Karl J. Ellefsen

Crosswell seismic investigation of hydraulically conductive, fractured bedrock near Mirror Lake, New Hampshire

Abstract Near Mirror Lake, New Hampshire (USA), hydraulically conductive, fractured bedrock was investigated with the crosswell seismic method to determine whether this method could provide any information about hydraulic conductivity between wells. To this end, crosswell seismic data, acoustic logs from boreholes, image logs from boreholes, and single borehole hydraulic tests were analyzed. The analysis showed that, first, the P-wave velocities from the acoustic logs tended to be higher in schist than they were in granite. (Schist and granite were the dominant rock types). Second, the P-wave velocities from the acoustic logs tended to be low near fractures. Third, the hydraulic conductivity was always low (always less than to 10−8 m/s) where no fractures intersected the borehole, but the hydraulic conductivity ranged from low to high (from less than to 10−10 m/s to 10−4 m/s) where one or more fractures intersected the borehole. Fourth, high hydraulic conductivities were slightly more frequent when the P-wave velocity was low (less than 5200 m/s) than when it was high (greater than or equal to 5200 m/s). The interpretation of this statistical relation was that the fractures tended to increase the hydraulic conductivity and to lower the P-wave velocity. This statistical relation was applied to a velocity tomogram to create a map showing the probability of high hydraulic conductivity; the map was consistent with results from independent hydraulic tests.

Effects of layered sediments on the guided wave in crosswell radar data

To understand how layered sediments affect the guided wave in crosswell radar data, traces are calculated for a model representing a sand layer between two clay layers. A guided wave propagates if the wavelengths in the sand layer are similar to the thickness of the sand layer. The amplitude of the guided wave but not its initial traveltime is affected by the thickness of the sand layer. In contrast, both the amplitude and the initial traveltime are affected by the locations of the transmitting and receiving antennas, the electrical conductivity of the sand layer, and the dielectric permittivity of the sand layer. This permittivity can be estimated from the initial traveltime. The effects of the layering on the waves in these calculated traces also are observed in field traces, which were collected in layered sediments.

Phase and amplitude inversion of crosswell radar data

Phase and amplitude inversion of crosswell radar data estimates the logarithm of complex slowness for a 2.5D heterogeneous model. The inversion is formulated in the frequency domain using the vector Helmholtz equation. The objective function is minimized using a back-propagation method that is suitable for a 2.5D model and that accounts for the near-, intermediate-, and far-field regions of the antennas. The inversion is tested with crosswell radar data collected in a laboratory tank. The model anomalies are consistent with the known heterogeneity in the tank; the models relative dielectric permittivity, which is calculated from the real part of the estimated complex slowness, is consistent with independent laboratory measurements. The methodologies developed for this inversion can be adapted readily to inversions of seismic data (e.g., crosswell seismic and vertical seismic profiling data).

Shear-wave seismic reflection studies of unconsolidated sediments in the near surface

We have successfully applied of SH-wave seismic reflection methods to two different near-surface problems targeting unconsolidated sediments. At the former Fort Ord, where the water table is approximately 30 m deep, we imaged aeolian and marine aquifer and aquitard stratigraphy to a depth of approximately 80 m . We identified reflections from sand/clay and sand/silt interfaces and we mapped these interfaces along our transects. At an aggregate study site in Indiana, where the water table is at a depth of 1 to 2 m , we imaged stratigraphy in alluvial sand and gravel, and observe a strong reflection from the 32-m -deep bedrock surface. In both cases, we exploited the high resolution potential of SH waves, their insensitivity to water content, and the possibility of reducing Love wave contamination by working along a roadway. We accomplished our results using only sledgehammer sources and simple data processing flows.

Frequency-domain Green’s functions for radar waves in heterogeneous 2.5D media

Green’s functions for radar waves propagating in heterogeneous 2.5D media might be calculated in the frequency domain using a hybrid method. The model is defined in the Cartesian coordinate system, and its electromagnetic properties might vary in the x - and z -directions, but not in the y -direction. Wave propagation in the x - and z -directions is simulated with the finite-difference method, and wave propagation in the y -direction is simulated with an analytic function. The absorbing boundaries on the finite-difference grid are perfectly matched layers that have been modified to make them compatible with the hybrid method. The accuracy of these numerical Green’s functions is assessed by comparing them with independently calculated Green’s functions. For a homogeneous model, the magnitude errors range from −4.16% through 0.44%, and the phase errors range from −0.06% through 4.86%. For a layered model, the magnitude errors range from −2.60% through 2.06%, and the phase errors range from −0.49% through 2....

Numerical study of electromagnetic waves generated by a prototype dielectric logging tool

To understand the electromagnetic waves generated by a prototype dielectric logging tool, a numerical study was conducted using both the finite-difference, time-domain method and a frequency-wavenumber method. When the propagation velocity in the borehole was greater than that in the formation (e.g., an air-filled borehole in the unsaturated zone), only a guided wave propagated along the borehole. As the frequency decreased, both the phase and the group velocities of the guided wave asymptotically approached the phase velocity of a plane wave in the formation. The guided wave radiated electromagnetic energy into the formation, causing its amplitude to decrease. When the propagation velocity in the borehole was less than that in the formation (e.g., a water-filled borehole in the saturated zone), both a refracted wave and a guided wave propagated along the borehole. The velocity of the refracted wave equaled the phase velocity of a plane wave in the formation, and the refracted wave preceded the guided wave. As the frequency decreased, both the phase and the group velocities of the guided wave asymptotically approached the phase velocity of a plane wave in the formation. The guided wave did not radiate electromagnetic energy into the formation. To analyze traces recorded by the prototype tool during laboratory tests, they were compared to traces calculated with the finite-difference method. The first parts of both the recorded and the calculated traces were similar, indicating that guided and refracted waves indeed propagated along the prototype tool.

Frequency domain, waveform inversion of laboratory crosswell radar data

A new waveform inversion for crosswell radar is formulated in the frequency-domain for a 2.5D model. The inversion simulates radar waves using the vector Helmholtz equation for electromagnetic waves. The objective function is minimized using a backpropagation method suitable for a 2.5D model. The inversion is tested by processing crosswell radar data collected in a laboratory tank. The estimated model is consistent with the known electromagnetic properties of the tank. The formulation for the 2.5D model can be extended to inversions of acoustic and elastic data.

Radiation pattern of a borehole radar antenna

To understand better how a borehole antenna radiates radar waves into a formation, this phenomenon is simulated numerically using the finite-difference, time-domain method. The simulations are of two different antenna models that include features like a driving point fed by a coaxial cable, resistive loading of the antenna, and a water-filled borehole. For each model, traces are calculated in the far-field region, and then, from these traces, radiation patterns are calculated. The radiation patterns show that the amplitude of the radar wave is strongly affected by its frequency, its propagation direction, and the resistive loading of the antenna.

Reply to the discussion

We wish to address the concerns raised by Bulnes et al. regarding the magnetic dipole and the associated magnetic current density. These entities are mathematical constructs for calculating electromagnetic fields.