Download White Paper - Willowstick

White Paper
On
Willowstick Technology
Used For
Mapping and Modeling
Groundwater Systems
132 E 13065 S
Suite 100
Draper, UT 84020
USA
(801) 984-9850
www.willowstick.com
Table of Contents
1.0 Introduction ............................................................................................................... 3 2.0 Process and Application of the Technology ............................................................ 4 3.0 Electrical-Hydraulic Correlation ............................................................................ 4 4.0 Survey Design and Energizing Configurations ...................................................... 8 5.0 Equipment ................................................................................................................. 9 6.0 The Physics behind the Technology ...................................................................... 10 7.0 Quality Control Measures ...................................................................................... 13 8.0 Data Normalization and Reduction....................................................................... 14 9.0 Criteria to Distinguish Near-Surface Interference .............................................. 16 10.0 Magnetic Field Contour Map ................................................................................ 18 11.0 Predicted Magnetic Field Map and Ratio Response Map................................... 19 12.0 Modeling .................................................................................................................. 21 13.0 Summary.................................................................................................................. 23 14.0 Contact Information ............................................................................................... 24 15.0 Patent ....................................................................................................................... 24 © 2014 Willowstick Technologies LLC
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1.0
Introduction
Willowstick® Technology (the “Technology”) delineates and characterizes subsurface aqueous
systems in complex hydrogeologic settings. It has consistently proven valuable in: 1) the
diagnosis of seepage through earthen dams and levees; 2) characterizing groundwater infiltration
into surface and subsurface mines; 3) tracking pollution plumes influenced by groundwater
transport; 4) optimizing well placement for production and/or monitoring purposes; 5) identifying
and mapping geothermal production zones; 6) delineating salt and fresh water reaction fronts; and
7) optimizing water flood activities in oil and gas recovery operations as well as other in-situ
solution mining processes.
The Technology has clearly demonstrated that a better understanding of groundwater conditions
can significantly reduce costs, increase revenues, and improve safety factors for those dealing
with groundwater-related issues. In the case of a mine, for example, groundwater control may be
a key to long-term sustainability of productive and safe mine operations. In the case of dams,
being able to understand the location of seepage flow paths allows for cost-effective remediation
to prevent dam failure and mitigate danger to lives and property.
Historically the most rigorous methods of characterizing and delineating subsurface features have
been by direct observation or measurement of subsurface properties. Generally, this involves
drilling observation wells. Although this approach can be effective, it becomes increasingly costprohibitive and impractical beyond a certain extent—yielding only a limited set of data from
which broad interpolations and extrapolations must be made. Too often critical decisions are
based on interpolations that fail to depict complex and acute changes that occur in the subsurface.
To mitigate the risk factors involved in making difficult groundwater related decisions,
Willowstick developed the Technology to quickly and efficiently locate preferential groundwater
flow paths without being intrusive or harming the environment. The Technology significantly
reduces both time and expense associated with seepage diagnosis or general groundwater
characterization, especially when used in conjunction with monitoring well data, and other
hydrogeologic information.
The Technology measures the magnetic field produced by the distribution of electric current to
track patterns that help characterize preferential groundwater flow. It differs in many ways from
traditional resistivity and other electromagnetic (EM) methods. First, it capitalizes on the fact
that water content is a dominant factor in enhancing the subsurface electrical conductivity of soil
and rock. Second, by directly energizing a conductive groundwater medium with strategic
electrode placement, the electric field can more effectively “illuminate” the target of interest with
less interference from overlying layers.
This “White Paper” presents an explanation of the Technology, including:
 a discussion of processes and typical application of the Technology
 a discussion on the electrical-hydraulic conductivity correlation to understand why the
Technology works
 a high level presentation of how the Technology works, including field work procedures,
quality control measures, data reduction approaches, and interpretation methods used to
accurately identify, map, and model subsurface groundwater systems.
