Consideration of Oblique Incidence in 3-D Imaging of a Planar Interface With a Circular Dipole Array in an Air-Filled Borehole

Abstract

We consider the effects of oblique incidence of a wave on the creation of a 3-D image of a planar interface with an array-type directional borehole radar. In this study, we focus on the situation where the radar probe is close to the planar interface. In such circumstances, the reflected wave from the planar interface may be incident on the receiving array antenna at very steep elevation angles. As a result, borehole effects cause differences in the arrival times of the wave at the array elements, and consequently some errors emerge in imaging the planar interface. Observing the arrival time differences, we present an algorithm to compensate those errors in creating a 3-D image of a planar interface. Computer simulations predict that the errors may occur when the circular dipole array antenna is in an air-filled borehole in rock. Numerical simulations show that our proposed algorithm generates a 3-D image of an interface around an exact position, whereas conventional methods produce some spurious images opposite to the correct position (i.e., out of position by 180°). We then applied the proposed method to analyze reflected waves from a real-world fault in rock. A 3-D image of the fault could be successfully created, which was not possible using the conventional method.

Keywords

• Critical elevation angle
• dipole array antenna
• directional borehole radar
• oblique incidence
• plane wave