Gravity Methods 3

1. Ali Oncel [email_address] Department of Earth Sciences KFUPM Gravity Methods 3 Introduction to Geophysics 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

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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

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:

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