Multi-frequency Focusing Theory And The Application In Multi-component Induction Logging

Multi-component induction logging tool is comprised of three pairs of mutuallyorthogonal transmitter-receivers measuring all nine magnetic field components. Andthen, the horizontal as well as the vertical resistivity, the relative dip of layeredformations and the formation anisotropy are also inverted. It is essential forcharactering and developing reservoirs especially the thinly laminated formations.Multi-component induction logging response depend largely on formationhorizontal conductivity, vertical conductivity, borehole (or formation) dip and thetool azimuth.In addition to that the XX and YY measurements are always influencedby borehole, washouts. All of which made response of3DEX highly non-linear withrespect to formation parameters.Generally, the interpretation for multi-component logging depends on inversiontechniques which is a time consuming work. When the multi-frequency focusingmethod is applied to the multi-component induction logging data, the information forthe interpretation of induction logging data can be determined. The MFF theory isbased on the relationship of the induction electromotive force with the frequency.We expand the induction electromotive force into a series with respect to thefrequency, the second term proportionalω3/2is linear function of conductivity inhomogeneities, eliminating the influence of skin-effect. We apply this feature in thelogging data to derive the coefficient of the second term using the multi-frequencymeasurements and the linear fitting technique, which means MFF.We apply MFF in a homogeneous anisotropic formation, the horizontal and thevertical resistivity can be derived. As it is a desirable result, we extend this methodinto layer formation, the conductivity in anisotropically layered formation reflect thetrue horizontal and the vertical conductivity.In this paper, we study the MFF theory and then apply the MFF in the multi-components induction logging, not only in the homogeneous anisotropicformation but also the layered formation with vertical and title bore, and the results ofMFF processing is systematically analyzed.From the results, MFF is considered to be a good method to eliminate thenonlinear of XX and YY measurements and also provide the conductivity more closeto the true formation conductivity. Similarly to the resistivity, the formationanisotropy and the relative dip can also be algebraically determined when the MFFmethod is applied to the multi-component induction logging data. In the formationwith tilted bore, We get the relative dip and the anisotropy. The algorithm is easy thatmakes the interpretation for multi-component induction logging data not so trouble,nevertheless, the multi-frequency leads obvious nonlinearity in the shoulder-bed, andthe anisotropy effect, the shoulder-bed effect, the resistivity effect can also affect theaccuracy of the results of MFF processing.