Geology 228/378Applied & Environmental Geophysics

Lecture 8

Induced Polarization (IP) andNuclear Magnetic Resonance (NMR)

Induced Polarization (IP) and Nuclear Magnetic Resonance (NMR)

1. Time domain IP and Frequency domain IP 2. Membrane and electrode polarization 3. Maxwell-Wagner effect 4. Statement on IP for environmental applications5. Magnetic spin of hydrogen nuclei6. Surface NMR: principles and applications

Induced Polarization• Induced polarization is an electromagnetic method that uses

electrodes with time-varying currents and voltages to map the variation of electrical permittivity (dielectric constant) in the Earth at low frequencies. Induced polarization is observed when a steady current through two electrodes in the Earth is shut off: the voltage does not return to zero instantaneously, but rather decays slowly, indicating that charge has been stored in the rocks. This charge, which accumulates mainly at interfaces between clay minerals, is responsible for the IPeffect. This effect can be measured in either the time domainby observing the rate of decay of voltage, or in the frequencydomain by measuring phase shifts between sinusoidal currents and voltages. The IP method can probe to subsurface depths of thousands of meters.

In nature, the induced polarization (IP) effect is seen primarily with metallic sulfides, graphite, and clays. For this reason, IP surveys have been used extensively in mineral exploration. Recently, IP has been applied to hazardous waste landfill and groundwater investigations to identify clay zones. As with electrical resistivity surveys, vertical or horizontal profiles can be generated using IP. IP can also be used in borehole logging. Constraints: IP cannot be done over frozen ground or asphalt because good contact with the ground is required, like DC resitivitgy. IP is affected by changes in surface relief and lateral changes in resistivity. The electrode array length is about 10 times greater than investigation depth.

•detection of disseminated metallic minerals

•discrimination of clay from silt or sand where formation DC resistivities are similar

Method: Induced polarization is the capacitance effect, or chargeability, exhibited by electrically conductive materials.

Time-domain IP is done by pulsing an electric current into the earth at one or two second intervals through metal electrodes. Disseminated conductive minerals in the ground will discharge the stored electrical energy during the pulse cycle. The decay rate of the discharge is measured by the IP receiver. The decay voltage will be zero if there are no polarizable materials present.

Generally, both IP and resistivity measurements are taken simultaneously during the survey. Survey depth is determined by electrode spacing. The final report products are similar to those of resistivity surveys.

Polarizable Ground

Current injected into the ground causes some materials to becomepolarized. There are two microscopic causes of this macroscopic effect. The phenomenon is called induced polarization, and the physical property that is measured is often called chargeability. The figure below illustrates the phenomenon observed. Note how the measured potential exhibits a delayed response when ground is chargeable. Chargeable ground may take several seconds to returnto equilibrium after it has been polarized with a current source.

Rock / Soil System

Grain

Surface

Pore-Solution

Electrical Transport = Flow + Storage

What is the Interfacial Polarization?

The interface between material with different electrical properties results in charge accumulation under alternating electrical field.Accumulated charges result in polarization (spatially non-uniform charge distribution).

Complex Conductivity

StorageFlow

EitDJD ωε=∂∂

=EJC σ=

EEiJJJ DC** )( σωεσ =+=+=

Value of the complex dielectric constant

"' εεε i+=

is the parameter responsible for the observed phenomena in IP measurements

Nomenclature

**

* 1 ωερ

σ i==

σσσ ′′+′= j*

εεε ′′+′= j*

εωσ ′′−=′

σωεκωε ′′==′ 0'

Flow

Storage

0.010.0120.0140.016

1.E-03 1.E+00 1.E+03 1.E+06

Frequency (Hz)

' (S/

m)

1.E-05

1.E-04

1.E-03

1.E-02

1.E-03 1.E+00 1.E+03 1.E+06

Frequency (Hz)

'' (S

/m)

1.E+001.E+031.E+061.E+09

1.E-03 1.E+00 1.E+03 1.E+06

Frequency (Hz)

κ'

Complex ConductivityBerea Sandstone 0.01M NaCl

Flow

Storage

∞κ

dcσ

0ωεσκ ′′=′

IP

σ ′

Two microsopic effects that cause ground to be chargeable

1)Membrane polarization

2)Electrode polarization

Electrode polarization

Electrode polarization occurs when pore space is blocked by metallic particles. Again charges accumulate when an electric field is applied.

The result is two electrical double layers which add to the voltage measured at the surface.

Membrane polarization

Membrane polarization occurs when pore space narrows to within several boundary layer thicknesses.

Charges accumulate when an electric field is applied.

Result is a net charge dipole which adds to any voltage measured at the surface.

Measured IP data

There are four types of commonly measured IP data.