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2.0
Process and Application of the Technology
After determining the groundwater of interest, the process deployed in using the Technology
involves placing electrodes in direct contact with that groundwater to create an AC electric circuit
that follows the groundwater’s natural course. The electric current may also flow through
surrounding geology to some degree. Resulting flow patterns are characterized by the magnetic
field signature they produce. These magnetic field components are measured at numerous
stations to then define the electrical current’s subsurface distribution and flow patterns. As a
critical element to data processing, measurement station coordinates are obtained from the Global
Positioning System (GPS) and recorded along with the magnetic field data. Measured data is
processed and compared to the predicted magnetic field from a theoretical homogeneous earth
model to highlight the deviations from this uniform model. Finally, magnetic field contour maps
and inversion models are created and are interpreted in conjunction with other hydrogeologic data
to provide enhanced definition of preferential groundwater flow paths.
The Willowstick methodology is illustrated plainly by considering the case of a leaking dam.
Electrodes are placed upstream and downstream of the dam to drive the electrical energy through
the dam and more particularly through the leakage flow paths. The upstream electrode is placed
in the reservoir at a sufficient distance from the dam to allow electric current sufficient space to
spread out in the reservoir before reaching the face of the embankment. The downstream
electrode is placed in a strategic location (seep, observation well, or seepage collection system
such as a toe drain) to facilitate contact with the water seeping through the dam. As the electric
circuit flows between the two electrodes, the subsurface distribution of electric current is
measured at the earth’s surface by recording the associated magnetic field at pre-defined
measurement station locations. The result, after filtering and modeling of the data is the
demonstration of paths or zones in the subsurface of highest transport porosity.
3.0
Electrical-Hydraulic Correlation
Although the two processes of electrical and hydraulic conduction are governed by very different
principles, electric current flow can be used to qualitatively infer a general distribution of
hydraulic conductance in the subsurface.
Hydraulic conductivity is the ability of a material to conduct water when pressure is applied. It is
a function of interconnected pore volume (effective porosity—sometimes referred to as transport
porosity). The larger and better connected the pore spaces, the greater the hydraulic conductivity
and the easier and faster water will flow through the earthen material given a potentiometric
gradient.
Electrical conductivity of earthen materials is largely a function of the availability of free ions
and the presence of a transporting medium (water) to allow ion movement. Most earthen
materials are fundamentally electrical insulators with electrical conductivities ranging between
10-12 and 10-17 mho/m. Yet, in-situ measurements of electrical conductivities range from 10-1 to
10-8 mho/m—many orders of magnitude higher. This discrepancy is due to conduction of
electrical current by way of ions dissolved in the groundwater. Recognizing that water is usually
the primary facilitator of electric conduction in the typical geologic environment, the Technology
efficiently tracks groundwater paths by detecting differences in the magnetic field intensity
arising with changes in electric current density.
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The Technology naturally works best in environments where the degree of water saturation varies
(i.e., between dry and highly saturated areas). It also works well within a completely saturated
environment. When electrical conduction occurs primarily in open pore space of a saturated
matrix, a positive slope correlation exists between electrical and hydraulic conductivities –
meaning that hydraulic conductivity can be tracked along the higher electrical conductivity zones.
This relationship has been documented and supported by many published laboratory and field
investigations1. When electrical conduction occurs primarily along pore surfaces, such as in wet
clay, the positive correlation may disappear and can in fact become a negative correlation2. In
each environment, the Technology provides valuable information by highlighting edges of zones
with greater effective porosity, thus revealing pathways where groundwater flows and areas
where groundwater does not flow.
To better illustrate the point, consider water flowing around a large boulder in a river. Even if the
boulder itself could not be observed directly, its shape and location is still revealed by the pattern
and direction of water flow around it. Electric current flows in much the same way. If we
consider the opposite case, where a large conductive body attracts the electric current flow to
itself, the analogy would be more like that of water flowing into a submerged drain. Here the
anomalous gradient in the water surface would reveal the drain’s location, just as an increase of
electric current density within a conductive body would reveal its location.
Figure 3A – (Left) Water flows around a boulder in a river. (Right) Water passing by a
submerged drain.
1
Wong, P., J. Koplik, and J. P. Tomanic, Conductivity and permeability of rocks, Phys. Rev. B Condens.
