Gravity L3 PDF

06/11/2014 Reference : Catherine Snelson (with modifications by M Gobashy) Gravimeters Modern gravimeters… – Can detect a change of 1/100,000,000th g Or 0.01 mGal – Rely on a mass pivoted on a beam attached to a spring A...

06/11/2014 Reference : Catherine Snelson (with modifications by M Gobashy) Gravimeters Modern gravimeters… – Can detect a change of 1/100,000,000th g Or 0.01 mGal – Rely on a mass pivoted on a beam attached to a spring A thermostat is present to prevent thermal contraction or extension – Must be carefully leveled before a reading is made (time-consuming) – In CG5 , an automatic leveling is available. – Are somewhat delicate and must be transported in protective boxes But even with all of this complexity, the data from a gravimeter is not directly useful – data must be reduced to correct for several effects Because gravity anomalies are small these corrections are often comparable in size to the anomalies and are thus very important 1  06/11/2014 Gravity Corrections Take the simple example of a gravity measurement made at two different elevations – Because the distance to the center of Earth is farther for higher elevations, the gravity must be less. – There are actually several types of corrections that must be applied to raw gravity data in order for anomalies to be identified. 1. Drift 2. Latitude correction 3. Eötvös correction 4. Topographic correction a. Free-air correction Elevation correction b. Bouguer correction c. Terrain correction Temporal variations Instrumental Drift - Time dependent Tidal Affects Spatial variations Latitude Variations Place dependent Elevation Variations Slab Effects Terrain Effects 10/29/2013 4 2  06/11/2014 Relative geometry of Geoid and Ellipsoid : Datums Sphere Ellipsoid Geoid 10/29/2013 5 Drift Drift is a change in readings that would occur even if the device was not moved throughout the day. – The spring inside the gravimeter may slowly creep or stretch – Diurnal variations in tides Drift is corrected by periodically returning to a base station to get the temporal variation. – The drift is then subtracted from the rest of the data. 3  06/11/2014 Drift Example Because most land-based surveys can only collect one data point at a time, temporal drift variations must be corrected – Base station readings are used to determine the temporal variations – The base station readings are normalized and then subtracted from the data to correct for drift. – The example below is idealized…assumes all other corrections have been made. A Field Procedure Let's now consider an example of how we would apply this drift and tidal correction strategy to the acquisition of an exploration data set. Consider the small portion of a much larger gravity survey shown to the right. To apply the corrections, we must use the following procedure when acquiring our gravity observations Prof. M Gobashy- fall 2013 8 4  06/11/2014 : Establish the location of one or more gravity base stations. The location of the base station for this particular survey is shown as the yellow circle. Because we will be making repeated gravity observations at the base station, its location should be easily accessible from the gravity stations comprising the survey. This location is identified, for this particular station, by station number 9625 (This number was choosen simply because the base station was located at a permanent survey marker with an elevation of 9625 feet). Establish the locations of the gravity stations appropriate for the particular survey. In this example, the location of the gravity stations are indicated by the blue circles. On the map, the locations are identified by a station number, in this case 158 through 163. Before starting to make gravity observations at the gravity stations, the survey is initiated by recording the relative gravity at the base station and the time at which the gravity is measured. Prof. M Gobashy- fall 2013 9 We now proceed to move the gravimeter to the survey stations numbered 158 through 163. At each location we measure the relative gravity at the station and the time at which the reading is taken. After some time period, usually on the order of an hour, we return to the base station and re-measure the relative gravity at this location. Again, the time at which the observation is made is noted. If necessary, we then go back to the survey stations and continue making measurements, returning to the base station every hour. After recording the gravity at the last survey station, or at the end of the day, we return to the base station and make one final reading of the gravity. The procedure described above is generally referred to as a looping procedure with one loop of the survey being bounded by two occupations of the base station. The looping procedure defined here is the simplest to implement in the field. More complex looping schemes are often employed, particularly when the survey, because of its large aerial extent, requires the use of multiple base