aglo

Unique characteristics of IP


 

Introduction

As for other sections of this module on IP surveying, the physical principles of DC resistivity surveying should be understood prior to learning about induced polarization.

Modeling the chargeability phenomenon

The behaviour of charging and decay curves versus time is logarithmic, not exponential as for a simple parallel resistor-capacitor circuit. Therefore, a more complicated model is required for explaining the induced polarization phenomenon. One model is the circuit shown below (from Ward, 1990). The impedance between points 1 and 2 is complex and is modeled empirically as Z(w).

This is known as the Cole-Cole model, and the three parameters in the complex part (m or M, c, & τ) are known as Cole-Cole parameters. M (or m) is chargeability, τ is a time constant (of the decay curve), and c is a parameter controlling the frequency dependance. From several studies, τ appears to depend on rock type, and c tends to be poorly dependent on rock type.

For more discussion, see the page on spectral IP.

The adjacent figure (top) shows the frequency and phase behaviour of this circuit with its complex impedance. Phase is maximum at the amplitude curve's inflection point.

In the time domain, response of this circuit to a transient shut-off is an instantaneous drop from VDC to mVDC, followed by a decay, with time constant determined by the reactive component (bottom panel).

Note that m (different from M in the discussion of data acquisition) has units of mV per V, i.e. it is unitless. Its value is 0 > m > 1, and it is one "definition" of chargeability, due to Seigle, 1959.

Frequency response, sine-wave excitation 


Transient response square-wave excitation.

Inductive coupling

The fact that data are gathered using very high powered time-varying signals that are imposed on wires lying on the ground means there will be electromagnetic effects in the data. Think of it as the receiver seeing two impedances in parallel; one is due to the physical properties in the ground, and the other is due to the coupled system of wires and ground. This effect is most significant over conductive ground.

Time domain measurements can try to avoid the effect by recording at later times after the effects of the wiring have decayed, but then signals also become very small.

EM coupling cannot be easily removed from phase and frequency measurements because the measured effect (PFE or phase) is the sum of the ground's complex resistivity and the EM coupling effect. But these methods are often preferred in conductive ground because they are less susceptible to other types of noise.

There has been plenty of work aimed at separating EM effects (inductive coupling) from true chargeability effects. Much of the work is based on how the Cole-Cole parameters differ for natural and coupling effects; the inductive coupling component of the signal, τ tends to be small compared to the geologic response, while the component, c, tends to be large compared to the geologic response. In fact, most researchers model the complete situation as consisting of two Cole-Cole impedances instead of only the one from the ground. For details see the appendix on spectral IP. The system response is written as Z(w) = Z1(w) + Z2(w), so there are two versions each of m, τ, and c; one set for the ground's response, and one set for the inductive response. The figure above from Telford, Geldart and Sheriff, 1990, (figure 9.10) shows an example of the situation.

The effect can be forward modeled if the conductivity structure is known, but this is rarely the case since estimating resistivity structure is one of the goals of the survey. However, if a model of intrinsic resitivities in the earth can be obtained (for example, by rigorous inversion of primary voltage data), that resistivity model can be used to calculate the EM response. Then that response can be subtracted from the chargeability data and the residual inverted for the ground's true IP response. See Routh and Oldenburg, 2001, (referenced below) for details of this approach.

Negative apparent chargeabilities

Occasionally, negative apparent chargeability values will be recorded. Note that intrinsic chargeability can never be negative, but apparent chargeability can be negative. In particular, negative IP measurements will occur on time domain data when the off-time voltage drops below zero before decaying. This effect can be caused by EM coupling on flanks of 3-D targets, and over layered Earth structures of types K (ρ1 < ρ2 > ρ3) and Q (ρ1 > ρ2 > ρ3).

To understand how negative apparent chargeabilities can occur, think of what a time domain survey records. Secondary voltages (off-time voltages) are usually the same sign as primary (on-time) voltages because current flow during dis-charging (as charges revert to equilibrium) is in the same direction as during charging. If net current flow seen by the potential electrodes is in the opposite direction, the off-time decay curve will look upside down. The result is a negative apparent chargeability. Negative apparent chargeability is also possible in phase data.

2D and 3D chargeable bodies can cause negative effects on account of the combined geometry of discharge currents and electrode arrays.

To understand the mechanism with layered media, it is best to refer to Nabighian and Elliot, 1976 (see below). They also list numerous earlier papers that show field examples of negative IP response in the presence of 2D and 3D targets.


References

  1. Ward S.H., 1990, "Resistivity and induced polarization methods, in Geotechnical and Environmental Geophysics", Published by the Society of Exploration Geophysicists, 1991.
  2. Siegel. H.O., 1959, "Mathematical formulation and type curves for induced polarization", Geophysics, 38, 49-60.
  3. Routh, P.S., and Oldenburg, D.W., 2001, "Electromagnetic coupling in frequency-domain induced polarization: a method for removal", Geophysical Journal International, Vol 145, pp 59 - 76.
  4. M.N. Nabighian and C.L. Elliot, "Negative induced-polarization effects from layered media", 1976, Geophysics, 41, 6A, pg 1236-1255.