Matter, 30, 6606–6614, 1984
2
Purvance, D. T., and R. Andricevic, On the electrical-hydraulic conductivity correlation in aquifers,
Water Resources Research, 36, 2905–2913, October 2000
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A simple lab experiment demonstrates how the distribution of electric current flow identifies the
edges of resistive and conductive bodies. Two electrodes were placed in a 4 ft by 8 ft tub of
silty/clay, and saline water. Three granite slabs were placed in the tub with the silty clay and were
arranged so that electric current would have to flow around the slabs to reach the opposite
electrode (see Figure 3B). An AC electrical current was passed through the tub and a magnetic
field was measured over the surface of the tub with a three axis AC magnetometer. Measurements
on a fine grid (1.6 x 1.6 cm) were used to detail the anomalous zones around and between the
granite slabs.
Figure 3B – Experimental Setup with Granite Slabs and Silty/Clay Fill
Figure 3C – Magnetic Field map identifies areas of anomalous electric current flow in tub
Figure 3C shows the experiment’s magnetic field map with each slab’s position indicated on the
map. The dark green magnetic field anomalies clearly indicate that electric current flows around
and between the granite slabs in the saturated soil. The areas under the granite slabs have
relatively low magnetic fields—lighter green shading from the absence of current flow in these
areas. Two other small anomalous features are worth mentioning. Anomaly “A” is due to water
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pooling in a low spot, and Anomaly “B” is where small amounts of water seeped beneath the
slab.
Next, an inversion of the magnetic field data was performed to generate a model of
electric current distribution in the tub. Figure 3D is a horizontal slice from this model.
The green shading identifies where electric current is more concentrated, while the purple
shading identifies where electric current is less concentrated. As can be seen, the
inversion identifies accurately where current flow is the greatest between and around the
slabs. The slabs edges are also highlighted well in most places (sharp transitions between
conductive and nonconductive areas). It is easy to see in this example where to locate a
well, because the higher relative electrical conductivity of the saturated soils between the
rocks is the preferential flow path for both water and electric current.
Figure 3D – ECD model identifies areas of anomalous electric current flow in the tub
Compared to this experiment, geologic conditions in real-world scenarios present
much weaker contrasts in electric current density, but the Technology’s magnetic field
sensors are also far more sensitive than that used for this experiment. Conductivities in
saturated, unconsolidated sediments generally do not vary dramatically. In many
instances saturated clays have a slightly higher conductivity than saturated sand or waterfilled void space because of the clay surface conduction pathways. Therefore, there is
still a question as to whether this Technology would illuminate a seepage flow path in a
saturated clay environment. Experience with the Technology shows that, even in a
saturated clay environment, seepage flow paths can be identified by detecting edges
where the conductivity changes. If the water pathway is less conductive compared to the
clay, electric current will “bunch up” around the edge because it prefers to flow in the
more conductive medium. More often than not, seepage flow is bounded on all sides;
therefore, electric current will concentrate around the seep and flow horizontally along
the seepage pathway. As a result, the zone of highest transport porosity or highest
hydraulic conductivity is identified.
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4.0
Survey Design and Energizing Configurations
In any Willowstick groundwater investigation, electrode placement is critical to targeting
groundwater flows of interest. In general, electrode configurations may be classified into two
types: a horizontal configuration or a vertical configuration. For most investigations, a horizontal
electrode configuration is employed to inject the electric current into the groundwater of interest.
Electrodes are specifically placed in contact with the groundwater of interest on either side of the
study area. A horizontal configuration establishes a predominantly horizontal flow of electric
current in the subsurface study area (see Figure 4A).
Figure 4A - Typical Horizontal Electrode Configuration (Cross Sectional View)
For some investigations, a vertical electrode configuration is more appropriate, such as when
mapping a contamination plume’s growth from a central source (see Figure 4B). This type of
setup can also be utilized to reduce interference from surface culture like metal pipes, the power
grid grounding wires, railroad tracks, steel fences, etc. For this type of configuration to work
well, a relatively resistive layer should exist between the upper and lower electrodes so that
electric current will spread out sufficiently from the upper electrode (see Figure 4B).
Figure 4B - Typical Vertical Electrode Configuration (Cross Sectional View)
Typical Willowstick surveys can range from less than one acre to many square kilometers in
coverage. The only condition is that an electric circuit must be properly established with the
groundwater of interest sufficient to create a detectable magnetic field.
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Electrode placement is critical to every investigation. Electrodes are often placed in wells,
reservoirs, ponds, seeps, springs, canals or other sources where there can be direct contact with
the groundwater of interest. In some circumstances, electrodes can be placed directly in the
ground. Electrode placement depends entirely on site-specific conditions and the overall purpose
of the investigation. Normally, wells are required for deep groundwater characterization and
confined aquifers. However, for shallower applications (unconfined aquifers), wells are often
ideal, but not required.
