ENV-5004B/ENVK5005B. Figure 6. Student Registration No. ENV-5004B/ENVK5005B Version 2

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1 ENV-5004B/ENVK5005B Figure 6 Student Registration No

2 UNIVERSITY OF EAST ANGLIA School of Environmental Sciences Main Series UG Examination SOLID EARTH GEOPHYSICS SOLID EARTH GEOPHYSICS WITH FIELDCOURSE ENV-5004B / ENVK5005B Time allowed: hours Answer THREE questions. Write each answer in a SEPARATE booklet. PROVIDED: Equation Sheet Graph Paper Figure 6 Non-programmable calculators are allowed Notes are not permitted in this examination. Do not turn over until you are told to do so by the Invigilator. ENV-5004B/ENVK5005B Module Contact: Dr Jessica Johnson, ENV Copyright of the University of East Anglia Version

3 Page 1. (a) Explain each term in the Bouguer anomaly equation: GB = Gobs G + GF - GB + GT [30%] (b) Gravity readings taken over the suspected location of a tunnel yielded the Bouguer Anomaly profile shown in Figure 1. Assume that the tunnel may be modelled as a horizontal cylinder, orientated perpendicular to the profile line and that the bedrock has a density of 500 kg/m 3. Figure 1. Gravity profile over a suspected tunnel. (i) Estimate the regional field. [5%] (ii) Use the residual anomaly to calculate an estimate for the depth to the top of the cylinder and the radius of the tunnel assuming it is filled with air. [30%] (iii) Is there a way to determine whether the tunnel is filled with air or water? Explain your answer using the equation you used above. [15%] (c) List four factors that cause the acceleration due to gravity (g) to vary across the surface of the Earth. For each factor explain why and state where you would expect g to be lowest due to the factor. [0%]

4 Page 3. (a) Explain what is meant by the terms: (i) (ii) (iii) (iv) Magnetic inclination; Magnetic declination. Induced magnetism Remnant magnetism (b) Two magnetic anomalies are shown in the North-South profiles in Figure. East-West trending ligneous dykes with the same shape, size, and direction of magnetisation cause both anomalies. Explain why the two dykes create different magnetic anomalies. Compare their relative depths, magnitude of magnetisation, and latitude in your answer. [30%] Figure. Magnetic survey profiles over two dykes. (c) Explain why the Earth s magnetic field can vary temporally and why it is important to have base station measurements when conducting a magnetic survey. [30%] TURN OVER

5 Page 4 3. (a) Explain what determines the vertical resolution of an interface imaged in a seismic reflection profile. What is the vertical resolution of a seismic reflection survey using a source with a frequency of 50 Hz in sandstone with a seismic velocity of km/s? [15%] (b) Sketch the diagram (Figure 3) into your answer book, complete the axis labels and identify the types of rays responsible for each curve. Figure 3. (c) Draw a simple sketch showing the source and receiver locations, subsurface structure, and the ray-paths responsible for the arrivals in Figure 3. (d) Calculate the complete subsurface structure corresponding to the travel time curves in Figure 3. [30%] (e) Briefly explain the normal move-out and how to correct for it. [0%] (f) Describe the ideal source characteristics for a reflection profile, with arguments for and against some common sources. [15%]

6 Page 5 4. (a) In your own words explain the following terms: (i) Resistance [5%] (ii) True resistivity [5%] (iii) Apparent resistivity (b) Study Figure 4, below, which represents the sub-surface geology of area A determined from boreholes. Figure 4. Sub-surface geology. (i) (ii) A geoelectrical survey is required to determine the sub-surface geology of Area B, the survey may extend beyond the area in the figure above. Propose a geoelectrical survey design and explain the reasons for your choice of parameters such as electrode spacing. Include a sketch with your answer to show the positioning of survey/surveys lines. [50%] Briefly explain a suitable method for processing data obtained in (i). (iii) How could the sub-surface geology be interpreted from the results obtained from (ii)? Include in your answer examples of problems in interpretation, and any possible solutions to minimise the uncertainties of the results of the geoelectrical survey. [0%] TURN OVER

7 Question Earthquake seismology (a) An earthquake on a thrust fault ruptures with an offset of m. The fault plane was 00 km by 30 km. Page 6 The shear modulus of the crust at this location is 100 GPa. 5. (a) Describe, with the use of a sketch, what is meant by the hypocentre of an What earthquake. is the moment magnitude of the earthquake? (3 points) (b) Two earthquake focal focal mechanisms mechanisms are shown are below shown (A and in Figure B) 5 (A and B). For each, name the type of fault that caused the earthquake. For each, name the type of fault that caused the earthquake. Explain Explain how how each is each earthquake earthquake is is related related to its to location. its location. (7 points) [0%] Figure 5. Earthquake focal mechanisms. (c) Draw a sketch map showing a transform fault on a mid-ocean ridge. Sketch the focal mechanism of an earthquake on the transform fault. How did this focal mechanism give evidence for seafloor spreading? (6 points) (Q Total = 16 points) Page 3 of 6

