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Lecture 16 Electromagnetic Surveying Chapter 13 Induced Polarization IP and Self-Potential SP • IP charge stored in an ore when a current flows, it decays when current is turned off • SP small voltages (potentials) generated naturally IP • Conducting ores in non conducting matrix • As current flows electrons pass through conducting grain, but delays occur. • When I=0, acts as a capacitor that discharges with time - + Chargeability chargeability= 1 (area under curve) Vc Shallow , massive pyrrhotite Body (FeS) ore in steeply dipping sheets Chapter 14 Electromagnetic methods T frequency f=1/T=1/period BASIC PHYSICS Thumb in direction of I Fingers curl in direction of B Flux=Magnetic field Area =BA (1) FARADAYS LAW ( BA) t t B is magnetic field A is area is flux. emf= B (2) Magnetic field threading an conductor Bp=Bprimary Bs=Bsecondary Bp=Bprimary Emf=>IS Bs Bp Currents (eddy) are setup in the conductor that Try to cancel B. But if there is resistance they are out of phase and do not perfectly cancel. Ohm’s Law for AC field emf=I R 2 (2 fL) 2 I R 2 ( L) 2 L Inductance (Henries) Note at f=0 emf=IR (same as Ohm's law). phase =atan( voltage. 2 fL ) between current and R Phase let BP B0 cos( t ) B0 cos(2 ft ) B0 cos(2 t / T ) BS B0 cos( t ) Phase difference is 2 Note =2f= T is angular frequency (radians/sec) f is frequency (Hz) T is period (sec) Phasor Advanced in phase cos(wt+Ф) Ф In phase cos(wt) VR resistance V VL Voltage in inductor Leads voltage in Resistor by 90 degrees Inductor V Total voltage leads Current by Ф VL Ф tan L R VR Magnetic versus non magnetic PHASE B t emf from induced currents is 90o out since emf A of phase with inducing field. But if the body has inductance the phase may be different > 90o However if the body is magnetic and the secondary field is mainly due to magnetism rather than eddy currents BSecondary BPr imary i.e., in phase. So phase can be used to distinguish between gold (non-magnetic) and steel (magnetic). Decay of electromagnetic radiation with depth in earth due to eddy currents Velocity f Amplitude A0 e z / zS = wavelength v=velocity f=frequency =1/=conductivity =resistivity z s 500 1 500 f f High frequency Low frequency GPR at Parkfield 2006 •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. 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 EM wave in air Refracted wave Reflected wave Steel at 6.9 meters distance? T 2 2 x h2 V x h 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))]) 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.