•Two in the time domain.•Two in the frequency domain•If "small" chargeabilities are assumed, the linear relationship means measured data and chargeabilitiesrecovered by inversion have the same units.•Therefore, all types of data can be approximated byJ = d.

Two types of time domain data

1. Dimensionless, where M = (φs) / (φη), using parameters from the adjacent waveform diagram. This form is difficult to measure directly, but some instruments provide induced polarization measurements in units of mV/V by measuring the decaying portion of this curve at several positions and normalizing these measurements by dividing by the primary voltage (φη). The result is sometimes multiplied by 100 so the apparent chargeability can be thought of as a percent. Also, several such measurements (perhaps 10 or more) may be combined, or recorded individually.

2. The most commonly measured form of time domain IP is the area under the decay curve, specified by the following equation,using parameters specified in the figure.

dttMt

t sm

)(1 2

1∫= φφ

Two types of frequency domain data

1. Data with units known as percent frequency effect (PFE) require the response to be measured at two frequencies. At higher frequencies, the ground has less time to respond, therefore the signal is expected to be smaller. Below is the equation providing PFE, and a figure illustrating how the data are gathered.

1

12 )(

a

aaPPEρ

ρρ −=

2. Data with units of phase are gathered by maintaining careful synchrony between transmitted sine wave and the received signal. Then the phase difference between the source and received signals is recorded as a measure of chargeability. Units are usually milli-radians. The following figure illustrates:

IP surveys use non-polarization electrodes

Rio Nuevo Landfill

A test was conducted in1998 to determine the applicability of geophysics for locating buried waste.

A series of test boring showed high correlation between IP high’s and waste.

A full 3D survey was then conducted which detected not only waste, but also pockets of clay fill.

Interpretation: some techniques & pitfalls

The following are a few comments on interpreting raw chargeability data, listed in no particular order.

•Chargeability measurements involve dynamic signals that are often 10 to 100 times smaller than signals required to obtain resistivity. Therefore results are quite susceptible to noise of all types.•Recall that variations in pseudosections should be "smooth". Spikes or outliers, especially at depth, are likely due to data errors. Stripes on the other hand may be due to individual electrode placements.•Remember also that each value in the pseudosection is an apparentchargeability, so intrinsic chargeability of the earth (i.e. the chargeability structure) must be interpreted just as for resistivity surveys.•The effects of overburden are the same as those discussed in resistivity, but remember that potentials measured are much smaller, so conductive overburden is more difficult to deal with for chargeability.•Occasionally negative apparent chargeability values will be recorded. Intrinsic chargeability can never be negative, but the apparent chargeability can be negative.

Nuclear Magnetic Resonance (NMR)

• NMR is the single geophysical tool directly inquiring the information of the pore fluids• Fluid saturation• Fluid type• Fluid viscosity• Permeability

Proton Precession Magnetometer

• A bottle of liquid (water, or other fluid with a large number of hydrogen nuclei) surrounded by a suitable coil• Accuracy of 0.1 nT (nano-Tesla), constrained by the polarization time,

Proton Precession Magnetometer

• A bottle of liquid (water, or other fluid with a large number of hydrogen nuclei) surrounded by a suitable coil• Accuracy of 0.1 nT (nano-Tesla, or gamma), constrained by the polarization time,bottle of liquid (water, or other fluid with a large number of hydrogen nuclei) surrounded by a suitable coil

BProton Precession

Surface Nuclear Magnetic Resonance (NMR) Survey

Many atomic nuclei, including protons of the hydrogen atoms in water molecules, have a magnetic moment µ. These nuclei can be described in terms of a spinning charges particle. Generally speaking µ is aligned with the local magnetic field B0 of the earth. When another magnetic field is applied, the axis of the spinning proton is deflected, owing to the torque applied. When the second field is removed, the protons generated a relaxation magnetic field as they become realigned along B0 while precessing around with the Larmor frequency:

ω0=γ B0,where γ=0.267518 Hz/nT, the gyromagnetic ratio for hydrogen protons. In SNMR surveys, the measurements use a circular or rectangular loop. An alternating current with a frequency of ω0 is passed through this loop for a limited time τ, so that an excitation intensity (pulse moment) of q=I0τ is achieved. After the current in the loop is shut off, a voltage is induced in the loop by the relaxation of the protons. The initial amplitude of this induced voltage is directly related to the water content; meanwhile, the relaxation time T2 is directly associated with the porosity or grain size.

The protons generated a relaxation magnetic field as they become realigned along local Terrestrial geomagnetic field B0 while precessing around B0 after the excitation current turning off, with the Larmor frequency,

ω0=γ B0,= 0.267518 Hz/nT X 55000 nT = 14,713 Hz

In SNMR surveys, the measurements use a circular or rectangular loop. An alternating current with a frequency is passed through this loop for a limited time t, so that an excitation intensity (pulse moment) of q=I0τ is achieved.

