Groundwater Geophysics Phần 7 ppsx

324 Gerald Gabriel

applying formulas for simple source bodies (e.g. Telford et al. 1990). For

most investigations in the frame of groundwater geophysics point spacing

between 50 m and 100 m is sufficient. The surveyed area should exceed

the dimension of the geological target in order to map the corresponding

gravity anomaly completely and to distinguish between regional and resid￾ual gravity anomalies. In areas where less information is available a survey

should start with a coarse net of points, in areas of interest additional

measurements can be performed later.

Fig. 11.1. Inclination-insensitive points of gravimeter G-662 on 02nd July 2002

(1 Volt ≅ 1 mGal)

During the survey gravity stations have to be selected properly. Read￾ings can be affected by microseismics (natural and artificial) and wind

(causing strong disturbances by trees). Gravity stations near steep slopes,

buildings, frequented roads, and ditches should be avoided. Ideally each

gravity station within the surveyed area is recorded twice in order to avoid

outliers.

The reading procedure itself should be the same at each point of the sur￾vey. The dial has to be approached from the same side each time, other￾wise its backlash will cause errors that can amount to some 10 μGal. The

reading can be taken as soon as the gravimeter output is stable, best con￾trolled by a feed-back system. The total time required for the observation

of one single station is between 5 and 10 minutes. Therefore about 30 to 50

stations can be surveyed during a day, provided that the time for transport

between the stations is negligible. Unfavourable environmental conditions

like bad weather or microseismics can cause delays.

Local gravity investigations in the frame of groundwater geophysics

will often be performed by densifying an existing data base by comple-

11 Microgravimetry 325

menting measurements. In order to assure the compatibility of the gravity

values resulting from different campaigns, relative gravity measurements

should be tied to existing absolute gravity points, in general available from

the ordnance surveys. In practise a local base point not influenced by tem￾poral gravity changes should be established within the investigated area.

The absolute gravity value for this local base point results from repeatedly

measured ties to at least two absolute gravity points of a regional network.

If possible a local gravity network should be established including the cal￾culation and correction of loop misclosures in order to achieve a higher ac￾curacy of the local base point.

A high accuracy of the observed gravity differences requires a precise

recording of the gravimeter drift. The drift of a gravimeter is caused by ex￾ternal effects (e.g. temperature and air pressure changes, mechanical

shocks) as well as internal effects (fading of spring tensions). Practical ex￾periences show, that the drift should be observed at least every two hours

by measurements on a control point (Fig. 11.2). Generally, the drift should

not exceed 100 μGal/day.

Fig. 11.2. Artificial jump observed with gravimeter G-662 on 16th June 2004.

Black lines with bullets represent the observed gravity and grey lines with crosses

represent the tide corrected gravity values. Knocking the gravimeter against the

transport box caused a jump of about 60 μGal. Correcting the jump (grey line with

diamonds) yielded a smooth, nearly linear drift

326 Gerald Gabriel

If the gravimeter is knocked or jolted, either during transport or during

the measurement procedure, the drift has to be checked immediately. Fur￾thermore these incidents should be noted in the protocol. Gravity observa￾tions made in a period where great drift rates indicate larger artificial

jumps in gravity caused by external influences on the gravimeter (Fig.

11.2) must be cancelled and replaced by new observations. For recording

the gravimeter drift different measurement schedules like the difference

method, the star method, the step method, or the profile method are estab￾lished (Watermann 1957). Parallel observation by operating more than one

gravimeter also increases the accuracy and reliability.

11.3.2 Data processing

Absolute gravity values do not only reflect the density contrasts within the

earth’s crust, but also the shape of the earth itself. They are influenced by

the geodetic latitude, the elevation, and temporal gravity changes. In order

to get anomaly values that can be interpreted in geological terms, known

temporal effects have to be corrected and known disturbing mass distribu￾tions such as topography have to be reduced.

