A multi-component induction tool provides the data necessary to determine directional resistivity, i.e., resistivity anisotropy. The tool is comprised of three mutually orthogonal transmitter-receiver pairs that allow measurement of the full magnetic field matrix at multiple frequencies. In TI-anisotropic formations (e.g., thinly laminated sand/shale sequences, the data also contain enough information to determine the structural formation dip and azimuth. However, extracting this information from the measurements is a challenging problem due to the simultaneous dependence of the data on multiple parameters and strong environmental effects. We have developed a new algorithm based on the use of multi-frequency focusing that allows us to reduce environmental effects and simplify the data dependence on the formation parameters. The multi-component induction tools can measure all nine magnetic field components that non-zero if the tool is arbitrary oriented in a TI-anisotropic formation. Rotating the full magnetic matrix to the principal coordinate system associated with the formation leaves five non-zero components: XX, YY, ZZ, XZ, and ZX (the first and the second characters indicate the orientation of the transmitter and receiver, correspondingly. In layered formations, all five remaining components may be different. Applying the multi-frequency focusing (MFF to the measured magnetic matrix and rotating the matrix to the principal coordinate system reduces the number of non-zero components to three (XX, YY, and ZZ. In addition XX equals to YY. This means that all MFF components can be expressed through two angles (relative dip and rotation and two principal MFF components (ZZ and XX. It is worth noting that the ZZ principal component depends only on horizontal resistivity. At every logging depth, we derive formation dip and formation azimuth and compute the two principal components based on rules of tensor rotation and the least-squares fit to the data. Using the obtained information, we sequentially solve for Rh and Rv. A minimum of four measured components are required. Additional components are used to reduce the uncertainties and suppress the measurement noise. An additional benefit of this approach is that the processing for Rh and Rv is performed with data-consistent formation dip and azimuth. The algorithm is fast and can be easily applied in real time. After validating the algorithm with synthetic examples, we tested the approach on many field data sets and found a good agreement between the computed formation dips and azimuths and those obtained from diplog and borehole imaging data.

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