After the current in the loop is shut off, a voltage is induced in the loop by the relaxation of the protons. The initial amplitude of this induced voltage is directly related to the water content; meanwhile, the relaxation time T2 is directly associated with the porosity or grain size.

Spin is a fundamental property of nature like electrical charge or mass. Spin comes in multiples of 1/2 and can be + or -. Protons, electrons, and neutrons possess spin. Individual unpaired electrons, protons, and neutrons each possesses a spin of 1/2. In the deuterium atom ( 2H ), with one unpaired electron, one unpaired proton, and one unpaired neutron, the total electronic spin = 1/2 and the total nuclear spin = 1. Two or more particles with spins having opposite signs can pair up to eliminate the observable manifestations of spin. An example is helium. In nuclear magnetic resonance, it is unpaired nuclear spins that are of importance.

deuterium helium

Properties of Spin

When placed in a magnetic field of strength B, a particle with a net spin can absorb a photon, of frequency f. The frequency f depends on the gyromagnetic ratio, γ, of the particle.

f = γ B

For hydrogen, γ = 42.58 MHz / T.

Nuclei with SpinThe shell model for the nucleus tells us that nucleons, just like electrons, fill orbitals. When the number of protons or neutrons equals 2, 8, 20, 28, 50, 82, and 126, orbitals are filled. Because nucleons have spin, just like electrons do, their spin can pair up when the orbitals are being filled and cancel out. Almost every element in the periodic table has an isotope with a non zero nuclear spin. NMR can only be performed on isotopes whose natural abundance is high enough to be detected. Some of the nuclei routinely used in NMR are listed below.

Nuclei Unpaired Protons Unpaired Neutrons Net Spin γ(MHz/T)1H 1 0 1/2 42.582H 1 1 1 6.5431P 1 0 1/2 17.2523Na 1 2 3/2 11.2714N 1 1 1 3.0813C 0 1 1/2 10.7119F 1 0 1/2 40.08

Energy Levels

To understand how particles with spin behave in a magnetic field, consider a proton. This proton has the property called spin. Think of the spin of this proton as a magnetic moment vector, causing the proton to behave like a tiny magnet with a north and south pole.

When the proton is placed in an external magnetic field, the spin vector of the particle aligns itself with the external field, just like a magnet would. There is a low energy configuration or state where the poles are aligned N-S-N-S and a high energy state N-N-S-S.

Low energy state High energy state

Transitions

This particle can undergo a transition between the two energy states by the absorption of a photon. A particle in the lower energy state absorbs a photon and ends up in the upper energy state. The energy of this photon must exactly match the energy difference between the two states. The energy, E, of a photon is related to its frequency, f , by Plank's constant (h = 6.626x10-34 J s).

E = hf

In NMR and MRI, the quantity is called the resonance frequency and the Larmor frequency.

Energy Level Diagrams

The energy of the two spin states can be represented by an energy level diagram. We have seen that f= γB and E = hf, therefore the energy of the photon needed to cause a transition between the two spin states is

E = hγB

When the energy of the photon matches the energy difference between the two spin states an absorption of energy occurs.

In the NMR experiment, the frequency of the photon is in the radio frequency (RF) range. In NMR spectroscopy, is between 60 and 800 MHz for hydrogen nuclei. In clinical MRI, is typically between 15 and 80 MHz for hydrogen imaging.

Boltzmann Statistics

When a group of spins is placed in a magnetic field, each spin aligns in one of the two possible orientations.

At room temperature, the number of spins in the lower energy level, N+, slightly outnumbers the number in the upper level, N-. Boltzmann statistics tells us that

N-/N+ = e-E/kT.

E is the energy difference between the spin states; k is Boltzmann's constant, 1.3805x10-23 J/Kelvin; and T is the temperature in Kelvin.

As the temperature decreases, so does the ratio N- /N+. As the temperature increases, the ratio approaches one.

Summary: IP and NMR

• Both need more physical insight and high demand of skills• High potential• Surface NMR is still in infancy• NMR holding the promise for environmental & groundwater research

Review Points:1, SI unit system:

base units and derived units;2, Site investigation:

purpose and approaches;3, Material properties:

Mechanic, electric, and electromagnetic;4, Seismic refraction (G228):

how to get 2-layer velocity structure (v1, v2, and layer thickness);5, The Maxwell Equations (G278/378):

constitutive relations, governing equations, and Helmholtz eq.6, DC resistivity:

different type of arrays and their K-factor;7, Geomagnetism:

decomposition of the local geomagnetic vector;features of near-surface anomalies caused by local sources;

8, IP and NMR:types of IP measurements, chargeability, NMR Larmor frequency.