The Technology can be used to characterize groundwater at depths over 300 meters (1000 feet) as
long as the Willowstick receiver can resolve the magnetic field emanating from the targeted zone
of interest. In the case of a vertical configuration, the depth of investigation is usually fixed along
a separation of hydrogeologic layers; therefore, the separation between electrodes is largely
dependent upon geologic conditions.
To minimize interference from the circuit wire in a horizontal electrode configuration, the circuit
wire is carefully placed in a large loop around the area of investigation. A strong but predictable
magnetic field is created by electric current flowing in the circuit wire. In the case of a vertical
electrode configuration, the two circuit wires connecting the power supply to the electrodes are
wound in a twisted pair along the ground surface to create a canceling effect on the magnetic field
produced by AC electric current flowing in the two wires, since electric current in each wire
flows in an opposite direction at any given moment. As a result, the circuit wire on the ground in
a vertical configuration has little or no effect on the magnetic field measurements. Electrode
configurations are designed to maximize the amount of electric current to flow through the
subsurface zones of interest.
As electricity flows through the circuit and subsurface study area, magnetic field measurements
are recorded from pre-designed measurement stations. Generally, a survey is performed on a grid
with measurement station spacing between 5 and 33 meters, depending upon resolution
requirements, the target depth, and other site conditions. The grid pattern proposed for any
particular investigation is designed to provide sufficient detail and resolution to adequately
delineate the groundwater of interest without exceeding budgeted expenses for the investigation.
It should be noted that although the Technology can quickly and accurately infer the location of
groundwater and preferential flow paths, it does not necessarily identify the volume of water or
the direction or flow along a particular pathway. The groundwater flow rate and direction should
be determined by other field methods such as pump tests, water bearing formation characteristics,
regional groundwater flow, topographic slope, and/or potentiometric head differences, etc.
5.0
Equipment
The field equipment used to carry out a Willowstick investigation includes: electrodes, circuit
wire, power generating equipment (frequency converter and generator), GPS unit, and the
Willowstick Receiver.
The Willowstick Instrument measures subtle changes in the magnetic field associated with
subsurface electric current flow. It is capable of detecting the magnetic field produced by 1/10th
of an amp of current from up to one mile away. The Instrument is attached to a surveyor’s pole
and hand-carried to each measurement station (see Figure 5A).
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Figure 5A – The Willowstick Instrument
6.0
The Physics behind the Technology
The Willowstick Technology uses a controlled source to inject electrical current into the
groundwater of interest. A specific signature frequency is used which avoids the harmonics of
the power frequencies that are in common use around the world. With adherence to the BiotSavart Law—which precisely describes how magnetic fields are generated by electric currents—
the distribution of subsurface electric current flow can be mapped by carefully measuring the
magnetic field.
Figure 6A demonstrates a well known concept in physics, that an electric current flowing through
an infinite wire produces a magnetic field looping around the wire. In this simplified example,
the magnetic field intensity is given by B   0 I / 2R , where R is the radial distance from the
center of the wire, I is the current in Amps, and  0 is the permeability of free space constant,
4  x10-7 Tm/A.
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Figure 6A – Magnetic Field Lines
around an Electric Current-carrying Wire
The magnetic field’s direction is given by the right-hand rule: if the wire is grasped with the right
hand so that the thumb points in the direction of positive electric current flow, the fingers curl
around the wire in the magnetic field direction.
Measured differences in magnitude and direction of the magnetic field are used to identify the
vertical and horizontal position of subsurface electric current flow. In Figure 6B for example, at
Point A left of the current source both the vertical (V) and horizontal (H) components of the
magnetic field are positive (up and to the right, respectively), hence they both have positive
polarity.
Figure 6B – Magnetic Field Components
over an Electric Current Source
At Point B to the right of the current source, the vertical field is negative (downward) while the
horizontal component is still positive. Hence, V and H have opposite polarity at Point B. When
survey lines cross over a source of concentrated electric current flow, these changes in the V and
H signals can be observed.
