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Gravity Methods 3

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- 1. Ali Oncel [email_address] Department of Earth Sciences KFUPM Gravity Methods 3 Introduction to Geophysics Introduction to Geophysics-KFUPM
- 2. Previous Lecture <ul><ul><li>Gravity Methods 2 </li></ul></ul><ul><ul><ul><li>Bouguer Correction </li></ul></ul></ul><ul><ul><ul><li>Bouguer Gravity Anomaly on Land </li></ul></ul></ul><ul><ul><ul><li>Bouguer Gravity Anomaly on Sea </li></ul></ul></ul><ul><ul><li>Mid-Term Exam </li></ul></ul>Introduction to Geophysics-KFUPM
- 3. Grade Students Grade Distribution in Mid-Term Exam 204317 214269 222736 226202 234345 Introduction to Geophysics-KFUPM
- 4. Mid-Term Exam Solutions h 1 X CR h 1 V 1 V 2 1200 3200 0.4 0.6 Meters Seconds V 1 , V 2 , h 1 ? 0.3 0.2 0.1 Introduction to Geophysics-KFUPM Simplified version of Assignment 2
- 5. Introduction to Geophysics-KFUPM For example, a double spike function , 2, 0, 1 convolved with an impulse response function 4, 3, 2, 1 . It was class example of Lecture 9.2 From Kearey, Brooks, and Hill, 2002
- 6. Given that the P-velocity of a rock is 6.8 km/s, the S-velocity is 3.82 km/s, and density 2.95 g/cm 3 , calculate µ and k? Introduction to Geophysics-KFUPM Modified version asked in Quiz 1
- 7. Where possible, supply the missing quantity in each case in the following table, where: i = angle of incidence r = angle of refraction v1 = wave speed in upper layer, v2 = wave speed in lower layer. The wave originates in the upper layer. Introduction to Geophysics-KFUPM Modified version asked in Quiz 2
- 8. The same question solved in Class v 1 =1500 m s -1 v 2 =2000 m s -1 v 3 =2345 m s -1 t 1 =2.14 s t 2 =1.21 s t 3 =1.13 s v rms at the base of layer 3? Introduction to Geophysics-KFUPM v rms at the base of layer 1? v rms at the base of layer 2?
- 9. Introduction to Geophysics-KFUPM
- 10. Introduction to Geophysics-KFUPM
- 11. Introduction to Geophysics-KFUPM
- 12. Recall Grading Introduction to Geophysics-KFUPM
- 13. Homework Status Introduction to Geophysics-KFUPM
- 14. Homework Status Introduction to Geophysics-KFUPM
- 15. Homework Status Introduction to Geophysics-KFUPM
- 16. Summary of Equations for Free Air and Bouguer Gravity Anomalies <ul><li>Standard parameters used to compute gravity anomalies on land and at sea. </li></ul><ul><li>FAC =Free-Air Correction; BC =Bouguer Corrections; </li></ul><ul><li>BC s =Bouguer correction at sea </li></ul><ul><li>ρ =reduction density; h =elevation (m) and hw =water depth (m) </li></ul>Introduction to Geophysics-KFUPM
- 17. Bouguer Gravity Anomaly on Sea Introduction to Geophysics-KFUPM Δ g fa = g – g t + FAC Δ g B = Δ g fa - BC BC = 0.419 ρ h FAC = h x (0.308 mGal/m)
- 18. Terrain Correction Introduction to Geophysics-KFUPM Δ g BC = Δ g B +TC terrain correction is no needed in areas of low relief but is required where changes in topography is significant and equation for a complete Bouguer anomaly is:
- 19. <ul><li>Terrain correction is needed in areas of high relief in order to account decrease of observed gravity due to </li></ul><ul><ul><li>mountains above the slab (1), </li></ul></ul><ul><ul><li>and overcorrection due to valleys (2). </li></ul></ul>Terrain Correction Introduction to Geophysics-KFUPM Δ g BC = Δ g B +TC
- 20. Terrain Correction For both situations, the terrain correction is positive, making the complete Bouguer anomaly higher than the simple Bouguer anomaly. Introduction to Geophysics-KFUPM
- 21. Gravity Measurement Introduction to Geophysics-KFUPM True gravitational acceleration ( ρ ) Reflecting the difference in gravitational acceleration ( Δρ ) at one station ( ρ 1 ) compared to another ( ρ 2 ).
- 22. Measurement of relative gravity A gravimeter measures the length of a spring (L), which is proportional to the gravitational acceleration (g). + Δ L Increase in gravity - Δ L Decrease in gravity Map of relative gravity survey. The traverse starts with a measurement at the base station , the each of the 16 stations, followed by re-measurement at the base station. Introduction to Geophysics-KFUPM
- 23. Microgravity surveys require that we measure g with precision of better than 1 part in 40 million • we measure either absolute gravity or more commonly, relative gravity ( change in g between two stations ) Methods: 1. Falling body 2. Pendulums 3. Mass-spring gravimeters Gravity Measurement Introduction to Geophysics-KFUPM
- 24. Gravitational acceleration can be measured directly by dropping an object and measuring its acceleration. Free Fall Methods • distance a body falls is proportional to the time it has fallen squared z = ½ g t 2 g = 2 z /t 2 g inst = 2 ·50 m/(3.19 s) 2 = 9.8 m/s 2 Introduction to Geophysics-KFUPM
- 25. Pendulums Gravity first measured by Pierre Bouguer in 1749 ( 257 years ago ) using Pendulum: period of oscillation T of pendulum is inversely proportional to g T = 2 K /g K = constant related to pendulum design Introduction to Geophysics-KFUPM
- 26. Gravity Units Most of us are familiar with the units of g as feet/sec 2 or meters/sec 2 , etc. From Newton’s law of gravity g also has units of Introduction to Geophysics-KFUPM
- 27. Using the metric system, we usually think of g as being 9.8 meters/sec 2 . This is an easy number to recall. If, however, we were on the Martian moon Phobos, g p is only about 0.0056meters/sec 2 [m/sec 2 ] might not be the most useful units to use on Phobos. Some unit names you will hear when gravity applications are discussed include: 9.8 m/sec 2 980 Gals (or cm/sec 2 ) 980000 milligals (i.e. 1000th of a Gal) We experience similar problems in geological applications, because changes of g associated with subsurface density contrasts can be quite small . Gravity Units http://www.esa.int/SPECIALS/Mars_Express/SEM21TVJD1E_0.html Introduction to Geophysics-KFUPM
- 28. 1 mGal = 10 microns/sec 2 1 milligal equals 10 -5 m/sec 2 or conversely 1 m/sec 2 = 10 5 milligals. The gravity on Phobos is 0.0056m/s 2 or 560 milligals . Are such small accelerations worth contemplating? Can they even be measured? Gal Gal = 1 cm/sec 2 = 0.01 m/sec 2 1 mGal = 10 -3 Gal Istituto e Museo di Storia della Scienza Introduction to Geophysics-KFUPM 1564-1642

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