Chapter 8. Processing procedures and formulas

Instrument readings conversion to gravity units

First of all, gravimeter dial readings are converted to gravity units with the use of gravimeter calibration table. Calibration table can be edited in the Instruments window. Each item in the calibration table represents a linear calibaration interval defined by instrument dial reading and gravity value at the beginning of the interval and calibration coefficient appliend for all readings in the given interval. Calibration table entries must be sorted in dial readings ascending order.

Gravimeter dial reading r falling into dial interval from r _i to r _i+1 with start gravity value g _i and coefficient k _i is converted to gravity value g with the following formula:

(8.1)

Instruments readings conversion does not apply for Scintrex CG-5 and CG-3 instruments. Their readings as presented in the instrument dump files are expressed in mGals already.

Removal of instrument computed tidal correction

This step applies to data imported from Scintrex CG-3/CG-5 instrument dump.

If the instrument applies tidal corrections to the readings (Tide Correction: YES in the dump file header), instrument-computed tidal corrections are stripped from gravity readings:

(8.2)

where g represents gravity value cleaned from instrument tidal correction, g _i represents instrument reading and t _i represents value of instrument-computed tidal correction.

Import from CG-3/CG-5 dump procedure stores value of g as instrument reading and value of t _i as tidal correction into BlueWhaleProcessing database. Imported values can be inspected in the Loop table.

Instrument height reduction

Value of g representing relative gravity value at the instrument sensor position is reduced to the ground using free air reduction coefficient:

(8.3)

where g ₁ is the reduced value of gravity, h _i is instrument height and f = 0.3086 mGal/m is free air reduction coefficient. [Blakely 1995] p. 140.

Tidal correction

Fortran computer program ETGTAB http://www.geo.uni-jena.de/geophysik/etc/etcdat/etgtab/ has been adapted to Java and the adapted version is used for computation of Earth's tidal effects. This program is able to compute tidal effects with precision better than 0.001 mGal.

Program ETGTAB computes tidal effect using spherical harmonical analysis for time-space tidal potential development. [Wenzel 1976]

Four tidal potential development models are available:

Detailed information concerning procedure and data used for tidal corrections computation can be found following provided references.

Instrument residual drift correction and reduction to the base

Polynomial equation in the form

(8.4)

is used to compute residual instrument drift d _r for each reading in a given gravity loop where t is time of observation and t ₀ is time of the first observation in the loop. Vector A represents set of coefficients of the polynomial drift model,. E.g. A ₀ is drift start value at time t ₀ and A ₁ is linear residual drift of the loop.

With known vector A, absolute gravity g _A can be computed from the value of g ₁ as follows:

(8.5)

So, for absolute gravity value at the i-th repetition of the m-th station with in-loop repetition g _A,m can be written a linear equation:

(8.6)

Similarly for i-th base reading:

(8.7)

where g _B is base absolute gravity value.

Equation 8.6 and Equation 8.7 define over-determined linear system with unknown residual drift coefficients A and absolute gravities at each non-base station g _A,m . This system is solved with the use of RMS method.

Absolute gravity

When linear system defined by Equation 8.6 and Equation 8.7 is solved, absolute gravity g _A at each loop station based on gravity value at the base station and residual drift model is computed using equations Equation 8.4 and Equation 8.5.

For each station with repetitions and for the base station, average of absolute gravities for each repetition, standard deviation and maximum difference from the average value is computed and presented in reports.

Gravity formula and latitude correction

Theoretical gravity value g ₀ in mGal for each station latitude is computed using one of the three available options, depending on gravity formula setting in Project Properties [Blakely 1995] pp. 135-136:

	Caution
	Please note that the IGF-1930 formula theoretical gravity values differ from newer formulas for as much as approx. 17 mGal!

Free Air Anomaly

Correction of gravity decrease with station elevation is called Free Air correction. Gravity value corrected of station elevation influence is called Free Air Anomaly.

Free Air Anomaly g _F is computed by the following formula [Blakely 1995] p. 140:

(8.11)

where h is defined as station elevation above geoid in meters.

	Note
	Software uses station elevation referenced to the vertical datum defined in the Project Properties. EGM-96 is recommended datum for gravity reductions.

Bouguer Anomaly

Bouguer correction reflects influence of rock slab existing between level of geoid and station level. Gravity anomaly corrected for influence of this slab is called Bouguer Anomaly.

Bouguer Anomaly g _B is computed with the formula [Blakely 1995] p. 143:

(8.12)

where is slab density in g/cm ^-3 and is Newton's gravitational constant 6.67 . 10 ^-11 m ³kg ^-1s ^-2.

	Note
	Reduction density can be set in the Project Properties. Average density of the upper part of the Earth's crust is 2.67 g.cm-3 which is the default for a new project.

Terrain corrections

Terrain corrections compensate influence of the surrounding terrain, i.e. deficiency of masses below the station elevation and excessive masses above the station. BlueWhaleProcessing software currently supports two methods of terrain corrections computations, Hammer method and Plouff method.

Hammer method [Hammer 1939] models terrain surrounding the station by segmented concentric rings as defined in the following table:

Gravity effect of a segment with minimum diameter r₁ and maximum diameter r₂ is computed by the formula:

(8.13)

where h is elevation difference from the station to the average elevation of the segment and N is number of segments in a given zone.

SRTM3 data are used by default as a digital terrain model. Hammer corrections are computed from SRTM3 data starting from Zone D. Corresponding elevation differences are computed as average value of all valid SRTM3 data nodes which fall into the given segment.

If user terrain data are provided for a project, any segment containing at least one terrain reading is included into terrain corrections computation for Zones B and C. Any readings in Zone A are ignored. User terrain data which fall into Zones D - M are combined with SRTM data.

Plouff method [Plouff 1976] models terrain as a series of vertical prisms. Currently, BlueWhaleProcessing software can compute terrain corrections using the Plouff method from SRTM data only, any user terrain data are ignored.

Vertical component of the gravity field caused by a vertical prism with sides parallel to coordinate axes and limits relative to the station position x₁, x₂, y₁, y₂, z₁ and z₂ is computed by the formula [Blakely 1995] page 187:

(8.14)

where

(8.15)

(8.16)

Center of each prism is sited in the SRTM3 reading position. When the distance of the prism center from the station is less than 80 m or more then 120 km, terrain correction is not computed.

	Tip
	The software can compute average difference between each station elevation approximated from SRTM data and the precise station elevation in the project. SRTM data can be corrected for this difference. According to official SRTM documentation, absolute difference of SRTM data can be up to 15 meters.

Complete Bouguer Anomaly

Complete Bouguer anomaly g_C is defined as Bouguer anomaly with terrain corrections g_t included. Because terrain effect always lowers measured value of gravity, complete Bouguer anomaly is defined by the formula

(8.17)

Reduction density assessment

Analytical Jung method, which is a modification of Nettletton method, is used to assess reduction density from line data [Jung 1953]. New density assessment in g/cm³ is made with the use of the following formula:

(8.18)

where and are average complete Bouguer anomaly and elevation over all stations of the line, and are station's complete Bouguer anomaly in mGal and elevation in meters and represents reduction density in g/cm³ used for computation of complete Bouguer anomalies.