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Lecture 19

Lecture 19. VLF GPR. Phase. Phasor. Advanced in phase cos(wt+ Ф ). Ф. In phase cos(wt). V R. resistance. V. V L. Voltage in inductor Leads voltage in Resistor (current) by 90 degrees Total voltage leads Current by Ф. Inductor. V. V L. Ф. V R. Magnetic versus non magnetic.

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Lecture 19

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  1. Lecture 19 VLF GPR

  2. Phase Phasor Advanced in phase cos(wt+Ф) Ф In phase cos(wt)

  3. VR resistance V VL Voltage in inductor Leads voltage in Resistor (current) by 90 degrees Total voltage leads Current by Ф Inductor V VL Ф VR

  4. Magnetic versus non magnetic

  5. Decay of electromagnetic radiation with depth in earth due to eddy currents High frequency Low frequency

  6. GPR at Parkfield 2006

  7. Velocity in air>velocity in ground • Gives rise to a critically refracted • ray at the surface • Critical angle obeys Snell’s law • Sin(ic)=v1/v2 • Direct air wave always • arrives first.

  8. Ground Penetrating Radar f=100 Mhz V=0.3c=1x108 m/s=0.1 nm/s lambda=108/108=1m. zs=500sqrt(20/108)=0.22 meters

  9. EM wave in air Refracted wave Reflected wave

  10. Steel at 6.9 meters distance? x h

  11. func.m for GPR Hyperbola % these are in nanosecs gpr5=[85 70 62 50 45 50 60 70 80]; %v=0.3 m/ns in air %a=[75 0.3 2]; y=gpr5; xx=[62.5:2.5:82.5]; x0=a(1); v=a(2); z=a(3); x=xx-x0; f=2/v*sqrt(x.^2+z^2); plot(x,f,x,y,'*') figure(1); xlabel ('Distance, (m)') ylabel('Time (ns)') title('GPR Line 5 hyperbola') text(-5,80, ['depth ',num2str(a(3)),' v= ',num2str(a(2))])

  12. Very Low Frequency method (VLF) Portable f=23 KHz used skin depth several hundred m compared with GPR Used to contact submarines Antennas Hawaii, Maine, Portland, Moscow, France etc.

  13. - Vlf meter measures tilt Of field. If secondary Field is zero tilt is zero

  14. Inducing field Bocos(wt) Current=> BS emf from Faraday’s law emfT I L IR Secondary field is less than 90+ degrees out of phase With the primary inducing field. Good conductor Poor conductor

  15. VLF over a dike t h

  16. Mt Etna 2001 Lava Flow

  17. Tilt and Ellipticity in % across 2001 Etna Flow Showing molten magma persists at depth in 2004

  18. Uses of Electromagnetic methods • Magma bodies • Buried chambers • Polluted water table • Buried tanks, pipes • Mineral exploration (e.g sulphides) • Archaeology • Oil reservoirs from boreholes

  19. Magnetotellurics

  20. From: Stacey, Physics of the Earth

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