Environmental and Exploration Geophysics I tom.h.wilson Department of Geology and Geography West Virginia University Morgantown, WV Terrain Conductivity Basic Theory

Factors Affecting Terrain Conductivity 1. Porosity: shape and size of pores, number 2. Permeability: size and shape of interconnecting passages 3. The extent to which pores are filled by water, i.e. the moisture content 4. Concentration of dissolved electrolytes 5. Temperature and phase state of the pore water 6. Amount and composition of clays

Clay particles are a source of loosely held cations

Sources of electrolytes include cations adsorbed to clay minerals (i.e. Ca, Mg, H, K, Na and NH 3 ), by-products of chemical weathering (e.g. K and HCO 3 released during the dissolution of feldspar), or as contaminants introduced into the soil or water table Electrolyte conductivity is proportional to total number of ions in solution, their charge and velocity. Net velocity depends on geometry of the current flow path, viscosity and effective cross sectional area. Conductivity of Soils and Rocks As McNeill notes, the conductivity of soils and rocks is primarily electrolytic.

Conductivity of salt solutions is approximated as where C i is the number of gram equivalent weights of the ith ion and M i is the mobility of the ith ion

Conductivity is also influenced by temperature variations in the following form Given  = 0.022/ 0 C  (25 o C) = 20 millimohos/meter

How does the conductivity of the mixture change as we add spherically shaped non- conductive particles to this water filled container? Empirical relationships have been derived that relate conductivity/resistivity to formation porosity for different lithologies

Archie’s Law The general form of Archie’s law noted by McNeill is  b is the conductivity of the mixture (bulk conductivity) and  l the conductivity of the liquid which we assume is water. n is the porosity and m is an empirically derived exponent Note thatand the formation factor

Humble formula for sandstone The Shell formula for low porosity carbonates where McNeill also notes that empirical studies of soil conductivity give rise to additional formulas

One can use these relationships to determine porosity, since the preceding relationships can be rearranged into the general form Archie also modified the relationship for use in determining the proportions of hydrocarbons and water in different parts of a reservoir S water saturation  rw formation resistivity completely saturated with water  rhw resistivity of rock containing the mixture of hydrocarbons and water k empirically derived constant

Plots of porosity vs. formation factor. Recall that the log of this equation will yield a straight line relationship between n and F.

Terrain Conductivity Survey EM31 EM34 Geonics Limited has specially designed these terrain conductivity meters to take advantage of simple relationships between secondary and primary magnetic fields. As the title of McNeill’s Technical Note - Electromagnetic Terrain Conductivity Measurements at Low Induction Number indicates, these instruments assume low induction number.

Low Induction Number A simple linear relationship exists between the primary and secondary fields when subsurface conductivity and the operating frequency of the terrain conductivity meter are confined to certain limits. The general relationship that is made possible by low induction number conditions is that the ratio of the secondary to the primary magnetic field is linearly proportional to the terrain- conductivity. Since the secondary and primary fields are measured directly, their ratio is known. Hence, the net ground conductivity is also known.

HpHp Surface Contamination Plume HsHs TransmitterReceiver

HpHp Surface Contamination Plume HsHs H S secondary magnetic field at receiver coil H P primary magnetic field  = 2  f f = frequency  o = magnetic permeability of free space  = ground conductivity s = intercoil spacing (m) i =

HpHp Surface Contamination Plume HsHs s f refers to the frequency of the alternating current in the transmitter coil The operating frequency is adjusted depending on the intercoil spacing Together, the EM31 and EM34 provide 4 different intercoil spacings and two different coil orientations. The coils can be oriented to produce either the vertical or horizontal dipole field.

What is induction number? B induction number s intercoil spacing  skin depth depth at which amplitude of the em field drops to 1/e of the source or primary amplitude e natural base - equals /e ~0.37 In general for a plane wave, the peak amplitude (A r ) of an oscillating em field at a distance r from the source will drop off as -

 is an attenuation coefficient The distance  is referred to as the skin depth

The attenuation factor  varies in proportion to the frequency of the electromagnetic wave. Higher frequencies are attenuated more than lower frequencies over the same distance. Hence if you want to have greater depth of penetration/investigation, lower frequencies are needed. As a rough estimate,  (the skin depth) can be approximated by the following relationship

We could also write this as  is the skin depth f is the frequency of the em wave  is the conductivity  is the resistivity The operating frequencies for the different intercoil spacings are

Note that the frequency drops as the intercoil spacing is increased. The larger intercoil spacings and lower operating frequencies provide greater depth of penetration Induction number Recall, induction number B is the ratio of intercoil spacing to skin depth and that skin depth is a function of operating frequency and ground conductivity.

In the following table we examine the effect of operating frequency, intercoil spacing and ground conductivity on the induction number. Recall -

McNeill suggests in the case of the EM31 that operation under the assumption of low induction number is valid for ground conductivity of about 100 mmhos/meter and less.

McNeill doesn’t provide us with specific numbers. One gets the impression that induction numbers of 0.2 or less can be considered “low” induction numbers. Using that as a criterion, we can see that the EM34 exceeds the low induction number criterion in high ground conductivity areas. However - in favor of this assumption is the fact that ground conductivity in general tends to be much less than 100 mmhos/meter

Terrain conductivities in the darker areas are 22 mmhos/meter and greater. The terrain coductivities in the white areas are less than 6 mmhos/meter. Fahringer (1999)

Vertical Dipole Horizontal Dipole Changing the dipole orientation changes the depth of penetration and thus the instrument response will provide information about apparent ground conductivity at different depths. McNeill refers to these “depths of investigation” as exploration depths. The orientation of the dipole is easily controlled by changing the orientation of the coil. As suggested by the drawing, the vertical dipole will have a greater depth of penetration than the horizontal dipole.

