Rotation about an inclined axis: Three dimensional matrices for reconstructing paleomagnetic and structural data

Ram Weinberger*, Amotz Agnon, Hagai Ron, Zvi Garfunkel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


We derive matrices for calculating the three-dimensional finite rotation that restores a rigid block to its pre-displacement attitude. To use this technique an initial horizontal bedding is assumed, and the following orientations must be known: the expected field orientation of magnetization, the situ orientation of the paleomagnetic vector and the bedding normal. The restoring rotation is decomposed into two convenient steps, represented by rotation matrices, such that they restore the in situ paleomagnetic vector together with the tilted bedding normal to their original orientation. These auxiliary rotations combine algebraically to a single finite rotation from which an inclined axis and amount of rotation arc obtained. We demonstrate this method by reconstructing a distinct section of the Mount Sedom salt diapir (Dead Sea Rift Valley, Israel). Here, the conventional tilt correction that brings the bedding to horizontal fails to position the paleomagnetic vector in its expected orientation. Only a rotation of 125 ° about an axis which plunges 50 ° southward can restore both bedding and magnetization to their expected orientations.

Original languageAmerican English
Pages (from-to)777-782
Number of pages6
JournalJournal of Structural Geology
Issue number6
StatePublished - Jun 1995

Bibliographical note

Funding Information:
Acknowled~~~rnrs-We greatly apprcclatetl \tlmulatlng d~w~\\~cm\ with I. Zak as well as his field assistance WC thank W H. Owen\ ior helpful suggestions concerning the rcllabllitr of ouv solution and critical review of the paper. We also thank B Katz for her careful reading of the manuscript. This research was supporrcd by the Earth Science Research AdminIstratIon of the Mini\trv of tncrgy and h\ grant no. 89-232 for the US-liracl Rlnatlonal Scicncc Foundation (BSF).


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