Surveys for targets with anomalies smaller than about 0.1 mGal (100 μGal) are called microgravity surveys. They are important for environmental and civil engineering surveys, such as checking sites for the presence of caves or mine workings.
Especially sensitive gravimeters, often called microgravimeters, are used, with stations often only a few metres apart on a grid, and heights measured to a precision of a few centimetres. Terrain correc-tions have to be carried out with great care and may include the effects of buildings. Examples are given in Sections 24.4, 27.3 and 27.4.
Summary
1. Gravity surveys measure variations of g, the acceleration due to gravity, over the surface of the Earth. These are produced by lateral varia-tions in subsurface density and are used to investigate subsurface bodies and structures.
2. Gravity surveying depends on Newton’s Law of Gravitation (Eq. 8.1).
3. Most rock densities fall in the range 1.5 to 3.0
Mbody Mexcess body
body surroundings
Figure 8.20 Modelling a basin by slabs.
Mg/m3 (11⁄2 to 3 times the density of water).
Density contrasts are often small, 0.1 Mg/m3or less, though some metalliferous ores have a con-siderably greater contrast.
4. A gravity anomaly is the difference of g above or below its value in the surrounding area. The magnitude of an anomaly is often less than a millionth of the average value of g.
Units of gravity are the mGal (10–5 m/s2 ≈ 10–6g) or the g.u. (10–6m/s2); 1 mGal = 10 g.u.
Gravimeters are extremely sensitive, able to measure changes in g of 1 part in 108or smaller.
5. Field gravimeters measure differences in gra-vity between two stations. To determine the
‘absolute’ value of g at a station, it must be compared with the value at a Gravity Standard-isation Network station.
6. Data reduction is very important and comprises instrumental calibration factor and drift, plus several corrections: tides, latitude, Eötvös (when the gravimeter is moving), free air, Bouguer, and terrain. Estimated densities – and geological judgement – are needed for the last two correc-tions. Densities of a several fresh samples of the rocks are better than tabled values.
7. The corrected data forms a Bouguer anomaly, corrected to sea level except for local surveys; a free air anomaly is used out at sea.
The regional anomaly is removed to leave the residual Bouguer anomaly, which may be the anomaly due to the body or structure of est. The regional anomaly itself may be of inter-est in the study of the deeper structure.
8. The spacing, direction (for elongated targets), and precision of gravity surveys are chosen to detect the likely size and shape of a target body; auxiliary measurements – particularly of heights – need to be made sufficiently precisely to allow corrections to match the precision of the readings.
9. Interpretation is either by approximating the target body to a simple geometrical shape or by modelling it with an assemblage of polygons, using a computer, in 2, 21⁄2, or 3D, as appropri-ate to the structure and data. Depth can be esti-mated from the half-width or maximum slope of the anomaly profile.
10. Modelling is limited by non-uniqueness of shape, and because only density differences can
be detected (as well as by the quality of the data). Therefore geological, geophysical, and borehole constraints are needed to produce plausible models.
11. The total excess (or deficit) mass can be deter-mined without theoretical limitation. The den-sity of the country rock is needed to deduce the mass of the body.
12. Microgravity extends the method to smaller sized anomalies and is useful for investigating small bodies, including site investigations.
13. You should understand these terms: accelera-tion due to gravity, g, and G; gravimeter, mGal, g.u.; base station; drift, latitude, Eötvös, free air, Bouguer and terrain corrections; free-air and Bouguer anomalies; regional and residual anomalies; non-uniqueness; half-width; excess mass; microgravity.
Further reading
The basic theory of gravity prospecting is covered by chapters in each of Kearey and Brooks (1991), Parasnis (1997), Reynolds (1997), and Robinson and Coruh (1988), while Telford et al. (1990) covers it at a considerably more advanced level. Tsuboi (1983) is devoted exclusively to gravity and covers both chapters of this subpart, often at a fairly advanced mathematical level.
2. A horizontal sill that extends well outside the survey area has a thickness of 30 m and density of 0.5 Mg/m3in excess of the rocks it intrudes.