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The raw horizontal magnetic field contour map—or “footprint” map as it is sometimes called—
developed with the Technology is used to identify the horizontal position of electric current
distribution beneath the study area (see Figure 6C). The vertical position (depth) is determined
by further processing and modeling. The initial footprint map simply reveals anomalous areas of
high and low electric current flow beneath the study area.
Figure 6C – Typical Initial Magnetic Field “Footprint” Map
The Willowstick method is easily distinguishable from resistivity and other electro-magnetic
(EM) geophysical methods. The Technology, as a geophysical method, can be described
technically as a controlled-source, audio-frequency-domain magnetic method. Unlike EM
methods, it does not involve the transmission and receiving of coupled electro-magnetic fields,
which can be sharply attenuated by shallow conductive layers. It does not require galvanic
(point-contact) measurement of electric fields as with the much slower resistivity method. It also
allows targets of interest to be directly energized by the electric field, while the resulting
magnetic field largely bypasses the common inhibitors, such as shallow wet clay layers, that tend
to blind the EM and resistivity methods.
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7.0
Quality Control Measures
Three basic criteria are used to determine the quality of the magnetic field data measured and
recorded by the Willowstick Receiver:
1. Circuit continuity between electrodes
2. Signal-to-noise ratios
3. Signal repeatability
Circuit Continuity
As stated, the magnetic field is created by a large electric circuit consisting of (1) the power
supply, (2) the circuit wire, (3) the electrodes, and (4) the subsurface study area between the
strategically placed electrodes. Circuit continuity refers to whether or not an electric current, and
how much electrical current, can be driven through the subsurface study area from the given
points of coupling with the earth (electrodes). Depending on the size of the study area and depth
of investigation, a low level of electric current is typically sufficient to generate a strong enough
signal for a survey. In the case where too little or no electric current flow can be driven between
electrodes, the setup is said to have “poor continuity,” and an alternate location must be found for
one or both electrodes.
Signal to Noise Ratio
Signal to Noise Ratio (SNR) means the ratio of the signal to the mean ambient field noise, which
is determined from a sampling of other non-harmonic frequencies in the spectrum. This signal to
noise ratio is computed for each measurement and used to help indicate the data reliability (see
Figure 7A).
Figure 7A – Typical Signal to Noise Map
SNR is monitored continuously to ensure adequate signal strength. If the SNR falls below a
specified value, the data is considered unreliable. Low signal-to-noise ratios in a particular area
typically indicate one of the following conditions:
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1. There is no conductive media in the study area for the electrical current to concentrate or
follow.
2. The area of low signal-to-noise is partially isolated, limiting electric current flow.
3. The electric current flow is highly dispersed throughout the study area and is not
concentrating in any one particular area or pathway.
Considering the vastly different possibilities of geologic, electrical and hydrologic conditions,
every project is highly unique. Therefore the principal challenge of every survey is to establish
electric current flow that will follow and stay focused in the targeted study area. Signal-to-noise
maps show where the signal strength stands well above the background noise. If the signal-tonoise criteria is not met, then it can generally be inferred either that: (1) the study area lacks
preferential flow paths, or (2) a different electrode configuration needs to be employed to better
bias electric current flow through the area of interest.
Signal Repeatability
Repeatability is determined from base station and field instrument readings taken throughout the
course of the fieldwork. Repeatability tests are performed frequently to ensure proper calibration
and performance of field equipment.
8.0
Data Normalization and Reduction
The analysis of the magnetic field data entails reduction of the data modeling and interpretation.
In so doing, the data is subject to a number of comparisons and corrections to account for: (1)
possible differences between instruments used in the investigation; (2) transmitter current drift or
diurnal magnetic drift related to ionosphere activity, etc.; (3) ground noises or man-made
interferences (power grid grounding wires and other long continuous conductors including metal
pipelines, railroad tracks, steel fence lines, etc.); and (4) effects of the electric current bias
(electrode and circuit wire locations).
Correction for differences between Instruments
Sensitivities of instruments used on any particular project may vary slightly. To account for
instrument differences, each instrument takes measurements at the same position (base station)
numerous times throughout the course of the survey. The mean of each instrument’s base
readings is compared to the static base and the other field instruments, allowing for slight
adjustments to be made that effectively normalize the instruments.
