Errors in paleomagnetism: Structural control on overlapped vectors – mathematical models

The reliability of paleomagnetic data is a keystone to obtain trustable kinematics interpretations. The determination of the real paleomagnetic component recorded at certain time in the geological evolution of a rock can be affected by several sources of errors: inclination shallowing, declination biases caused by incorrect restoration to the ancient field, internal deformation of rock volumes and lack of isolation of the paleomagnetic primary vector during the laboratory procedures (overlapping of components). These errors will limit or impede the validity of paleomagnetism as the only three-dimension reference. This paper presents the first systematic modeling of the effect of overlapped vectors referred to declination, inclination and stability tests taking into account the key variables: orientation of a primary and secondary (overlapped to the primary) vectors, degree of overlapping (intensity ratio of primary and secondary paleomagnetic vectors) and the fold axis orientation and dip of bedding plane. In this way, several scenarios of overlapping have been modeled in different fold geometries considering both polarities and all the variables aforementioned, allowing to calculate the deviations of the vector obtained in the laboratory (overlapped) with respect to the paleomagnetic reference (not overlapped). Observations from the models confirm that declination errors are larger than the inclination ones. In addition to the geometry factor, errors are mainly controlled by the relative magnitude of the primary respect to the secondary component (P/S ratio). We observe larger asymmetries and bigger magnitudes of errors along the fold location if the primary and secondary records have different polarities. If the primary record (declination) and the fold axis orientation are perpendicular (Ω = 90°), errors reach maximum magnitudes and larger asymmetries along the fold surface (different dips). The effect of overlapping in the fold and reversal tests is also qualitatively analyzed in this paper.

► First systematic modeling of overlapped paleomagnetic vectors of common application.
► Depends on structural geometry, orientation of components and degree of overlapping.
► Declination errors are larger than the inclination ones.
► Larger asymmetries appear with different polarity records or with an orthogonal array.
► The effect of overlapping affects significantly fold and reversal tests.