1. Problem 10

2. Reduction to pole This is where the magnetic anomaly is transformed to be that of the anomaly at the north pole (as if the same body is placed at the pole) The result is that the anomaly becomes more symmetric and is more centred above the causative body.

3. By comparison with the theoretical curves, the width of the anomaly suggest a Z of between 3.6 and 3.8 m., and a horizontal location of ~ 23 m (Just to the right of the positive peak). With 2m/z 2 = 1, and z = 3.7m, the max height of the anomaly is ~ 0.9 nT. In the observed data, the max height of the anomaly is ~190 nT. Thus we need to make 2m/z 2 = 190/0.9 ~210 (to match the observed data) m = 210 x 3.7 2 /2 ~ 1440 Wbm

4. Lecture 7 GPR The Exam Set exercise

5. Electromagnetic (EM) waves (also referred to as radio waves). All electromagnetic radiation consists of oscillating electric and magnetic fields Heat and light from the sun Frequencies between 30 kHz and 300 GHz are widely used for telecommunication. AM radio: 180 kHz -1.6 MHz TV: 470 to 854 MHz. Cellular mobiles operate within ranges 872-960 MHz, 1710-1875 MHz and 1920 - 2170 MHz.

6. An electomagnetic (EM) wave is generated at surface. This wave travels down through the subsurface. The generated wave has a “conical” footprint. The source is a short pulse of EM energy with a frequency of 10-1000 MHz

7. The velocity of the wave is most dependent on the permittivity of the rocks, with wet conductive porous rocks having a permittivity that is up to 10-20 times larger than dry rocks. The velocity of the EM wave in dry rocks is ~0.2 m/ns The velocity of the EM wave in wet rocks is ~0.05 m/ns [Note that 0.05m/ns = 5 x 10 7 m/s]

8. The EM wave is reflected back to surface when there is a change in velocity (electrical properties of the rocks) and the amplitude of this reflected energy is increased when the velocity contrast is increased. The reflection coefficient (k) is: The arriving EM wave is detected by the antenna and plotted as a function of travel-time.

9. Plot as a radargram (most common) or velocity tomogram or as reflection amplitudes Depth slices radargram

10. Depth penetration in metres for different materials Depth of penetration is poor in conductive layers, good in dry rocks (insulators) and excellent in ice.

11. Hand-held Variety instrument designs Some allow you to produce images in the field

12. Applications Relatively new technique Applications increased in recent years

13. Penetration in ice is excellent Is now being used to determine ice thickness in the Arctic, Antarctic, lakes, glaciers and Mars 0 m 300 m

15. Locating man-made objects beneath the ground Underground storage tanks are centred at top of hyperbolae

17. Forensic applications Locating graves, buried bodies

18. Locating buried geological features Karsts in limestone

19. Locating top of bedrock

20. Over time, bridges and road surfaces deteriorate. Re-paving hides the effects of deterioration, but inside the road surface, damage still exists. Ground Penetrating Radar surveys, can be used to identifying areas of damage. Used to look at asphalt thickness on airplane runways

21. GPR High resolution imaging Wide range applications Uninvasive Relatively cheap and fast Limited penetration Affected by rain Difficult to survey in vegetated terrains

22. Examination Answer any 2 of 4 questions Exam format is as per my example on the ESE website Formulae will be supplied – but you need to know how to use them

23. Question 1: Write short notes using illustrations where appropriate on four of the following five topics: (50 marks) i.Corrections to gravity data; ii.Geometrical spreading and attenuation in seismology; iii.Magnetic properties of rocks; iv.Constant spacing traverse (CST) resistivity surveys ; v.The term “Induced polarization”. Answers – all straight from notes and problem sheets i)Drift, latitude, Free air, Bouguer, Eotvos, Terrain (explain what they are, what is their purpose) 12.5 marks each and 11.25 minutes each