Vertical dipole mode of operation Exploration Depths “Rule of Thumb”

The concept of an exploration depth is oversimplified though. The real truth of the matter - as McNeill points out - is that the apparent conductivity measured at the surface by the conductivity meter is a composite response - a superposition of responses or contributions from the entire subsurface medium. The contribution from arbitrary depths is defined by the relative response function  (z), where z is the depth divided by the intercoil spacing.

Note that the relative response function for the horizontal dipole  h is much more sensitive to near-surface conductivity variations and that its response or sensitivity drops off rapidly with depth Vertical dipole interaction has no sensitivity to surface conductivity, reaches peak sensitivity at z ~0.5, and is more sensitive to conductivity at greater depths than is the horizontal dipole.

The contribution of this thin layer to the overall ground conductivity is proportional to the value of the relative response function at that depth. Constant conductivity 

The contribution of a layer to the overall ground conductivity is proportional to the area under the relative response function over the range of depths (Z 2 -Z 1 ) spanned by that layer. Z1Z1 Z2Z2

As you might expect, the contribution to ground conductivity of a layer of constant conductivity that extends significant distances beneath the surface (i.e. homogenous half-space) is proportional to the total area under the relative response function.

So in general the contribution of several layers to the overall ground conductivity will be in proportion to the areas under the relative response function spanned by each layer.

You all will recognize these area diagrams as integrals. The contribution of a given layer to the overall ground conductivity at the surface above it is proportional to the integral of the relative response function over the range of depths spanned by the layer.

McNeill introduces another function, R(z) - the cumulative response function - which he relies on to compute the ground conductivity from a given distribution of conductivity layers beneath the surface. The following diagrams are intended to help you visualize the relationship between R(z) and  (z).

Each point on the R V (z) curve represents the area under the  V (z) curve from z to .

Z2Z2

Consider one additional integral - How would you express this integral as a difference of cumulative response functions?

Note that R(0) = 1, hence

According to our earlier reasoning - the contribution of a single conductivity layer to the measured ground (or terrain) conductivity is proportional to the area under the relative response function. The apparent conductivity measured by the terrain conductivity meter at the surface is the sum total of the contributions from all layers. We know that each of the areas under the relative response curve can be expressed as a difference between cumulative response functions

Let’s consider the following problem, which is taken directly from McNeill’s technical report (TN6).

Visually, the solution looks like this..

Compare this result to that of McNeill’s (see page 8 TN6). Mathematical formulation -

In this relationship  a is the apparent conductivity measured by the conductivity meter. The dependence of the apparent conductivity on intercoil spacing is imbedded in the values of z. Z for a 10 meter intercoil spacing will be different from z for the 20 meter intercoil spacing. The above equation is written in general form and applies to either the horizontal or vertical dipole configuration.

In the appendix of McNeill (TN6) notes that the assumption of low induction number yields simple algebraic expressions for the relative and cumulative response functions. We can use these relationships to compute specific values of R for given zs.

The simple algebraic expressions for R V (z) and R H (z) make it easy for us to compute the terms in the problem McNeill gives us. In that problem z 1 is given as 0.5 and z 2 as 1 and 1.5 Assuming a vertical dipole orientation R V (z=0.5) ~ 0.71 R V (z=1.0) ~ 0.45 R V (z=1.5) ~ 0.32

 1 =20 mmhos/m  2 =2 mmhos/m  3 =20 mmhos/m Z 1 = 0.5 Z 2 = 1 and 1.5 Substituting in the following for the case where Z 2 =1.

Here’s a problem for you to work through before our next class. Mine spoil surface AMD contamination zone Pit Floor A terrain conductivity survey is planned using the EM31 meter (3.66 m (or 12 foot) intercoil spacing). Our hypothetical survey was conducted over a mine spoil to locate migration pathways within the spoil through which acidic mine drainage as well as neutralizing treatment are being transported. Scattered borehole data across the spoil suggest that these paths are approximately 10 feet thick and several meters in width. Borehole resistivity logs indicate that areas of the spoil surrounding these conduits have low conductivity averaging about 4mmhos/m. The bedrock or pavement at the base of the spoil also has a conductivity of approximately 4mmhos/m. Depth to the pavement in the area of the proposed survey is approximately 60 feet. Conductivity of the AMD transport channels is estimated to be approximately 100mmhos/m. ~10ft ~60ft

A. Evaluate the possibility that the EM31 will be able to detect high conductivity transport zones with depth-to-top of 30feet. Evaluate only for the vertical dipole mode. It may help to draw a cross section.

How many different conductivity layers will you actually have to consider? Does it matter whether d (depth) and s (intercoil spacing) are in feet or meters? Set up your equation following the example presented by McNeill and reviewed in class, and solve for the apparent conductivity recorded by the EM31 over this area of the spoil. Bring your work in and be prepared to discuss it at the beginning of the next class. Note - a table of R values are presented on the following page.

Z R V R H

Continue the readings in Reynolds’ text Bring today’s problem to next class for discussion