8 Page 7 (c) Figure 6, on a separate sheet, shows a cross section of the Earth with angular distances. (i) (ii) On figure 6, sketch typical P and PcP seismic body waves through the Earth s mantle recorded at an angular distance of 45 o from the source to a seismometer. [5%] Using the same source, on figure 6, sketch typical PKP and PP seismic body waves recorded at an angular distance of 150 o from the source to a seismometer. [5%] (d) A shallow earthquake occurs at 17::5 GMT. A seismometer 55 km from the epicentre records the seismogram in Figure 7. Calculate the bulk and shear moduli of the regional crust rock given that the density is 900 kg/m 3. [45%] 17:5:00 17:6:00 Figure 7. Seismogram (e) Name and describe the nature of two types of surface wave including a sketch of the particle motion for each wave. [15%] TURN OVER

9 Page 8 6. (a) Describe what is meant by a mogi model and discuss the limitations of such a model. [0%] (b) Figure 8 shows the horizontal and vertical displacement derived from ascending and descending track interferograms across an active volcano. Previous work in this region has estimated that the magma chamber is approximately km in diameter, the top of which is 3 km below the surface. The shear modulus for the area is approximately 30 GPa. Calculate the volume of magma that has been added to the system, indicating key assumptions made. [40%] Figure 8. Horizontal and vertical displacement derived across an active volcano. (c) What method of deformation monitoring would you use for the following phenomena and why? (i) Strain accumulation at a subduction zone. (ii) (iii) (iv) Strombolian-type volcanic eruptions (repeating small eruptions due to gas slugs bursting within the volcanic conduit, lasting minutes~hours each). Subsidence at a geothermal power station in Iceland. Slumping and landslides at a road cut in Wales.

10 Page 9 7. The data in Table 1 were obtained from a seismic refraction survey 100 m long. The survey was carried out on level ground to determine the nature of the subsurface layering. Table 1 Offset (m) Travel Time of first arrival (ms) Assuming homogeneous and planar layers: (a) Draw a graph of the data on the graph paper provided and label the type of wave responsible for each part of the curve; [15%] (b) Calculate the velocity in each layer (to significant figures) and the depth to the layer beneath the profile; [30%] (c) Calculate: (i) the critical angle (ii) the critical distance (iii) the overtaking distance (d) Summarise your results and interpretation using an annotated crosssection, indicating key assumptions made. [15%] (e) Explain what is meant by a velocity inversion and the consequences of it. END OF PAPER

11 10 Seismology Speed of a wave P-wave velocity S-wave velocity V P = V = fλ K + 4μ 3 ρ V S = μ ρ S-P wave time t S P = r V s r V P Wyllie s porosity equation Snell s Law 1 V = φ + 1 φ V f V m sinθ 1 sinθ = V 1 V = n n 1 Travel time of refracted wave in a horizontal layer case t = x + z (V V 1 ) 1 V V 1 V Travel time of refracted wave in a horizontal multi layer case n 1 t n = x + [z (V n V i ) 1 ] V n V i V n i=1 The critical distance The overtaking distance x crit = z ( V V ) 1 1 x ot = z (V + V 1 ) (V V 1 ) Travel time of reflected wave in a horizontal layer case Dix formula t = t 0 + x V 1 V int = [ (V RMS n) t n (V RMS n 1 ) 1 t n 1 ] (t n t n 1 ) ENV-5004B/ENVK5005B Version 1

12 11 Gravity G (gravitational constant) = m 3 kg 1 s 1 mgal = 10 gravity units (g.u.)= 10 5 ms Free-air effect = mgal m 1 Bouguer correction g = πg ρh Gravity anomaly over a sphere g = 4 z 3 πgr3 ρ (z + x ) 3 Gravity anomaly over a horizontal cylinder g = πgr z ρ ( z + x ) Maximum gravity anomaly over a vertical cylinder g max = πg ρ(l + S 1 S ) Buried slab g max = πg ρl Magnetics Vertial field magnetic anomaly of a sphere B z = 1 3 μ (z 0R 3 x ) M z (z + x ) 5 Vertial field magnetic anomaly of a horizontal cylinder B z = 1 μ 0R M z (z x ) (z + x ) Straight slope method: horizontal extent of straight part of steepest section of anomaly profile = depth estimate. Peter s method: S=horizontal distance between the two points at which the tangent has half max. slope, then S/1.6 = depth estimate. Sokolov s method: S=horizontal extent of the inflection tangent as it rises from the minimum to the maximum value of the anomaly, then S/ = depth estimate. ENV-5004B/ENVK5005B Version 1

13 1 Geoelectrics Archie s Law Electrical potential at a point Skin depth ρ = aφ m s n ρ w V r = Iρ πr δ = 503(fσ) 1 Deformation Mogi model u r = 3a3 P 4μ x (x + z ) 3 u z = 3a3 P 4μ z (x + z ) 3 V = πpa3 μ END OF MATERIALS ENV-5004B/ENVK5005B Version 1