Drift Correction
During a survey, the magnetic field amplitude may drift slightly over time. The largest source of
drift is usually the transmitter current, given that the earth-circuit resistance can vary to some
degree. The transmitter current is logged continuously throughout the day. Normally, the
variation in the electric current is very small, but in some locations where water levels are
changing, the transmitter current may fluctuate by more than 10%. To correct for any drift
caused by the transmitter current (Figure 8A), the mean of the current is normalized to 1 and then
a correction factor is calculated for any deviation from the mean. This correction is applied to the
magnetic field data collected over the course of the survey.
To make sure the transmitter’s electric current source is the only cause of magnetic field drift, a
static receiver also monitors the magnetic field at the base station. This magnetic field log is then
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used to correct for any residual drift that may occur. These extra variations are rare but can occur
due to extraneous natural or man-made sources.
Figure 8A – Correction for Transmitter Current
Correction for Electric Current Bias, Circuit Wire, and Conductive Culture
When analyzing, interpreting and/or modeling magnetic field data, it is important to remember
that the three strongest influences on electric current flow through the subsurface are: (1)
groundwater and surrounding materials; (2) conductive cultural features such as underground
pipes or wires; (3) electric current bias (i.e., electrode placement).
1. Groundwater and surrounding materials. The Technology is based on the principle
that its signature electric current is strongly influenced by the presence of
groundwater or areas of greatest transport porosity where groundwater accumulates
and/or flows relatively freely through the subsurface. In most settings when the
electrodes are placed properly, the electrical current will naturally gather and
concentrate in areas or pathways of higher conductivity.
2. Conductive cultural features. The magnetic field may be influenced by near-surface
conductive man-made culture, such as metal pipelines, power system grounding
wires, steel fence lines, railroad tracks or other long continuous conductors. Culture
is not always present, but it is often a factor and sometimes very problematic because
it can cause large anomalies that overshadow the magnetic signal generated from
subsurface electric current flow. The best approach, when surveying an area with
conductive culture is to identify the conductive features before a survey is initiated
and strategically design the survey to avoid “as much as possible” any long
conductive feature. Because conductive features sometimes exist within a study area,
avoiding conductive culture can be difficult. Fortunately, the locations of most of
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these features are known. Therefore, the influence of cultural conductors can be
removed and/or taken into account when interpreting the data.
3. Electric Current Bias. The magnetic field in any given survey is always subject to
electrical current bias because of the placement and position of electrodes and circuit
wire. Electric current must travel from one electrode to the other to complete its
circuit. Therefore, the electrodes and circuit wire are a chief source of extraneous
magnetic fields. It is always true that 100% of the electric current must flow through
the circuit wire and concentrate in and out of the points of coupling (the electrodes).
Hence the magnetic field tends to grow much stronger as it nears the electrodes.
To properly interpret the magnetic field data, it is critical that these influences be identified and
separated. This is accomplished primarily with finite element computer codes that predict the
electric current flow and resulting magnetic field model for the given terrain and survey setup
based on a homogeneous subsurface scenario. Magnetic field effects from the circuit wire, and in
some cases from conductive cultural features, can also be predicted. In the next section, the
removal and/or attenuation of cultural effects will be discussed in more detail. Once the effects
from the electric current bias, the circuit wire, and any conductive culture are removed, the data
more easily reveals electric current flow patterns and thus aids in the determination of
groundwater flow based on the distribution of electric current beneath the study area.
9.0
Criteria to Distinguish Near-Surface Interference
Stray electric current flowing onto near-surface conductive culture can be problematic for
interpreting electric current flow at depth. Therefore, in some cases it becomes necessary to
remove near-surface interference in order to properly interpret the distribution of electric current
flow in the subsurface. Near-surface interferences are distinguished by three criteria:
1) Normalized Gradient Filter
2) Distance from Culture
3) Point-specific Professional Judgment
Normalized Gradient Filter
An analysis of magnetic field gradients provides a good way to separate signals caused by nearsurface conductors from signals that originate at depth. In Figure 9A, both shallow or overhead
(red dot) and deep (green dot) conductors are represented by energized wires running
perpendicular to the page through the points shown.
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Figure 9A – Normalized Gradient Filter
The red and green curves show the horizontal magnetic field measured at ground level for the
corresponding wires. Figure 9A demonstrates that near-surface conductors (red) cause anomalies
having much steeper slopes or higher gradients than signals originating from depth (green);
therefore, measurement stations influenced by electric current flowing on near-surface or above
ground conductive culture can be identified and removed from the data set with a magnetic field
gradient cutoff criteria.
