The precision of AMS determination is enhanced by measuring susceptibility in directions with a uniform orientation distribution that include the four body diagonals. Some standard 10.5 cm³ samples with mean susceptibility < 100µSI possess too few “magnetic” grains for reliable petrofabric interpretation whatever the measurement strategy. We should only interpret their AMS if they pass fabric homogeneity tests.

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For remanence-bearing minerals (RBM) such as magnetite-titanomagnetite, susceptibility to induced magnetism (M) measured in alternating fields (H AC ) is field-dependent. However, for fields B 400 A/m, measured in an AC induction coil instrument (at 19,100 Hz), susceptibility k 0 = M/H AC is sufficiently linear to provide a reproducible rock (or mineral) magnetic characteristic and its anisotropy may be related to arrangements of minerals in rock, or for single mineral grains to their crystalline or shape anisotropy. For any remanence-bearing mineral at higher fields k HF (¼ M/H AC ) is not constant and the term susceptibility is not normally used. This study bridges the responses between traditional low-field susceptibility measurements and those due to high applied fields, for example when studying hysteresis or saturation magnetization of RBM. Where |k HF | is measured in alternating fields that peak significantly above 400 A/m the M(H AC ) relation is forced to follow a hysteresis loop in which |k HF | > k 0 for small |H AC | and where |k HF | decreases to zero for very large fields that achieve saturation magnetization. Hysteresis nonlinearity is due to remanence acquired with one field direction requiring a reverse field for its cancellation. We investigate the transition from initial, traditional ''lowfield'' susceptibility (k 0 ) measurements at 60 A/m, through 24 different fields from 400 A/m to 40,000 A/m (for very high k 0 to 80,000 A/m). This reveals M(H AC ) dependence beyond from conventional k 0 through the range of hysteresis behavior in fields equal to and exceeding that required to achieve saturation magnetization (M S ). We show k HF increases with peak H AC until the peak field is slightly less than saturation magnetization in natural rock samples rich in magnetite (TM 0 ¼ Fe 3 O 4 ) and TM 60 (Fe 2.4 Ti 0.6 O 4 ). All sample suites predominantly contain multidomain grains with subordinate pseudo-single domain and single-domain grains. k/k 0 increases by B 5% for fields up to 2 kA/m. Above 4 kA/m k/ k 0 increases steeply and peaks, usually between 24 kA/m and 30 kA/m where all grains magnetic moments are activated by H AC since this exceeds the coercive force of most grains. For higher peak H AC , k/k 0 declines sharply as increased H AC values more effectively flip M with each field-direction switch, leading to the low gradient at distal portions of the hysteresis loop. For M 0 -TM 60 bearing rocks, susceptibility peaks for fields *12 kA/m and for magnetite rich rocks up to 24 kA/m. These values are approximately 10% of saturation magnetizations (M S ) reported for the pure minerals from hysteresis DC field measurements. Both the field at peak k/k 0 and the peak k/k 0 value appear to be controlled by the dominant domain structure; multidomain behavior has larger k/k 0 peaks at lower H AC . Stacked k/k 0 versus H AC curves for each sample suite (n = 12 to n = 39) were successfully characterized at the 95% level by a polynomial fit that requires the cubic form k/k 0 = a + bH + cH 2 + dH 3 . Thu...