stations. Prof. M Gobashy- fall 2013 10 5  06/11/2014 A graphical procedure for drift removal 10/29/2013 Prof. M Gobashy-fall-2013 11 Causes of tides Knowing the Lat and Ling for the station location, Modern gravimeters Can calculate the tidal affects and remove directly from the readings 6  06/11/2014 Effects of earth’s shape: Latitudinal Gravity Variations Even if all rocks were the same and there was no topography gravity would still vary with latitude Mini Earth – Least at Equator – Most at Poles – Total variation ~0.5% Why? Equator: 9.78 m/s2 Poles: 9.83 m/s2 Latitudinal Gravity Variations: Why? The Earth rotates on its axis… – Creates centrifugal force which depends on: Mini Earth Distance from axis Rate of rotation – The linear velocity of a person at the equator is much faster than someone at the poles. – Centrifugal force causes Earth to deform Fattest at equator Pinched in at poles 7  06/11/2014 Latitudinal Gravity Variations: Why? Because the Earth rotates on its axis… – The radius of the Earth is greatest at the equator, least at the poles Gravity depends on distance to center of Earth ME Mini Earth g G 2 RE Equator: 9.78 m/s2 Poles: 9.83 m/s2 Theoretical gravity : Normal ellipsoid, latitude correction Because gravity varies with latitude: – This correction is performed using an International Gravity Formula Usually named ( theoretical gravity) formula:  g  978031.8 1  0.0053024sin2   0.0000059sin2 2 mGal  – The correction ends up ~0.8 mGal/km, and given that a good gravimeter can detect a 0.01 mGal change, a N/S movement of only 12 m can be detected. – The above correction must be subtracted from all measured stations in the survey. 9.83 9.82 g (m/s2) 9.81 9.80 9.79 80 60 40 20 0 20 40 60 80 latitude (degrees) 8  06/11/2014 Theoretical gravity: 10/29/2013 17 10/29/2013 18 9  06/11/2014 Eötvös Correction If gravity measurements are made on a moving object (car, airplane, ship) a centrifugal acceleration is induced and the gravity measurements must be corrected. E.g. because the Earth rotates to the east (counterclockwise when looking down from the north pole): – Your weight is reduced due to centrifugal force (~0.34% on the equator due to a rotation of 465 m/s) – If you are traveling eastward: measured gravity is less because your motion adds with Earth’s rotation – If you are traveling westward: You cancel out some of Earth’s rotation and measured gravity is more gEötvös  4.040v sin cos  0.001211v 2 mGal v = speed in km/hr λ = latitude α = direction of travel (azimuth) This is a huge correction ~2.5 mGal per km/hr! The main limiting factor in aerial gravity surveys is accurate determination of the airplane velocity Topographic Corrections So far we have assumed that we were taking gravity measurements at the same elevation. When gravity measurements are taken at different elevations, up to three further corrections are needed. – We also need a way to deal with water! 10  06/11/2014 Free-Air Correction Imagine taking a measurement at A (base station) then floating up to evevation B in a balloon (i.e. in the free air!) – You just moved farther from the center of Earth, so gravity must decrease! Where – This turns out to be ~0.3086 mGal/meter of elevation change did this So a gravimeter will respond to changes in elevation of a few cm! come from?? – To find the rate of change in g with elevation, take the derivative of g ME dg M g – … g G  2G 3E  2 RE 2 dR R R The Free-Air Correction This is negative too, so The Free-air correction: the negatives cancel dg g Freeair  h  0.3086h dR When h is positive (mountain range): gFreeair  0 When h is negative (a Valley): gFreeair  0 11  06/11/2014 Another prove : The Free-Air Correction To account for variations in the observed gravitational acceleration that are related to elevation variations, we incorporate another correction to our data known as the Free-Air Correction. In applying this correction, we mathematically convert our observed gravity values to ones that look like they were all recorded at the same elevation, thus further isolating the geological component of the gravitational field. Taylor Series how big an effect? take g = 9.83 m/s2; r = 6371 km, 10/29/2013 Prof. M Gobashy-fall-2013 23 correction: add 0.3086 times elevation in meters above sea level To apply an elevation correction to our observed gravity, we need to know the elevation of every gravity station. If this is known, we can correct all of the observed gravity readings to a common elevation* (usually chosen to be sea level) by adding - 0.3086 times the elevation of the station in meters to each reading. Given the relatively large size of the expected corrections, how accurately do we actually need to know the station elevations? If we require a precision of 0.01 mGals, then relative station elevations need to be known to about 3 cm. To get such a precision requires very careful location surveying to be done. In fact, one of the primary costs of a high-precision gravity survey is in obtaining the relative elevations needed to compute the Free-Air correction. **This common elevation to which all of the observations are corrected to is usually referred to as the datum elevation. 