## 1. Introduction

[2] In environmental, paleo-, and rock magnetism, measuring magnetic hysteresis has become a routine process for characterizing the magnetic properties of rocks. In general, values of *M*_{s} (saturation magnetization), *M*_{r} (saturation remanence), and *B*_{c} (coercivity) are determined from hysteresis loops after an appropriate nonferrimagnetic slope correction (Figure 1a). Values of *B*_{c} and the ratio *M*_{r}/*M*_{s} (=hereafter squareness) provide the most convenient (yet complicated) quantities to estimate domain state of the magnetic phases in the rocks. Despite their common use, hysteresis properties often provide inconclusive information on average grain size of magnetic minerals because hysteresis behavior is governed by many factors, such as composition, initial state, grain-shape and size, stress, and temperature.

[3] Recently, *Fabian* [2003] proposed a new rock magnetic parameter derived from hysteresis experiments: transient hysteresis (TH). In empirical form, TH is the summation of the difference between the ascending and descending branches of partial hysteresis experiment that cycles from saturation to remanence state, and then back to saturation magnetization state (Figure 1b). This is one of a special form of hysteresis experiments known as “first-order reversing curves,” or FORCs [*Mayergoyz*, 1986], in which the turning point is at zero field. In the present study, these special FORCs are denoted as zero-FORC or ZFORC. TH is defined as

where Δ*H* is a fixed field-increment (e.g., 1 mT) used in hysteresis measurements. If we normalize magnetization to *M*_{s}, TH has a units of induction field (e.g., mT).

[4] Because the difference between the ascending and descending branches results from the action of self-demagnetization, TH represents the degree of irreversible hysteresis behavior [*Fabian*, 2003]. In other words, TH is absent in superparamagnetic (SP) or ideal single-domain (SD) grains whose remanent states are uniform or nearly uniform. Large particles with complex magnetic remanent states or those that contain domain walls exhibit transient hysteresis because the formation of these patterns of magnetization occurs at different fields on the descending branch than their destruction on the ascending branch.

[5] Micromagnetism concerns the calculation of detailed magnetization configurations and the magnetic reversal process in a magnetic system. Not only can micromagnetic calculations predict complex magnetic domain structures, they can also produce transient pictures of complex domain configurations [e.g., *Schabes and Bertram*, 1988]. The general method of micromagnetism involves considering all the fundamental energies at near atomic levels. The underlying assumption is that within a small element of volume, atomic spins are approximately parallel to one another, or at least a linear function of position. Unlike in classical domain theory of ferrimagnetism, micromagnetism shows that the most common remanent states are dominated by nonuniform magnetizations. Micromagnetic modeling is therefore necessary to decipher the fundamental behavior of nonuniform magnetization structures.

[6] The present study was intended (1) to elucidate fundamental aspects of TH from micromagnetic modeling, (2) to compare model predictions with the experimental observations, and (3) to provide a quick and useful granulometric indicator in paleomagnetism.