Environmental and Exploration Geophysics I

Environmental and Exploration Geophysics I Gravity Methods I tom.h.wilson tom.wilson@mail.wvu.edu Department of Geology and Geography West Virginia University Morgantown, WV Tom Wilson, Department of Geology and Geography

Gravity Passive source & non-invasive LaCoste Romberg Gravimeter Worden Gravimeter Tom Wilson, Department of Geology and Geography

Hooke’s Law x spring extension ms spring mass k Young’s modulus g acceleration due to gravity Colorado School of Mines web sites - Mass and spring Pendulum measurement Tom Wilson, Department of Geology and Geography

The spring inside the gravimeter The spring is designed in such a way that small changes in gravity result in rather large deflections of the movable end of the beam. Early gravimeters read the mechanical movement of the spring. Today’s gravimeters use electrostatic feedback systems that hold the movable end of the beam at a fixed position between the plates of the capacitor. The voltage needed to hold the beam at a fixed position is proportional to the changes in gravity. Tom Wilson, Department of Geology and Geography

m1 r12 m2 Newton’s Universal Law of Gravitation F12 Force of gravity G Gravitational Constant Newton.org.uk Tom Wilson, Department of Geology and Geography

ms spring mass mE mass of the earth RE radius of the earth gE represents the acceleration of gravity at a particular point on the earth’s surface. The variation of g across the earth’s surface provides information about the distribution of density contrasts in the subsurface since m = V (i.e. density x volume). Like apparent conductivity and resistivity g, the acceleration of gravity, is a basic physical property we measure, and from which, we infer the distribution of subsurface density contrast. Tom Wilson, Department of Geology and Geography

The milliGal Units Most of us are familiar with the units of g as feet/sec2 or meters/sec2, etc. From Newton’s law of gravity g also has units of Tom Wilson, Department of Geology and Geography

Using the metric system, we usually think of g as being 9.8 meters/sec2. This is an easy number to recall. If, however, we were on the Martian moon Phobos, gp is only about 0.0056meters/sec2. [m/sec2] might not be the most useful units to use on Phobos. We experience similar problems in geological applications, because changes of g associated with subsurface density contrasts can be quite small. Some unit names used in detailed gravity applications include 9.8 m/sec2 980 Gals (or cm/sec2) 980000 milliGals (i.e. 1000th of a Gal & 10-5m/s2) 10-6m/sec2=the gravity unit (gu) (1/10th milliGal) Tom Wilson, Department of Geology and Geography

If you were to fall from a height of 100 meters on Phobos, you would hit the ground in • 10 seconds • 1 minute • 3 minutes =189s • You would hit the ground with a velocity of • 1 m/s • 5 m/s • 30 m/s =1m/s • How long would it take you to accelerate to that velocity on earth? • 10 seconds • 1 second • 1/10th of a second 27x22x18km =0.1s The velocity you would reach after jumping off a brick. Tom Wilson, Department of Geology and Geography

6km How far could you jump? If you could jump up about ½ meter on earth you could probably jump up about 1.7 kilometers on Phobos. (It would be pretty hard to take a running jump on Phobos). Tom Wilson, Department of Geology and Geography

6km How far could you jump? That would give you a velocity of 4.43 m/s and on Phobos that would keep you off the surface for 26 minutes (13 up and 13 down). With a horizontal component of about 4 meters per second you’d come down on the opposite rim. Tom Wilson, Department of Geology and Geography

In perspective Tom Wilson, Department of Geology and Geography

Tom Wilson, Department of Geology and Geography

Astrological Influence? Diameter 12,756 km 78 x 106 km Diameter 6794 km Tom Wilson, Department of Geology and Geography

Summary relationships 1 milligal = 10 microns/sec2 1 milligal equals 10-5 m/sec2 or conversely 1 m/sec2 = 105 milligals. The gravity on Phobos is 0.0056m/s2 or 560 milligals. Are such small accelerations worth contemplating? Can they even be measured? Tom Wilson, Department of Geology and Geography

Spring sensitivity Today’s gravimeters measure changes in g in the Gal (10-6cm/s2) range. If spring extension in response to the Earth’s gravitational field is 1 cm, a Gal increase in acceleration will stretch the spring by 10-8m – a length covered by 100 hydrogen atoms lined up side-by-side. The spring response in today’s modern field portable gravimeters is amplified so that detection of these small changes is possible…. for the modest price of $80,000 to $90,000 Tom Wilson, Department of Geology and Geography

Calculated and observed gravitational accelerations are plotted across a major structure in the Valley and Ridge Province, Note that the variations in g that we see associated with these large scale structures produce small but detectable anomalies that range in scale from approximately 1 - 5 milliGals. Tom Wilson, Department of Geology and Geography

Rp = 6356.75km RE= 6378.14km We usually think of the acceleration due to gravity as being a constant - 9.8 m/s2 - but as the forgoing figures suggest, this is not the case. Variations in g can be quite extreme. For example, compare the gravitational acceleration at the poles and equator. The earth is an oblate spheroid - that is, its equatorial radius is greater than its polar radius. 21.4km difference Tom Wilson, Department of Geology and Geography

Rp = 6356.75km RE= 6378.14km Difference in polar and equatorial gravity Substitute for the different values of R gP=9.83218 m/s2 gE=9.780319 m/s2 This is a difference of 5186 milligals. If you weighed 200 lbs at the poles you would weigh about 1 pound less (199 lbs) at the equator. Tom Wilson, Department of Geology and Geography

Significant gravitational effects are also associated with earth’s topographic features. R. J. Lillie, 1999 Tom Wilson, Department of Geology and Geography

Isostatic compensation and density distributions in the earth’s crust R. J. Lillie, 1999 Tom Wilson, Department of Geology and Geography

Some problems to consider 1. Given that G=6.672 x 10-11 m2kg-1s-2, that g = 9.8 m/s2, and that the radius of the earth is 6366km, calculate the mass of the earth. 2. At birth assume that you were delivered by an obstetrician with a mass of 75kg, and that the obstetrician’s center of mass was 0.5 meters from yours. Also assume that at that very point in time, Mars was closest to the earth or about 78 x 106 km from your center of mass. The mass of Mars is approximately 6.42 x 1023 kg. Determine the acceleration due to the gravitational field of the obstetrician and of Mars. Which was greater? Tom Wilson, Department of Geology and Geography

3. A space traveler lands on the surface of a spherically shaped object that produces an acceleration due to gravity of 0.000003086m/s2. The object has average density of 5500 kg/m3. What is the radius of this object? How long would it take you to fall 5 meters assuming a constant g of 0.3086 milliGals? 30 minutes Due this Thursday Tom Wilson, Department of Geology and Geography

Start doing some background reading for the gravity lab …. Tom Wilson, Department of Geology and Geography

Does water flow downhill? ? Tom Wilson, Department of Geology and Geography

questions? • Keep reading Chapter 6. • Look over the three problems handed out in class today. • We’ll finish these up in class on Thursday • Just a reminder that the gravity papers are available in the mailroom. Tom Wilson, Department of Geology and Geography

Environmental and Exploration Geophysics I