Directional resistivity measurements are commonly utilized to provide information about remote geological features not intercepted by the measurement tool (e.g., remote beds, bed boundaries, and/or fluid contacts). Such information includes, for example, the distance from and direction to the remote feature. In geosteering applications, directional resistivity measurements may be utilized in making steering decisions for subsequent drilling of the borehole. For example, an essentially horizontal section of a borehole may be routed through a thin oil bearing layer. Due to the dips and faults that may occur in the various layers that make up the strata, the distance between a bed boundary and the drill bit may be subject to change during drilling. Real-time distance and direction measurements may enable the operator to adjust the drilling course so as to maintain the bit at some predetermined distance from the boundary layer. Directional resistivity measurements also enable valuable geological information to be estimated, for example, including the dip and strike angles of the boundary as well as the vertical and horizontal conductivities of the formation.
Methods are known in the art for making LWD directional resistivity measurements. These measurements commonly involve transmitting and/or receiving transverse (x-mode) or mixed mode (e.g., mixed x- and z-mode) electromagnetic waves. Various tool configurations are known in the art for making such measurements. For example, U.S. Pat. No. 6,181,138 to Hagiwara teaches a method that employs an axial (z-mode) transmitting antenna and three co-located, circumferentially offset tilted receiving antennae. U.S. Pat. No. 6,969,994 to Minerbo et al., U.S. Pat. No. 7,202,670 to Omeragic et al., and U.S. Pat. No. 7,382,135 to Li et al teach a method that employs an axial transmitting antenna and two axially spaced tilted receiving antennae. The receiving antennae are further circumferentially offset from one another by an angle of 180 degrees. U.S. Pat. Nos. 6,476,609, 6,911,824, 7,019,528, 7,138,803, and 7,265,552 to Bittar teach a method that employs an axial transmitting antenna and two axially spaced tilted receiving antennae in which the tilted antennae are tilted in the same direction. U.S. Pat. Nos. 7,057,392 and 7,414,407 to Wang et al teach a method that employs an axial transmitting antenna and two longitudinally spaced transverse receiving antennae.
In order to detect a remote boundary (e.g., a bed boundary or a fluid contact), the transmitted electromagnetic signal must typically reflect off the boundary and then propagate back to the measurement tool (where it is received). As known to those of ordinary skill in the art, the intensity of this reflected signal tends to decrease with increasing distance to the remote boundary. In order to detect distant bed boundaries (e.g., on the order of 10-20 feet from the wellbore), direct couplings between transmitter and receiver antennae are preferably eliminated. This can be accomplished, for example, via the use of a transmitter and a receiver having orthogonal moments.
One difficulty, however, is that bending of the directional resistivity tool in the borehole introduces direct couplings by changing the angle between the transmitter and receiver moments (such they are no longer perfectly orthogonal). For a distant bed boundary (e.g., on the order of 20 feet from the wellbore), even moderate tool bending (e.g., about 5 degrees per 100 feet) can significantly distort the reflected signal. Such distortion renders it difficult, or at times even impossible, to determine a reliable distance and/or direction to the boundary layer. Therefore, there is a need in the art to address the effect of tool bending on directional resistivity measurements. In particular, there is a need for a method for removing the direct couplings caused by tool bending from directional resistivity measurements.