During alternating field demagnetization with the three-axis stationary method, the acquisition of a spurious magnetization, the intensity of which increases with increasing peak field, is observed in a wide range of samples, mainly of volcanic rock type. We show that this magnetization is clearly linked to high field anisotropy of the sample and to the applied AF direction, supporting Stephenson's theory on gyroremanent magnetization. GRM linked to the sample anisotropy can be of the same order of magnitude as RRM at low speeds of rotation. Another kind of gyromagnetic remanence can also be created when stationary alternating field treatments are applied to successive non orthogonal axes. Such results put constraints on AF demagnetization procedures: (1) The multiaxis stationary procedure proposed by McFadden to improve the efficiency of the three orthogonal axis method is not suitable. (2) If GRM is observed during a three orthogonal axis procedure, the method described by Dankers & Zijderveld must be used (3) Provided that the noise level introduced by the RRM is reduced by an alternating sense of rotation, the tumbler method should be the most appropriate.
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