24. Question 1: i.Corrections to gravity data; Do not tell me about gravimeters, regional versus residual gravity anomalies, isostatic anomalies You will only get marks for answering the question

25. Question 3: i)Describe the acquisition and plotting of seismic refraction data (25 marks). ii) A numerical calculation – for example determine the seismic velocity and dip of a sub-surface layer (equations would be given). First half – descriptive, straight from notes Second half will be a “close” to something that you have done in the problems

26. Question 2: i) A company wishes to identify the location of a faulted contact between a basalt and a porous water-filled sandstone. The contact is sub-vertical and buried beneath unconsolidated soils and sands. They conduct gravity, magnetic, refraction and resistivity surveys across the area. Outline how these geophysical data might change across the contact, and use annotated sketches to illustrate how these surveys might be used to identify the contact. (40 marks) ii) Identify some reasons why these surveys may fail to locate the contact. (10 marks) NOT Straight from notes You would need to guess what the velocity, gravity, resistivity and magnetic signature of these two rock types was.

27. Question 4: Write an essay entitled “Forward and inverse modelling of geophysical data”. This year, this question will be about “non-uniqueness” Exercise for next week is to read about non-uniqueness in modelling and interpretation of geophysical data

28. Question 4 Use any sources you can Lecture notes Extracts from Dobrin’s text book are on the ESE site Paper by Colin Zelt (Geophysical Journal Int., 1999, v. 139, p. 183-204). Also on ESE site.

29. Paper by Colin Zelt Describes modelling strategies and model assessment Modelling seismic data Determine crustal velocity model that fits travel-time data

30. Paper by Colin Zelt (Geophysical Journal Int., 1999, v. 139, p. 183-204) Introduction Travel-time data – insensitive to velocity gradient versus a velocity discontinuity

31. Problem - Non-uniqueness A range of models may fit the data equally as well Solution - Need model assessment In final model, need to distinguish between structure that is required by data and structure that is consistent with the data Introduction

32. Section 2 Pre-modelling conditions Uncertainty in data Handle by assigning pick uncertainty 10-200ms Pick heavily where arrivals are clear Fit measured by Chi 2 Normalised (observed –expected) 2 Clear arrivals – small uncertainty, lots of picks Weak arrivals – large uncertainty, few picks

33. Fit measured by Chi 2 Aim to get this equal to 1 Normalised (observed –expected) 2 Called objective function Aim is not to over-fit or under-fit the data

34. Starting model Two extremes: 1D or lateral homogeneous Or include a priori information Test more than one

35. Section 3 Modelling Disadvantage forward modelling With a large complex dataset there is almost no possibility of deriving a model without introducing unnecessary structure Advantage inverse modelling It is possible to avoid this problem

36. Goal Obtain minimum parameter or minimum structure model Occam’s razor analogy – obtain the simplest model that fits the data. Solutions: Node spacing in model ~ twice shot or receiver spacing (whichever is the largest) Restrict model perturbations by altering objective function so that it penalizes against model roughness. This is usually referred to as regularization Chi 2 = Normalised (observed –expected) 2 + regularization term

37. 4 Model assessment Ray coverage Gives indication of areas in the model that are well constrained

38. 4 Model assessment g and h = resolution plots identify areas of model that are well resolved (dark shading)

39. Checkerboards Add checkerboard of high and low velocity anomalies to final model

40. Use inversion to recover checkerboard Determine how well checkerboard is recovered (semblance) Identify areas of good recovery (dark)

41. Use to identify areas of model that are poorly constrained – coloured grey

42. Uncertainties in parameters Get absolute errors e.g. V = 5 ± 0.2 km/s or depth to boundary is 3.2 ± 0.1 km And can see how “smeared” the perturbation is

43. 3.07 Schedule and course outline will be us by the beginning of term Please check it

44. My availability Away 11 th -18 th March 12 – 1 Mon-Wed 20-22 nd March My office 2.38b Any queries on course