Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Chap 6 - Gravityon the face of it, more straightforward than resistivityyou measure gravity at the surface of the earth, interpret the valuesneed very sensitive equipmentcorrections must be appliedelevation (further up from sea level the less the pull)remove effects of nearby bodiesstill left with problem of multiple configurations giving the same gravityI. Fundamental relationshipsA. gravitational accelerationF = G m1m2 r2which also can be written as:g = GM R2where G = grav constant, M = mass of Earth, R = radius of EarthII. Measuring gravityA. relative msrmt discussed first1. using a pendulumperiod of an ideal pendulum represented by T = 2 K/gimprecise, but way we get around it is to make 2 msrmts at 2 diff points - we then can at least get the relative difference between gravity at the 2 stationsg = g obsy - g obsx2. Using a gravimeterclassic unit - the Worden gravimeter - still rely on relative diffs between 2 stations…but now the precision is 1 in 100 million, or 0.01 mGalcorrections need to be made for driftB. absolute measurementsfalling body approach, relies on amt of time it takes body to fallz = gt2 2III. Adjusting the observed gravity valuesneed to determine how grav varies…•variance in position on Earth’s surface latitudinally causes diffs in grav...- due to rotation of Earth, centrifugal force acts outward strongly at Equator, less at poles, so g is less at Equator by 3.4 Gal- due to flattened poles, g stronger by 6.6 Gal at the pole- less mass between pole and center of earth vs equator and center of Earth causes g to be less strong at pole by 4.8 Galsomehow all factors add up to be 978 gal at Eq, 983.2 at poleA. so…correct for latitiudeB. correct for elevation:•free air•Bouguer (“boo-gay”, not “booger” like something out of your nose…)1. Free air - get the first derivative of the gravity equation, dg = - g 2 = -0.3086 mGal dz r meterthat is, grav decreases by .31 mgal for each meter above the reference plane (sea level) DUE to ELEVATION ALONEso you add this amt to your observed gravity value when above sel level, subtract it when below sea level.2. Bouguer correction - this one is due to mass that is between observation pt and sea level…why do we need to correct for this?Fig 6-3 Because you need to compare what is under A and B 3. Terrain correction - Fig 6-5 - you may need to re-correct for the Bouguer correction, since it’s simplisticthis is time-consuming, complicatedB. Isostasy and anomalies - principle is like icebergs - low density mountains with deep roots, floating in a sea of high density oceanic materialOceanMountainIV. Field procedures - things to consider…A. Drift and Tidal effects - Fig 6-8 shows typical driftdrift due to 1) instrument changes, 2) tidal effects due to position of Sun and Moon1) “looping” with gravimeter brings you back to your base station periodically so you can check your instrument reading …then simply draw a line showing the drift through time at base, and a bunch of parallel lines running through the real data points. Back the readings down to far left, there are your drift-corrected values…2) the tidal correction curve is more complex..computer is useful for correction…must back out the tidal correction and the drift correction in order to have usable gravity valuesB. Establish base stations where you know absolute gravity if possible (use an IGSN71 locale…)..this helps you “root” your relative values.C. Determining elevations this shows the progression of technology in the past few years - •surveys originally by rod and transit, tied into USGS benchmarks (which were also surveyed in from other benchmarks); these are now accurate laser-based devices known as total stations (we’re trying to get one with the Dean’s $)•spot elevations are those to +/- one foot, usu located on topo maps•in urban settings, much of the data may be already available through city planners & engineers•reference to GPS as the new alternative to rod and transit surveys, “will become the dominant approach in the not too distant future”future is now - research proposal just submitted requesting $5000 for GPS unit accurate to .1 meter (4 “).D. Determine horiz positions - authors show how to get accurate to .01 minutes of latitude, but this is task excellent for GPS (GPS better for horiz positioning than vertical, just because of satellite geometry)E. Bouguer reduction density - discussion of what value to use - standard is 2.67 g/cc. Recall that Bouguer correction is the one where we remove the mass between the observation point and sea level.F. Survey procedure - example from the Smith College classTable 6-4 shows all the data collectedV. gravity effects of simple shapes (fun stuff)we’ve learned how to correct the dataonce we make the maps we’ll want to interpret the anomalies and relate them to subsurface geology and density anomalies.So one logical step is to determine what some basic shapes due in terms of creating gravity anomalies.•First, discuss rock densities - get bulk density (of saturated material) by adding the proportion of solid phase with the proportion of the liquid phasebulk = min 1-poro) + H2O  poro   100   100 B. gravity due to a spheresimple so this is good to start with..analog is an equidimensional ore bodyderive an equation for grav attraction on the surface due to the bodyg z sphere = G 4  R3 c cos  3 (x2 + z2) where c = density contrastFig 6-14 shows the curves for a shallow sphere and deep sphere- curve centered and strongest over the spheres, tails off on either side- bigger the dens contrast or shallower the body, the stronger the anomalycan use this shape characteristic to make estimates about depth to the anomalycan use Table 6-6 and vary parameters, graph the resultsC. grav effect of a horizontal cylindernow we can pretend that the sphere’s 2D gravity profile is just stretched out along the long axis of the cylinder...zxThe 2D equation, in the x-z plane, is g z cylinder = G 2  R3 c cos  (x2 + z2) note the similarity between the sphere and the cylinder (duh…!)D. gravity effect of a vertical cylinder also a useful model device…g vert cylinder = G 2  c h2-h1 = R2 + h12 -  R2 + h22 )however, note that this