Выпуск: 6 , Том: 47 , Год издания: 2006

A multi-component induction tool is comprised of three mutually orthogonal transmitter-receiver pairs that allow measurement of all nine magnetic field components at multiple frequencies. In anisotropic formations these measurements contain sufficient information to determine horizontal and vertical resistivities and to calculate the structural formation dip and azimuth. However, extracting these parameters 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 using multi-frequency focusing that reduces environmental effects and simplifies the data dependence on the formation parameters. All nine measured magnetic field components are non-zero if the tool is arbitrarily oriented in an anisotropic formation. Rotating the full magnetic matrix to the principal coordinate system associated with the formation leaves five non-zero components. 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. In addition, two of these principal components are equal. This means that all magnetic field components after MFF can be expressed through two angles (relative dip and rotation) and two principal MFF components. 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 principal components and relative dip, we sequentially solve for horizontal and then for vertical resistivities.