CORRECTIONS APPLIED TO GRAVITY DATA
The primary purpose of detailed gravity surveys is to provide a better understanding of the subsurface geology. Gravity data, i.e., the measurement of gravity at the surface not only includes the effects of rock densities, but also due to a large number of other factors which we have understood already. Certain corrections must therefore be applied do the measured gravity valued in order for the data to yield information about the densities, depths, shapes and sizes of subsurface rocks, structures and ore deposits. Having laid the foundations for quantifying the effects of various factors, both instrumental and external, on the gravity data, we will now proceed to quantify the corrections to be applied to compensate for these effects. Various factors that perturb the measured gravity values at the surface may be classified into the following categories:
VARIATIONS WITH TIME
We have discussed a number of factors, both internal to the gravimeter and external to it, which may cause changes in the observed gravimeter readings, with time. These include earth tides, long term instrumental drift, changes in battery supply voltage and atmospheric pressure changes.
EARTH TIDES CORRECTIONS— CT
Corrections for the tidal gravity effects of the Sun and the Moon are essential for all types of gravimetric surveys, since they can contribute up to 0.3 mGal difference to the measurements.
These corrections become particularly significant in micro-gravity measurements, since tidal rates of up to 30 µGals per hour can readily occur.
Correction for Earth tides may be made in various ways, depending on the circumstances. The most convenient method, valid to the order of ±3µGals, is to apply the formula and tables of Rapp 1983 or Longman 1959. This correction is based on the UTC, latitude and longitude of the measurement. It may be applied off-line, or, in the case of software controlled gravimeters, on line by virtue of embedded software. The operator is only required to enter his latitude, longitude and difference between UTC and his real time clock.
Care must be taken, however, to enter the proper values and sign (conventions) of these parameters in order to avoid introducing extraneous errors.
For example, in the Longman formula embedded in the CG-3 software, the convention of sign is as follows:
Time: The time parameter in the Longman formula is UTC. If the time to which the real time clock in the CG-3 is set differs from the UTC, then a UTC Difference parameter has to be entered into the CG-3, to provide the necessary information whereby the time UTC time may be obtained. If one sets the clock to UTC the UTC Difference is zero (0).
If the clock is set to local time, the difference is calculated by the following formula:
UTC Difference = UTC – CG-3 time
In general, this difference is defined positive for the zones west of Greenwich (0° Longitude) and negative for the zones east of Greenwich. These differences will change if the local time is moved ahead by one hour during summer months. For example, in Toronto, Canada, the UTC difference is 5 hours during standard time periods, but only 4 hours during daylight savings time periods. A reliable way to find the UTC difference is from the BBC shortwave radio news, which are broadcast hourly, with the time information given in UTC.
You should note that in some areas of the world their local time is one half hour different from that of their neighbouring time zones.
In theory, Earth tidal effects may be corrected by means of tie backs with sufficient frequency to a base, and regarding these effects to be just another time varying influence. However, since tidal-induced changes can readily reach 30 µGal/hr, it would hardly be realistic or economic to tie back often enough to ensure that corrections accurate to within 5 µGals are achieved.
Corrections using the Longman formula may leave residuals, due to ocean tide loading, etc. of ± 3µGal in the interior of continents and ±10µGal within a kilometre or so of the coast. Corrections for these residuals have been computed for various sources:
▲ Timmen and Ulenzel (1994) for the global ocean tide loading
▲ Baker et al (1991) for Europe
▲ Lambert et al (1991) for Canada.
These residual corrections may be significant in the case of high precision microgravimetric surveys. They can be applied, off-line, using the references given above.
INSTRUMENTAL DRIFT— CD
The various factors which may contribute to the instrumental drift of your gravimeter (long term drift, battery supply voltage changes, and vibration, etc.) have been dealt with earlier. If your gravimeter is software controlled, it may be assumed, for a start, that you have determined the mean long-term drift of your instrument by repeat measurements made over a period of at least 48 hours, at a convenient station. Such measurements must be corrected for tidal variations. Measurements can be made, for example, at the beginning and end of each day, or more frequently (e.g. even in a cycling mode, if convenient), over two or more days, for this purpose.
