Analyzing the Ambiguity of the Remanent‐Magnetization Direction Separated Into Induced and Remanent Magnetic Sources.

We developed a new ambiguity analysis method to investigate the remanence of a uniformly magnetized source. We wrote the unit vector of the total‐magnetization direction as the weighted sum of the unit vectors of the induced‐ and remanent‐magnetization directions. The unit vectors of the induced‐ and remanent‐magnetization directions are weighted, respectively, by the ratio between the induced and total‐magnetization intensities (λ), and by the multiplication of λ by the Koenigsberger ratio Q $\mathcal{Q}$. We obtained analytical estimators for Q $\mathcal{Q}$ and the remanent magnetic inclination Ir and declination Dr. We constructed a family of ambiguity curves of Ir×Q ${I}_{r}\times \mathcal{Q}$, Dr×Q ${D}_{r}\times \mathcal{Q}$, and λ×Q $\lambda \times \mathcal{Q}$ for a fixed total‐magnetization direction and for λ value. We estimated the total magnetic inclination It and declination Dt via the equivalent‐layer technique constrained by an all‐positive magnetic‐moment distribution. We also used some total‐magnetization directions associated with prespecified data‐residual errors. We performed a systematic search for both It and Dt to obtain a discrete data‐residual map on the plane It × Dt. We picked some It and Dt from the data‐residual map associated with a percent of data‐residual error and created some families of ambiguity curves of Ir, Dr, and λ versus Q $\mathcal{Q}$. These ambiguity curves are quickly built up because we inverted the data only once. Tests with synthetic and field data from the Goiás Alkaline Province, Brazil, illustrated a wider perspective of the relationships between the remanent‐magnetization direction and Q $\mathcal{Q}$ for different data‐residual errors. Plain Language Summary: We have presented a novel ambiguity analysis method for appraisal of the remanent‐magnetization directions and the Koenigsberger ratio Q $\mathcal{Q}$. The method is grounded on a new formulation of the total‐magnetization direction unit vector, that is described as the sum of the induced‐ and remanent‐magnetization directions unit vectors weighted by the ratio between the induced‐ and total‐magnetization intensities λ; the multiplication of λ by Q $\mathcal{Q}$. We derived analytical estimators for the remanent inclination Ir, declination Dr, and Q $\mathcal{Q}$. For each total‐magnetization direction and the values of λ, we construct a family of curves of Ir, Dr, and λ versus Q $\mathcal{Q}$. We use the total‐magnetization direction estimated via the equivalent layer constrained by an all‐positive magnetic‐moment distribution. We also use some total‐magnetization directions associated with prespecified data‐residual errors. Each family of ambiguity curve is related to each total‐magnetization direction associated with a percent error in the data residuals. These ambiguity curves are quickly built up because we used the derived analytical estimators and we inverted the total‐field anomaly only once. Tests on synthetic and field data show that the knowledge about the interval of Q $\mathcal{Q}$ can assist in the scan of remanent‐magnetization directions. Key Points: Ambiguity analysis method for the remanent‐magnetization directionQuick construction of a family of ambiguity curves of the remanent‐magnetization vector and the Koenigsberger ratioMathematical estimators for calculating the remanent‐magnetization direction and Koenigsberger ratio [ABSTRACT FROM AUTHOR]