Estimate the maximum depth at which it would be detectable using a gravimeter that can mea-sure to 0.1 mGal.
3. An extensive dolerite sill was intruded at the interface between horizontal sandstones. Sketch the gravity profiles expected if the sill and beds have been displaced by:
(a) A steeply dipping normal fault.
(b) A shallow thrust fault.
Problems ✦ 123
(c) A strike-slip fault. Repeat (c) when the beds dip at about 40°.
4. Calculate how much gravity changes, and whether it is an increase or a decrease, on going one km north from latitude: (a) equator, (b) 45°
N, (c) 45° S. What elevation changes in air would give the same changes of g?
5. Why is it more correct to talk of ‘determining the mass of the Earth’ rather than ‘weighing the Earth’? Does (a) a spring balance, and (b) a pair of scales measure mass or weight?
(Think about using them on the Earth and in a spaceship.)
6. A spherical cavity of radius 8 m has its centre 15 m below the surface. If the cavity is full of water and is in rocks of density 2.4 Mg/m3, what is the maximum size of its anomaly?
(i) 0.0209, (ii) 0.0213, (iii) 0.0358, (iv) 0.0890, (v) 0.153, (vi) 0.890 mGal.
7. Which one of the following is not true? The value of g varies over the surface of the earth:
(i) Because the density of rocks varies laterally.
(ii) Because the surface is not flat.
(iii) With longitude.
(iv) With latitude.
(v) With distance from the poles.
8. How much less is the value of g 1 km up in air, compared to its value at the surface?
(i) 15, (ii) 27, (iii) 75, (iv) 110, (v) 309 mGal.
9. If you took a gravimeter 1 km down a mine in rocks of density 2.3 Mg/m3, gravity would change by:
(i) 96, (ii) 212, (iii) 309, (iv) 406 mGal.
Would it be an increase or a decrease?
10. A person, having carried out a microgravity sur-vey to locate a lost shaft, produces a profile with a small dip in it, which he claims is due to the shaft. In support, he points out that the dip coincides with a depression in the otherwise level ground. Then you find out that he has not corrected his data for topography. Discuss whether making corrections might result in the dip disappearing.
11. The mean radius of the Earth is 6371 km. On taking a gravimeter 1 km up in a balloon you would expect the value of g to decrease by:
(i) 3%, (ii) 1%, (iii) 0.03%, (iv) 0.007%, (vi) 0.0001%.
12. The international gravity formula describes gravity:
(i) Only at the actual surface of the sea.
(ii) On a surface simplified to be a sphere approximating the Earth.
(iii) To allow just for the equatorial bulge.
(iv) To allow for the Earth’s rotation.
(v) To allow for both the Earth’s rotation and the equatorial bulge.
13. An ancient burial chamber is to be sought using a microgravity survey. The chamber is likely to be about 4 m across with a covering of up to 3 m, in material of density 2 Mg/m3. Estimate:
(a) The magnitude of the anomaly.
(b) A suitable grid spacing, assuming that the total error in measurement is 0.1 mGal.
14. Describe how you would carry out a micrograv-ity survey to determine the position of shallow mine workings in Coal Measure rocks (density 2.6 Mg/m3) beneath 20 metres of rocks of den-sity 2.1 Mg/m3. If your gravimeter can measure to 5 μGal, estimate the accuracy in height and position needed to use the instrument to its limit.
15. Calculate the average density of the Earth, given that g is 9.81 m/sec2, and the average Earth radius is 6371 km. How does this compare with the density of granite?
16. Explain why portions weighed on the high Tibetan plateau would be larger than portions weighed at sea level, if these are weighed using a spring balance, but not if using a pair of scales.
17. The radius of the planet Mars is 3394 km and its mass is 0.108 that of Earth. The value of g at its surface, in units of m/sec2, is:
(i) 0.031, (ii) 0.30, (iii) 0.56, (iv) 2.0, (v) 3.7.
18. Compared to the Earth, the mass of the Moon is about 1/80 and its radius a quarter. How does its surface gravity compare?