The slope of the best linear fit to the resultant curve of gravity values with time, will determine the residual long term drift rate of the gravimeter. This value is then used to adjust the drift correction factor, previously established in the instrument, in accordance with the instructions provided in your gravimeter’s Operator Manual.
Update on the long term correction in software, should be made weekly within the first month or so when the gravimeter is new, reducing to monthly once the drift rate has essentially stabilized.
Once the long term drift has been compensated, then all gravity measurements will be automatically corrected, in real time, for this factor. There may, however, be residual drifts during the survey day, due to such effects as battery supply voltage changes and vibration induced short term drifts, as well as recent power-downs of the instrument.
Such residual drifts are determined by means of repeat of measurements made at a base station, whose gravity value has been previously established, at least at the start of the day's survey and at its end. The reading at the start of the day will establish the correction for the offset of all that day's measurements, and for the cumulative residual drift since the start of the survey. The difference between the reading at the end of the day and that at the start of the day will determine the residual drift rate for that day. This drift will then be linearly distributed to all intervening measurements for that day, in accordance with the time of each measurement.
Particular care must be taken in respect of these base station readings, to avoid any error in them, which would then be propagated throughout the final gravity values for all stations measured that day. This would include such steps as:
Example: Let us assume that the following gravity values are observed at a specific base station, corrected for tidal effects and for linear long-term drift.
R0— base station gravity value, previously established and corrected
R1— observed value at the start of the day, at time T1at the base station
R2— observed value at the end of the day, at time T2 at the base station
R3— observed value at a new station, at time T3 (between T1 and T2)
Then, the residual correction CD to be applied to the new station will be given by:
CD = (R0 – R1) – (R2 – R1) * (T3 – T1)/(T2 – T1)
The first bracket is the day-to-day correction, which in effect, corrects for all residual drifts since the start of the survey. The second factor accounts for the effect of the drift during the day, assuming that this drift is, in fact linear, between the repeated measurements at the station.
Example: (readings in mGals)
R0=5024.372 , R1= 5024.583
R2= 5024.592 , R3= 5031.632
T1= 0805 Hours , T2= 1822 Hours
T3= 1310 Hours
Then the drift corrected reading for the new station is given by
R13 = R3 + CD = 5031.632 – 0,211 – 0.009 (5.10)/10.28
ATMOSPHERIC PRESSURE CHANGES— CP
The following equation provides the simple relationship between such barometric pressure changes and their effects on the observed gravity values.
Δgp = - 0.36 µGal/millibar
= - 3.6 µGal/kPa
On days with a normal weather pattern, barometric pressure variations are in the range of 0.3 – 1 kPa (i.e. 1 – 3 µGals) per day. There will be times, however, when a major pressure front (e.g. a thunderstorm) moves rapidly through the survey area. Such a weather system can give rise to pressure changes totaling 5 kPa (i.e. 18 µGals) in amplitude, with temporal gradients of the order of 0.5 kPa/hr (1.8 µGal/hr) and spatial gradients of the order of 0.2 kPa (0.7 µGal) in 10 km distances.
Whereas atmospheric pressure changes on normal weather days will only affect microgravimetric surveys (only in a minor way), there may be atmospheric conditions which can cause significant effects at the µGal level.
Corrections for these effects can be made in one of two ways:
1. For greatest precision, in microgravimetric surveys, carry a barometer with a resolution of 0.1 kPa, and read it at each gravity station, for cor-rection to the observed gravity values. In relatively small survey areas (e.g. within a radius of 25 km) the barometer may be kept stationary and its variation recorded with time. On normal weather days the barometric pressure will be constant, within 0.5 kPa over such an area; thus Cp so derived will be correct to within 2 µGals.
