual anomaly. State the reduction density; it is not the inferred breccia density.^[ref] For a fixed land traverse there is no moving-platform Eötvös correction to add.

Treat the quoted anomaly as the response of a slab of thickness $h$ replacing host rock. The Bouguer slab formula applies to the geophysical density contrast, not the absolute density:With $\Delta g=-2.5\times 10^{-5}\mathrm{m}{\mathrm{s}}^{-2}$, $h=400$ m and ${\rho }_h=2750\mathrm{kg}{\mathrm{m}}^{-3}$,Thus ${\rho }_b\simeq 2601\mathrm{kg}{\mathrm{m}}^{-3}$ in the slab approximation. The negative anomaly requires less dense infill. A finite bowl has a different geometric response, and water, post-impact sediment and the regional baseline can matter; the stated calculation is the requested slab estimate. The plotted minimum appears closer to $-2$ mGal, but the numerical instruction explicitly supplies $-2.5$ mGal and controls this calculation.

A gravity anomaly is measured gravitational acceleration, reduced to a stated reference surface and compared with a reference gravity field. A local geological interpretation further removes or models the regional background. An absolute negative Bouguer gravity anomaly is therefore not itself a local negative geophysical density contrast.

Measure relative gravity with a calibrated gravimeter at stations across the profile, tie it to a base station, repeat base readings to estimate instrumental drift, and measure station coordinates and accurate elevations, for example by GNSS and levelling. Record observation times for tide corrections. Subtract the latitude-dependent reference gravity, correct instrument drift and Earth tides, add the free-air correction for station height, and subtract the attraction of the reference-density Bouguer slab. A terrain correction accounts for relief missing from or exceeding that slab. Use a consistent density such as $2670\mathrm{kg}{\mathrm{m}}^{-3}$ for the topographic correction.^[ref]

The question's reference to the anomaly in panel b is a panel-label slip: the upper plot contains gravity, while the lower plot supplies geometry and elevations. A geological slab thickness is the vertical thickness of the anomalous body, not simply its height above sea level.

For a laterally extensive Bouguer slab of thickness $h$ and geophysical density contrast $\Delta \rho$,The greenstone belt reaches from roughly $+1.0$ to $-0.5\mathrm{km}$ near its deepest central part, so use $h\simeq 1500\mathrm{m}$. The gravity maximum is approximately $-100\mathrm{mGal}$; the exposed host-rock background in the south is approximately $-115\mathrm{mGal}$. Taking this as a constant regional reference gives a local excess $\Delta g\simeq 15\mathrm{mGal}=1.5\times 10^{-4}\mathrm{m}{\mathrm{s}}^{-2}$. ThusThis is an approximate density under a constant-background, infinite-slab model. The finite width, variable thickness and neighboring pluton require a fuller gravity inversion for a precise value. In particular, the absolute value $-100\mathrm{mGal}$ must not be inserted as the local excess.

Measure total magnetic field along the same south–north line with a calibrated magnetometer, recording position, time and sensor height. A simultaneous base-station magnetometer measures temporal variation so that diurnal changes can be removed from the moving survey. Avoid disturbed periods and magnetic contamination from vehicles, fences, power lines and equipment. Choose station spacing much smaller than the expected anomaly width, for example tens to hundreds of metres for a kilometre-scale target.

Subtract the epoch-appropriate International Geomagnetic Reference Field or another stated regional main-field model to obtain a total-field magnetic anomaly. Level overlapping traverses and remove offsets or drift where appropriate. Accurate terrain/sensor geometry is needed for comparison with a geological model, but there is no universal magnetic analogue of a constant-density Bouguer slab correction: the effect depends on the distribution and direction of magnetization. Measure magnetic susceptibility and remanent magnetization on representative greenstones, granite and host rock to test the assumed magnetic sources.

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.

Use the same surrounding basement density inferred in solution, carrying its unrounded value through the arithmetic. The intrusion's geophysical density contrast isThe Bouguer slab thickness needed to produce the same negative peak is thereforeThe smaller absolute geophysical density contrast requires a thicker body. This is an approximate vertical thickness and, if the top is close to the surface as drawn in Figure 1, an approximate base depth below that top. It is not an independent estimate of the intrusion's burial depth. For an infinite slab the anomaly does not depend on top depth; a buried top would require additional geometry. Finite width and the downward-widening outline in Figure 1 make 8 km a slab-equivalent estimate rather than a uniquely determined geological depth.