Therefore, during a gravimetric survey following information must be

noted in order to enable a reliable data processing: (a) station number (in￾cluding repetition measurements for drift estimation), (b) date and time of

gravity reading in UT (needed for earth tide correction and drift correc￾tion), (c) height of gravity sensor above the earth’s surface, (d) scale units,

(e) feed-back output (if available), and (f) air-pressure. At least for spring

gravimeters it is recommended also to note the temperature of the instru￾ment. Temperature changes caused by e.g low power supply affect the

reading. The operating temperature is different for each individual gra￾vimeter. Furthermore calibration factors for the used gravimeters (incl.

feed-back systems) and earth tides must be known as well as the co￾ordinates and elevations of the gravity stations and values for tied absolute

gravity points.

In solid earth physics interpretations are commonly based on the

Bouguer anomaly Δg (after the French scientist Pierre Bouguer, 1698–

1758). The Bouguer anomaly is defined as the difference of the observed

gravity value gobs at a given station and the theoretical gravity value gth due

to a homogenous earth for this station:

Δg = gobs − gth . (11.5)

11 Microgravimetry 327

The theoretical gravity value gth due to a homogenous earth is given by

(Fig. 11.3)

gth gh gbpl gter = γ + δ + δ − δ (11.6)

γ : normal gravity,

δgh : free air reduction,

δgbpl : Bouguer plate reduction,

δgter : terrain reduction.

Fig. 11.3. Calculating Bouguer anomalies requires the application of corrections

and reductions (further explanations are given in the text)

With Eq. 11.5 the Bouguer anomaly at the station height (Ervin 1977,

Hinze 1990, Li and Götze 2001) is

g gobs gh gbpl gter Δ = − γ − δ − δ + δ . (11.7)

The resulting value reflects gravity anomalies due to inhomogeneous

densities below the gravity station. They can either be plotted as profiles or

as contour maps.

Correction of temporal gravity changes in the observed gravity

In Eqs. 11.5 and 11.7 gobs represents the observed absolute gravity value

derived from relative gravity measurements including ties to an absolute

gravity point. Temporal effects like Earth tides and the gravimeter drift are

corrected.

328 Gerald Gabriel

Earth tides are caused by the varying gravitation of the earth and celes￾tial bodies – primarily moon and sun – at the different points of the earth

and the centrifugal acceleration due to the rotation of all bodies around

common centres of gravity (e.g. Melchior 1966). The maximum variation

of the Earth tides for an elastic earth is 0.29 mGal, about 1.16 times the

tides for a rigid earth. In addition to the earth tides also ocean tides occur.

Besides their direct gravitation (movement of water masses), ocean tides

also cause gravity changes due to periodic deformation (loading) of the

earth crust and corresponding height changes – the ocean loading tides.

Compared to the magnitude of Earth tides, correction for ocean tides and

ocean loading tides are small. They can be considered by a corresponding

choice of earth tide parameters.

The correction of Earth tides can either be done as part of the drift cor￾rection, or more accurately by using Earth tide models. The computation of

earth tides is based on the expansion of the tidal potential (e.g. Cartwright

and Taylor 1971, Cartwright and Edden 1973, Wahr 1980, Tamura 1993,

Hartmann and Wenzel 1995) taking into account the elastic behaviour of

the earth. Depending on the model used, earth tide corrections with accu￾racy better than 1 μGal can be provided applying correct amplitude factors

(differing from 1.16) and phases for the different tidal constituents. Be￾cause earth tides strongly depend on the latitude, the ellipsoidal co￾ordinates should be considered at least with a precision of 50 km.

The accuracy of gravity measurements can be increased by considering

air pressure variations. Although gravimeters are air-tight sealed gravity

measurements are affected by air pressure variations directly by the gravi￾tation of the air masses as well as by the deformation of the surface due to

loading effects. From high-resolution time dependent gravity recordings

regression coefficients from -0.2 to -0.4 μGal/hPa are known. In practise a

regression coefficient of -0.3 μGal/hPa can be used (e.g. Warburton and

Goodkind 1977, Torge 1989). Generally, the necessity of air pressure cor￾rections depends on the desired accuracy of each gravity survey. The cor￾rection should be considered at least for calibration or exploration surveys

in mountainous areas. For local gravity surveys, where air pressure differ￾ences mostly remain smaller 10 hPa, air pressure correction is not manda￾tory.

Normal gravity reduction

The theoretical gravity value gth strongly depends on the geodetic latitude

ϕ, the elevation of the gravity station, and topographic masses. Gravity as