10/29/2013 24 12  06/11/2014 The Bouguer Correction Now imagine that you float to point C. – You feel less gravity than at A’ due to elevation (Free-air correction) – You feel more gravity than B due to the mass of rock beneath you (Bouguer correction) – If you are on a wide and relatively flat plateau, the extra gravity can be approximated by an infinite sheet/slab m g Bouguer  2 G h  2  s  g Bouguer  0.04192 h (mGal) 13  06/11/2014 Prove: 10/29/2013 Prof. M Gobashy-fall-2013 27 = 0.04193 ρ h mGal, h in meters 10/29/2013 Prof. M Gobashy-fall-2013 28 14  06/11/2014 The Bouguer Correction Since we do not treat negative elevations (i.e. marine surveys) using the Free-air correction – We use the Bouguer Correction and apply a negative density to reflect the “missing” mass LAND: Same as before. It is common to use:   2.67 g cm3 g Bouguer  0.04192 h g Bouguer  0.112h (mGal) SEA: Bouguer is negative because the water acts like a mass deficit:   1.03 2.67 g cm3 g Bouguer  0.0688hw (mGal) The Combined Elevation Correction Because the free-air and Bouguer corrections both depend on h (elevation)… – we can combine them into a single “combined elevation correction g Bouguer  0.04192 h (mGal) gFreeair  0.3086h (mGal) gelevation  g Freeair  g Bouguer gelevation  h (0.3086 0.04192 ) (mGal) 15  06/11/2014 Selecting Reduction Density  while sea level may be datum, variation in elevation occurs in near subsurface  methods for selecting Bouguer density: 1. Standard Bouguer density = 2670 kg/m 3  nominally average crustal density  ensures continuity between surveys 2. Direct measurement  collect samples, core, drill samples, hand samples  inaccessibility; may not be representative 3. Geologic map to get rock type; get values from tables, graphs, etc.  handbooks (physical properties of rocks and minerals) Rock Type Density  sedimentary rock density histograms  rock density ranges ice 880 - 920  rock density means and ranges sea water 1010 - 1050  salt density vs. sediment shale 1950 - 2700 limestone, dolomite 2500 - 2850 sandstone 2100 - 2600 soil & alluvium 1650 - 2200 rock salt 1850 - 2150 felsic igneous rocks 2550 - 2750 mafic igneous rocks 2700 - 3000 ultramafic rocks 3000 - 3300 4. Density profile (Nettleton method)  collect closely-spaced g readings over topographic feature  make latitude, free-air correction  make Bouguer correction, with various values of   find  which gives least correlation with topography 16  06/11/2014 5. Logs  gamma-gamma density logs o -ray source (usually Cobalt), geiger counter o when -rays (photons) collide w/ electrons in rock, Compton scattering causes them to be reflected o intensity of reflected beam depends on density of electrons, which depends on density  neutron density logs  seismic velocity logs (due to rough correlation of density w/ velocity)  borehole gravity meter (see www.edcon.com) o measures g to 0.01 mgal o must overcome small hole size, hostile environment, self -leveling o "width" of investigation ("penetration into sides of borehole") ~ point separation o best method for getting true formation density Terrain Correction The Bouguer correction assumes an infinite slab – Reasonable at C, but not at D The pull of the mountain, H, would have the same effect as the valley, V – Both would reduce g due to the vertical component of pull The terrain correction aims to correct for this and depends on: – Shape and density of topography – Mostly only the nearby features matter (g α 1/R2) No simple way to do this, so computers are used in conjunction with digital elevation data and knowledge of local rock density Rule of thumb: If < 200 m from steep topography – You need to do a terrain correction 17  06/11/2014 Finally…The Bouguer Anomaly Once all of the previously mentioned corrections have been made g Bouguer anomaly  gmeasured  glatitude  g freeair  gbouguer  gterrain  g Eotvos – The result is called the Bouguer anomaly Not to be confused with the Bouguer correction, which is different. If the terrain correction is omitted, the result is the “simple Bouguer anomaly” – The purpose of the Bouguer anomaly is to give the anomaly due to the density variations below the datum, without the effects of topography and latitude Free-air, Bouguer, Isostatic Anomaly  latitude and free-air correction virtually always made, giving the Free-Air Anomaly (FAA)  for environmental/exploration work, some Bouguer correction is made  for gravity in mgals and elevation in meters, then  The Standard Bouguer Anomaly uses Bouguer density of 2.67 g/cm 3  note that, once  is chosen, FAC and BC can be combined into one correction: the elevation correction  the Complete Bouguer Anomaly also includes the terrain correction  sometimes make a correction for isostasy, giving Isostatic Anomaly 18  06/11/2014 Bouguer Anomaly of EGYPT Compiled by: M Gobashy 19