Estimating the 3D position and inclination of a planar interface with a directional borehole radar

Ebihara, Satoshi; Kawai, Hideaki; Wada, Kazushige

doi:10.3997/1873-0604.2012039

Cited by 22 publications

(13 citation statements)

References 39 publications

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“…The times

u

and

т

are the arrival time at the origin and the maximum time difference, respectively. We note that the difference between the equation () in this paper and the equation () shown by Ebihara et al () is the inclusion of rotation angle

φ

of the dipole antenna elements around the

z ‐axis

. We define

T_{i}, (i = 1, 2, \dots, M)

as the measured times when the array signals have the same phase in the time domain.…”

Section: Description Of Radar Systemmentioning

confidence: 95%

“…We define

T_{i}, (i = 1, 2, \dots, M)

as the measured times when the array signals have the same phase in the time domain. These times can be measured in the same manner as shown by Ebihara et al (). We may estimate the parameters

(\hat{ϕ}, \hat{u}, \hat{τ})

, solving the minimization problem

(\hat{ϕ}, \hat{u}, \hat{τ}) = \arg \min_{ϕ, u, τ} \sum_{i = 1}^{M} {| T_{i} - S_{i} (ϕ, u, τ, φ) |}^{2},

…”

Section: Description Of Radar Systemmentioning

confidence: 99%

“…The system is equipped with microelectromechanical system (MEMS)‐based sensors to measure the 3D attitude of the radar probe, removing the need for a rod to mechanically restrict the radar probe. Since there was no attitude sensor in the earlier systems used by Ebihara et al (, , ), the rotation of the radar sonde was controlled by a rod. The MEMS‐based sensors are included inside the thick part of the CCC, whose diameter is 40 mm and length 650 mm.…”

Section: Description Of Radar Systemmentioning

confidence: 99%

“…This was followed by the introduction of a dipole array antenna, whose elements were fed by an optical modulator system (Ebihara ; Ebihara et al ; Sato and Takayama ; Takayama and Sato ), or coaxial cables (Ebihara et al ). The latter system has been used for 3D imaging of a fault (Ebihara, Kawai and Wada ), and researchers succeeded in reducing the bore size of the antenna through the addition of ferrite cores (Ebihara et al ). With such an array antenna, one may measure the arrival time difference of the array signals to estimate the signals’ directions of arrival (DOA).…”

Section: Introductionmentioning

confidence: 99%

“…In the systems shown by Ebihara et al (, , ), the radar probe was fixed in a borehole with a dielectric rod, and we could control rotation of the radar probe. If the radar probe is placed at depths greater than a few scores of metres, it may be difficult to control the probe rotation mechanically.…”

Section: Introductionmentioning

confidence: 99%

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Probe rotation effects on direction of arrival estimation in array‐type directional borehole radar

Ebihara

Wada

Karasawa

et al. 2017

Near Surface Geophysics

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This paper discusses the relationship between feeding line delay compensation and direction of arrival estimation in an array-type directional borehole radar. In this radar, since the space available for an array antenna is limited by the borehole diameter, direction of arrival estimation is based on small travel time differences among array elements, and an accurate compensation of feeding line delays is important. Computer simulation confirmed that the radar probe rotation in a borehole leads to errors in the direction of arrival estimation of greater than 15° if the delays associated with the feeding array antenna elements are not compensated to within 0.1 ns. This may be caused by a failure to measure the time delays of electrical circuits around the feeding points of the antenna elements. In this case, we suggest that the lengths of system components other than the coaxial cables should be kept to less than 3 cm. Based on these investigations, we developed an array-type directional borehole radar for a geotechnical project to locate foundation piles. In a field experiment, we confirmed that direction of arrival estimation errors were below about 15°, although the radar probe rotated through more than 180° during the measurement, thanks to correct compensation of the cables. With the correct compensation, we demonstrated three-dimensional location of a buried cylindrical conducting object, which was located at 2 m from the radar in wet soil. We were able to estimate the reflection point position with an accuracy of 34 cm, which is the averaged error of the three-dimensional location, while allowing the radar probe to rotate. tool used in such projects (Daniels 2004). Soundings made with GPR have provided valuable information on objects buried in the subsoil up to several metres below the ground surface. Due to the sounding depth limitation of GPR, borehole radar has started to be utilised at construction sites. Borehole radar is a type of GPR (Slob, Sato and Olhoeft 2010) in which frequencies between 20 MHz and 100 MHz are used for long-range detection. Most conventional borehole radar systems for single borehole application use two vertical dipole antennae, which are omnidirectional. This type of radar has been applied to the detection of buried foundation piles (Yamashita and Toshioka 2002), and it is useful in two-dimensional space measurement for the determination of the depth and the radial distance (range) of targets parallel to the measurement borehole. However, to detect and range objects such as foundation piles in three-dimensional (3D) space using a single borehole, a directional borehole radar system is needed. As a directive antenna for the directional borehole radar, a cavity-backed antenna has been used; this system mechanically rotates the antenna inside the borehole

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“…The times

u

and

т

φ

of the dipole antenna elements around the

z ‐axis

. We define

T_{i}, (i = 1, 2, \dots, M)

as the measured times when the array signals have the same phase in the time domain.…”

Section: Description Of Radar Systemmentioning

confidence: 95%

“…We define

T_{i}, (i = 1, 2, \dots, M)

as the measured times when the array signals have the same phase in the time domain. These times can be measured in the same manner as shown by Ebihara et al (). We may estimate the parameters