Although the gradient filter method is effective, by itself it does not separate out all cultural
influences. Steep gradients can occur over very short distances, and they can sometimes pass
detection due to discrete station spacing, especially where the grid is sparse and near survey
edges. It is also important to consider that near-surface electric currents may be much weaker
than those at depth, but can still influence readings within a very short proximity—sometimes
less than the typical station spacing. The influence in such a case may be significant even if it
does not cause a measureable high gradient. For this reason, another criterion specifically for the
removal of readings near culture is necessary.
Distance from Conductive Culture
In some cases, measurement stations are located too close to conductive culture (e.g. an unknown
buried power line or pipeline, grounding grid wire, etc.). The objective of this filter is to remove
additional measurement stations that cannot be trusted given the high probability that they are
influenced by surface culture. The cutoff distance for this filter is determined by modeling and
careful analysis of the data because some cultural features will carry more electric current than
others.
Vertical to the Horizontal Magnetic Field Ratio
The vertical to the horizontal magnetic field ratio is a measure of what angle the current path is
resting in relation to the magnetic field measurement station. In most cases, a magnetic field
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measurement is used to observe subsurface preferential current flow which produces a
predominantly horizontal magnetic field and a ratio far below one; however, sometimes electric
current flows along near-surface conductive culture that generates a combination of vertical and
horizontal magnetic field depending on its orientation when compared to the measurement
station. If the vertical field is large compared to the horizontal field then the observer is making a
measurement to the side instead of on top of a flow path which is more likely conductive culture.
Therefore this ratio can be used to distinguish whether the source of the signal is predominately
near-surface or a subsurface flow path.
Point-Specific Professional Judgment
The gradient filter and distance from culture criteria remove the majority of measurement stations
affected by near-surface conductive culture. Nevertheless, in some cases there still remains a
“gray zone” where some data slips past these two criteria and should be considered by subjecting
it to point-specific professional judgment. Removal of measurement stations using professional
judgment usually takes place only when the above criterion breaks down due to survey edges or
gaps in the data as mentioned or from unknown and/or buried conductive culture. In any event,
professional judgment is used as the final criteria to determine the quality of all measurement
stations.
Filtered Magnetic Field Map
If a measurement station is determined to be influenced by stray electric current flowing onto
conductive culture, the measurement station is removed (filtered) from the data set. Magnetic
field contour maps are then generated that reflect magnetic field measurements unaffected by
surface culture. Stations that pass the quality control measures are shown with red crosses (“+”
signs) in the figures. Measurement stations removed after the three criteria have been applied are
shown with an “x” centered within a larger gray semi-transparent circle. Stations removed by
professional judgment are shown with a circled “x” within the larger gray semi-transparent circle.
10.0 Magnetic Field Contour Map
Following initial data reduction and removal of cultural interference, a filtered horizontal
magnetic field map or “footprint map” is prepared to help identify the electrical current
distribution beneath the study area (see Figure 10A).
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Figure 10A – Example Magnetic Field Contour Map Before
Correction for Electrode Bias and Circuit Wire Position.
The shape of the contour lines reveals electric current flow patterns related to subsurface
conductive pathways and is generally a more important detail than the shading of magnetic field
strength. By identifying high points and ridges and connecting them together through the study
area, the center position of preferential electric current flow can be identified.
11.0 Predicted Magnetic Field Map and Ratio Response Map
Predicted Magnetic Field Map
To more accurately identify areas of greater or lesser conductivity, a model is created which
predicts the magnetic field response expected at each measurement station given the position of
the circuit wire, electrodes, and topographic changes. The model usually assumes a
homogeneous or uniform subsurface environment. Figure 11A shows a typical predicted
magnetic field for an investigation.
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Figure 11A – Example Predicted Magnetic Field Map
The predicted magnetic field model is an important tool that helps to emphasize the subsurface
heterogeneity by removing the “background” or homogeneous electric current flow between the
electrodes and along the circuit wire. A comparison of the original survey data with the predicted
magnetic field model is then performed and the results are presented in the form of a Ratio
Response Map.
