This paper presents an inversion scheme for high-frequency electromagnetic (EM) data from a single borehole for detection and characterization of fluid-filled fractures. Water in the fracture zone may be characterized by its high electrical permittivity and, if saline, by high electrical conductivity. High electrical conductivity results in increased attenuation of EM fields, whereas high electrical permittivity reduces the phase velocity of propagating EM fields. Taking advantage of these effects, we use high-frequency EM fields to detect and characterize fluid-filled fractures. To demonstrate the feasibility of single-hole EM imaging, we develop a three-step inversion scheme to map a fluid-filled fracture near the borehole and to evaluate its electrical conductivity and permittivity.
We assume that a fluid-filled fracture can be simulated by a conductive thin sheet. To test our inversion scheme, we generated synthetic data using the thin-sheet integral equation method. A vertical magnetic dipole was used as a source, and the resultant magnetic fields were inverted using a nonlinear least-squares method. First, the background conductivity and permittivity were obtained using vertical magnetic field data from below and above the transition frequency, at which conduction and displacement current magnitudes are equal. Next, using the phase difference between EM fields at two neighboring frequencies in the wave propagation realm, both the vertical and dipping sheets were successfully mapped using NMO and migration techniques. Electrical properties of the sheet were well resolved by subsequent inversion after having fixed the location of the sheet and host electrical properties.
This study shows the potential of imaging the fracture using high-frequency EM data obtained from single-hole surveys.