Electrical Resistivity

Current Flow - a simple electrical circuit with a battery, ammeter, resistor, and a voltmeter.

Resistivity - a material property which is equal to resistance times area divided by length (ohm-m). Electrical Resistivities varies with porosity, pore fluid salinity, and clay content (1 (wet clay) to 10,000 (low porosity igneous/metamorphic rock) Ohm-m). Resistivity is determined using the potential difference (voltage) between two electrodes for a known current and correcting for the geometrical pathway of current through the earth (i.e., distances between the current and potential electrodes).

Electrode Configurations

Wenner - spacing between electrodes is the same. Easy mathematics. However, more work in the field because all electrodes have to be moved between each measurement.

Schlumberger - spacing between potential electrodes is smaller than current electrodes. It is easier to use in the field.

Dipole-Dipole - current and potential electrodes are separated from each other by a large distance. Used for very deep (kilometers) profiling.

Horizontal Interfaces

Current refracts or bends at an interface much like seismic waves. Current flowing from low/high resistivity into high/low resistivity bends away/towards the interface. Current preferentially flows in the least resistive layer.

Depth of current penetration depends on the spacing between electrodes. Depth of current penetration is higher/lower when the lower layer is lower/higher resistivity.

Apparent Resistivity - At small spacing between electrodes, apparent resistivity is close to the resistivity of the upper layer. With increased space between electrodes more current passes through the lower layer and apparent resistivity changes. Apparent resistivity never reaches the resistivity of the lower layer because some current always travels through the upper layer. Changes in apparent resistivity with electrode spacing depend on depth to the interface and the contrast in resistivity.

Equivalence and Suppression - Electrical resistivity analysis is not unique. More than one model may give an acceptable fit to the data (equivalence). It is also possible that some layers that are thin or have a small contrast in resistivity will not be resolved (suppression).

Applications - mapping gravel aquifers, basement, contaminate plumes (either brines or NAPL (non-aqueous phase liquids)), cavities.

Ray Paths

Reflection, Refraction, and Snell’s Law - wave energy is reflected or bent across an interface. The angle of reflection or refraction depends on the angle of incidence and the ratio of the velocities across the interface.

Critical Refraction - wave is refracted parallel to the interface and travels at the velocity of the lower layer.

Diffraction - new waves are generated in all directions when a wave hits a sudden change in an interface (e.g., fault) that is the same size as the wavelength

Wave Arrivals - Air wave, direct wave, ground roll, reflected wave, and head wave. Wave velocities vary from 200 to 6,000 m/s. Either the direct wave or head (refracted) wave are the first arrival at a geophone.

Horizontal Interface(s) -

Single - Distance versus Travel-Time Equation is a straight line.

Velocity of upper layer - is the inverse of the slope of the direct wave arrivals

Velocity of lower layer - is the inverse of the slope of the direct wave arrivals

Depth to interface - is determined from the intercept time (x=0) for the head wave arrivals

Multiple - additional horizontal interfaces can be determined using the same techniques (e.g., velocity from the inverse slope of the head wave arrivals and the intercept time). Intercept time for the deeper interfaces must be adjusted for the time spent traveling through the overlying layer(s).

Dipping Interfaces - A single traverse cannot determine if an interface is dipping. Both a forward and a reverse traverse are required. The presence of a dipping layer is indicated by asymmetry between the forward and reverse distance versus time curves.

The traverse where the energy source is down dip will have a larger incept time. Apparent velocity determined from the slope of the travel time curve is too high.

The traverse with an up dip energy source will have a smaller incept time. Apparent velocity determined from the inverse slope of the travel time curve is too low.

Critical angle and the dip of the interface are determined from the apparent velocities and the velocity of the upper layer.

Depth to the interface is determined from the intercept time, the velocity of the upper layer, and the critical angle.

Nonideal Surfaces

Low-Velocity zones - cannot be detected by the refraction method because there is no critical refraction. The inferred depth to an interface below the low-velocity layer will be too shallow.

Thin layers - may be missed by the refraction method because the head waves produced at the interface are never first arrivals. The inferred depth to an interface below the thin layer will be too deep.

Interface Discontinuities (diffractions) - produce an offset in the travel time curve.

Corrections to data - If the surface has significant topography then the raw data must be corrected for elevation to some horizontal datum (e.g., sea level).

Applications - typical shallow use of refraction method is depth to bedrock or depth to the water table.

Single Horizontal Interface - any interface with a variation in acoustic impedance (velocity times density) will produce a reflection

Travel - Time Equation - is a hyperbola rather than a straight line (depends on x² rather than x) so cannot use methods developed in refraction

Normal Move-Out (NMO) - is the amount of curvature in the x-t line. It is the actual travel time less the two-way vertical travel time.

Dipping Interfaces - can only be recognized with geophones on either side of the energy source. Arrival times are asymmetric (less time updip and more time down dip).

Radar Waves

Wave Terminology - amplitude, frequency, and wavelength; velocity equal to frequency times wavelength. Frequencey of radar waves is 10 to 1,000 MHz. Wavelengths are in centimeters to meters.

Radar Wave Velocity - is proportional to the speed of light divided by the square root of dielectric permittivity. Velocities range from 0.3 m/ns for air, 0.03 m/ns for water, and 0.03 to 0.07 m/ns for most sediments and rocks. Velocities are in meters per NANOsecond.

Ray Paths

Reflection and Refraction, and Snell’s Law - radar wave energy is reflected or bent across an interface between materials of different conductivities.

Diffraction - new waves are generated in all directions when a wave hits a sudden change in an interface (e.g., underground pipe) that is the same size as the wavelength

Penetration depth - is dependent on radar frequency and conductivity of the subsurface. Low frequency waves in resistive material (sand) can penetrate as much as 30 meters. High frequency waves in a conductive material (clay) may penetrate only one meter.

Reflections at Interfaces

Electromagnetic radiation with frequencies between 10 and 1,000 MHz is emitted in pulses into the subsurface. At any interface with a variation in electrical conductivity, some of that energy is reflected back. Electrical conductivity is primarily controlled by clay content, water saturation (porosity), and pore water salinity.

Determining Depth to Interface - Depth to the interface can be determined from the velocity times the intercept time divided by two. Velocity is often inferred from known depths to interfaces from cores or lithology. Multiple interfaces can be determined by summing each time interval and velocity. Ray paths are nearly vertical so travel time is essentially the intercept time.

Acquiring and Recognizing Reflections

Diffractions - Diffractions also appear as noise on GPR records. They have a hyperbolic shape and are symmetrical about the point of diffraction. Reflections from trees or power line noise also appear as point sources.

Field Procedures - GPR works on air, water, ice, and land. In general, one or two antennas are dragged along at some fixed rate (2-3 km/hr).

Resolution - both vertical and horizontal resolution are dependent on the wavelength (centimeters) of the radar energy. Very high resolution data

Applications - densities and fractures of tunnel rocks, salt domes, buried pipes and cables, mapping water table, consecutive configurations of contamination plumes, moisture content in soil, mapping thickness and distribution of sediments in lakes, and karst dissolution features