Ratio Response Map
To better distinguish areas of greater or lesser conductivity through the subsurface study area, the
observed magnetic field map (Figure 10A) is corrected based on the predicted magnetic field
model (Figure 11A), creating a Ratio Response Map (Figure 11B). The Ratio Response Map
removes the effect of electric current bias and the resulting magnetic field due to the circuit wire
and electrode positions, thereby highlighting areas of greater or lesser magnetic field intensity due
to the subsurface electric current flow distribution.
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Figure 11B – Example Ratio Response Map
The white shaded areas indicate where electric current intensity is approximately equivalent to
that predicted by the homogeneous model. Pink or purple indicates where electric current flow is
less than predicted and green shows where electric current flow is greater than predicted. It is
important to emphasize that pink or purple areas are not overlooked. They can provide insightful
information and can help identify potential preferential flow paths as revealed by the shape of
contour lines.
12.0 Modeling
The filtered magnetic field map, predicted magnetic field map, and Ratio Response Map are
provided to identify preferential electric current flow from a “map view” perspective. To better
characterize the preferential pathways in three dimensions (3D), Willowstick has developed two
modeling methodologies based on the Biot-Savart relationship. The primary and most important
method utilizes a powerful inversion method to produce a subsurface Electric Current
Distribution (ECD) model. The second method is called Electric Current Flow or ECF modeling
because it uses discreet channels or ribbons of current to simulate the observed magnetic field at
the earth’s surface. These channels represent paths where electric current concentrates strongly in
the subsurface. Figure 12A portrays an example of an ECF model with a number of different
flow paths shown by dark blue lines.
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Figure 12A – Example of an ECF Model
Figures 12B and 12C portray horizontal and vertical slices, respectively, through an ECD
inversion model.
Figure 12B – Example of Horizontal Slice through an ECD Inversion Model
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Figure 12C – Example ECD Model Vertical Slice along an Embankment
In Figures 12B and 12C, the green shading identifies areas of higher conductivity where electric
current is more concentrated, while the purple shading identifies areas of lower conductivity
where electric current is observed to be less concentrated. It is important to note here that
because all the data is collected on the surface, the ECD inversion models always cast a
downward “shadow” below an area where higher electric current flow (green shading) is
detected. The effect is like shining a flashlight from above on a dark subsurface. Therefore, a
preferential flow path can be discovered by the sharp transition from purple to green, or in this
case where that transition is elevated above the bedrock. This important location is highlighted
by the blue circle marked “Zone of leakage.” The strong green anomaly on the upper right side
can be dismissed as it is caused by near-surface conductive culture.
Willowstick uses MATLAB software to generate and analyze ECD models in the form of volume
data. The model viewer can generate slices at any elevation or cross-section position within the
volume. The inversion model and all associated information can be provided to the client in
common electronic formats. This enables clients to view, compare, and analyze the results of the
investigation on their own if desired.
13.0 Summary
The modeling and interpretation of electric current flow distribution through the subsurface is a
powerful tool for characterizing groundwater flow paths in most geologic settings, and is based
upon widely known and accepted scientific theory and principles. Proper data interpretation
requires an understanding of site geology, groundwater physical principles, electromagnetic
theory and experience working with and developing the technology. A great deal of effort has
been put forth to eliminate error in the data collection, data reduction/normalization, modeling
and interpretive process.
The Willowstick survey method is intended to provide a quick and accurate characterization of
groundwater conditions. The Technology is viewed as a means to guide and direct traditional
exploratory work such as drilling campaigns in order to improve groundwater characterization
efficiencies (cost and time) and to arrive at conclusive answers about specific groundwater issues.
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A Willowstick survey is particularly useful in helping identify and confirm groundwater flow
path locations. The results obtained from a Willowstick geophysical investigation should be used
in conjunction with all known information at a site to make the most informed decisions
regarding how to monitor and remediate groundwater problems. There is no technology better
suited for this assignment.
14.0 Contact Information
For more information about how Willowstick Technologies can specifically help you with your
groundwater or seepage problems visit our web site at www.willowstick.com or call our main
office at (801) 984-9850.
15.0 Patent
The Willowstick method of identifying, mapping and modeling seepage through subsurface
environments is protected by Patent 5,825,188 and 8,688,423 B2 plus other patents are pending.
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