The correction to the observed gravity values for changes in barometric pressure is given by
Cp = +3.6 (P1 – P0) in µGals,
where P1is the atmospheric pressure at the field station (or at the field station time) and P0 is the atmospheric pressure at the base station (or base station time) at the start of the day, in kPa. For example, if P0 was 98.1 kPa and P1 was 101.3 kPa, then CP= +11.5 µGals (23)
Note that when the pressure increases, the correction is positive, and vice versa.
2. Tie back to a gravity base station sufficiently often to correct for the pressure-induced effect through the linear drift correction (page 37). On normal days, a mid-day tie (as well as the usual start-of-day and end-of-day tie) will suffice. When a weather front is moving in, however, the ties will have to be more frequent. In the extreme, when a major pressure front is moving through, the pressure at the field station may be different from that at the base station, but this may have to be chanced.
In any case, implicit in the drift correction procedure outlined in Instrumental Drift — CD on page 37 (where a base station is read at the beginning and end of each day) is a correction for the barometric pressure at those times.
This includes any day-to-day pressure changes since the start of the survey. There will also be changes in atmospheric pressure with elevation, and consequent changes in the observed gravity values. Of course, these will, likewise, be compensated through the use of a moving barometer. If no moving barometer is employed, there is, nevertheless, little practical consequence because, as we shall see, the barometric pressure effect is negligibly small in respect of the elevation effect, and the uncertainty in the latter.
Near sea level the normal vertical atmospheric pressure gradient is approximately –1.44 x 10-2 kPa/m. This gives rise to a change of – 0.052 µGals/m.
For a surface density of 2.5 g/cm3, the combined elevation effect (Free-Air plus Bouguer) will be (Equation (9) on page 5) 203.8 µGals/m. The pressure effect is clearly insignificant relative to the other elevation effects.
CHANGES IN GROUNDWATER AND SURFACE WATER LEVELS— CGW
Precipitation and Ocean Tides (Sea Level Changes) may affect the measurements of the Earth's gravitational field. Changes in groundwater levels are likely to be seasonal and will reflect the wet and dry seasons, where such a specific seasonality is present (e.g. in monsoon-prone countries in South and South-east Asia).
It would be tedious to attempt corrections for the seasonal variation of groundwater levels on an individual station basis, for this would require a measure of the porosity of the local soils and the local level of the groundwater. Such measurements could, however, be made periodically at one site, at least in topographically flat areas, and a seasonal correction applied to all readings, based on the variation of the water table level at the test site, and the porosity of the soil there.
The correction CGW for a variation ∆w (m)of the ground water level will be given by:
CGW = -0.04192∆w . b mGals
where b is the porosity of the soil.
In the case of surface water changes, such as measurements made near the margins of a sea, lake or river, these would have to be made with a knowledge of the location of the station relative to the body of surface water.
Sea tide variations can be rapid and large in some parts of the world, reaching up to 10m in level, for example. It is known that ∆gT = 0.02 mgal/m of tidal change. For a station at the very edge of the sea coast, the correction for tidal action will be given by:
CST = – 0.02 mGals/m of tidal level change.
Note that when the tide rises the correction is negative. This correction can be made by the use of available tidal information for the local area, or by physical measurements of the tidal level at the time of the gravity reading.
Changes in lake and river levels are usually smaller and slow to occur. They are best corrected for by measurements of water levels in the field.
All of the above corrections may be pertinent in the case of microgravimetric surveys and for precise calibration of your gravimeter on a calibration range. The sea tide correction CST, can, however, be sufficiently large to affect all types of gravimetric surveys in coastal regions.
CORRECTIONS FOR LATITUDE – CL
CORRECTIONS FOR ELEVATION – CE
CORRECTIONS FOR TERRAIN – CTE
SUMMARY OF CORRECTIONS
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