please complete for me Document Preview: GOPH 453 Assignment #1 1. The Normal Gravity at latitude ?¦ ? on the reference ellipsoid is given by: ?¦ ? (?) = ge 1+ ?1 sin2(?) + ?2 sin2 [ (2?)] According to GRS80, ?¦ ge = 9.780327 m/s2, ?¦ ?1 = 5.30244 ?10-3 , ?¦ ?2 = -5.8 ?10-6. a) Compute the Normal Gravity at, the equator and Calgary (51oN). b) By differentiating the Normal Gravity formula above, develop an expression for the rate of gravity change with latitude ?¦ d? d? . c) Calculate the rate of gravity change in milligals per kilometer of northward displacement in the equator and Calgary ( Hint: ?¦ d? dS = d? d? d? dS where dS is horizontal distance (or arc length) in km, and the arc length dS on a sphere with radius ?¦ Re is: ?¦ dS = Red? . Here ?¦ Re = 6371 km for the Earth.) d) A gravity survey is conducted along a north-south profile, which starts in Calgary and ends at 50 km south of Calgary. What is the largest latitude effect in this survey? 2. In class, we derived the relation between the thickness of the Root and the height of a plateau that is compensated by the Airy Mechanism. Derive the relation between thickness of the Anti-root for an ocean basin of depth w and filled with water of density ?¦ ?w if the ocean basin is compensated by the Airy Mechanism. 3. Let go be the gravity on a plane surface of the earth. Next, put an infinite horizontal slab of thickness ?¦ ?z and constant density ?¦ ? on top. The gravity on the original plane surface (but at the base of the infinite slab) now becomes g2 . At the top of the slab, the gravity is g1 (see diagram below). a) Express g1 and g2 in terms of go, ?¦ ?z and ?¦ ? . b) Determine the gravity gradient between the top and base of the slab ?¦ g2 g( 1) ?z. c) Given that you can drill a borehole from the top to the bottom of the slab, measure ?¦ ?z, and use a gravimeter to measure g1 and g2 in the borehole, determine the mean density of the slab ?¦ ? from these measurements. ?z gg12 Infinite slab of density ?4. A mineral deposit in the shape of a circular disc slab Attachments: Assign-01-Gra.pdf; please complete for me Document Preview: GOPH 453 Assignment #1 1. The Normal Gravity at latitude ?¦ ? on the reference ellipsoid is given by: ?¦ ? (?) = ge 1+ ?1 sin2(?) + ?2 sin2 [ (2?)] According to GRS80, ?¦ ge = 9.780327 m/s2, ?¦ ?1 = 5.30244 ?10-3 , ?¦ ?2 = -5.8 ?10-6. a) Compute the Normal Gravity at, the equator and Calgary (51oN). b) By differentiating the Normal Gravity formula above, develop an expression for the rate of gravity change with latitude ?¦ d? d? . c) Calculate the rate of gravity change in milligals per kilometer of northward displacement in the equator and Calgary ( Hint: ?¦ d? dS = d? d? d? dS where dS is horizontal distance (or arc length) in km, and the arc length dS on a sphere with radius ?¦ Re is: ?¦ dS = Red? . Here ?¦ Re = 6371 km for the Earth.) d) A gravity survey is conducted along a north-south profile, which starts in Calgary and ends at 50 km south of Calgary. What is the largest latitude effect in this survey? 2. In class, we derived the relation between the thickness of the Root and the height of a plateau that is compensated by the Airy Mechanism. Derive the relation between thickness of the Anti-root for an ocean basin of depth w and filled with water of density ?¦ ?w if the ocean basin is compensated by the Airy Mechanism. 3. Let go be the gravity on a plane surface of the earth. Next, put an infinite horizontal slab of thickness ?¦ ?z and constant density ?¦ ? on top. The gravity on the original plane surface (but at the base of the infinite slab) now becomes g2 . At the top of the slab, the gravity is g1 (see diagram below). a) Express g1 and g2 in terms of go, ?¦ ?z and ?¦ ? . b) Determine the gravity gradient between the top and base of the slab ?¦ g2 g( 1) ?z. c) Given that you can drill a borehole from the top to the bottom of the slab, measure ?¦ ?z, and use a gravimeter to measure g1 and g2 in the borehole, determine the mean density of the slab ?¦ ? from these measurements. ?z gg12 Infinite slab of density ?4. A mineral deposit in the shape of a circular disc slab Attachments: Assign-01-Gra.pdf
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