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Directional borehole radar (BR) 3-D imaging is a challenging problem due to its limited observation space within a borehole. We present a linear prediction (LP)-based direction-of-arrival (DOA) estimation and a migration-based 3-D imaging algorithm for the directional BR, which is composed of a transmitting antenna and a uniform circular array including four small receiving antennas. Only the azimuth is estimated, while the elevation and the distance are included in the imaging process. LP is a useful tool for DOA estimation in the radar domain, but a single linear array (LA) has azimuth ambiguity in DOA estimation. The four receiving antennas are treated as two orthogonal uniform LAs. The combination of two arrays removes the ambiguity in DOA estimation. In addition, the moving window and the threshold-based estimation increase the calculation efficiency. According to the estimated azimuth angles, the measured signal at each depth is decomposed to the corresponding directions. Therefore, there is a time-series signal in each direction at each depth. After processing the measured signals at all depths, we obtain a 3-D data set that can be used for horizontal- and radial vertical-section displays. Then, the radial vertical-section data are processed by migration which transforms the time domain signal into a wavefield-based 3-D image. Simulated data from a fracture model are used to validate the algorithm, and the reconstructed image can reveal the real model well. It is concluded that the novel method we propose is an effective one with real-time processing capability. [ABSTRACT FROM AUTHOR]

Borehole radar is a powerful tool for detecting subsurface fractures. Fracture modeling and numerical simulation are essential means to study fracture detectability. In this article, we first propose a method to construct a single fracture model, which combines the Baecher disk model and random rough surface and includes features, such as roughness, pinch-out, and irregularity. As the precise description of the fracture raises the requirement for accuracy of the simulation algorithm, the 3-D conformal finite-difference time-domain (CFDTD) method is used in this work. Numerical simulations of a sphere and rough fractures show that the CFDTD has higher calculation accuracy than conventional FDTD. Then, we analyzed how the fractures with different roughness affect the electromagnetic wave response. It is found that as the fracture surface becomes rougher, the wave scattered by it becomes stronger, more fracture contour-related information is obtained, and the fracture morphology is recovered better. Combined with accurate fracture modeling and high-precision numerical simulation, the electromagnetic response characteristics of different forms of fractures are obtained, which provides a basis for the accurate detection and interpretation of fractures in the future. [ABSTRACT FROM AUTHOR]