Magnitude Distribution During Transformational Faulting: Implication for Deep‐Focus Earthquakes

Abstract Deep‐focus earthquakes occur at 300–660 km depth. Geophysical observations and deformation experiments have proposed the olivine‐spinel (wadsleyite/ringwoodite) phase transformation as the source of the mechanical instability. While geophysical observations indicate that fault geometry influences the ‐values of the Gutenberg‐Richter law for transformational faulting, deformation experiments reveal that ‐values are also influenced by rock properties, including structural heterogeneity. Grain sizes play a crucial role in the rate of phase transformation, impacting the occurrence of faulting. Consequently, grain sizes may also influence ‐values. We conducted deformation experiments on germanate olivine (), an analog to silicate olivine, with various grain sizes to reveal the effect of grain size on ‐value during transformational faulting. We used a Griggs‐type deformation apparatus and measured acoustic emissions (AE) with an AE transducer, which was calibrated by laser‐doppler interferometry. This calibration enabled the acquisition of AE waveforms with a unit of velocity (m/s), facilitating comparison to natural earthquakes. ‐values in the fine‐grained aggregates (a few ) are smaller than those in the coarse‐grained aggregates (hundreds of ) at the same deformation conditions. In coarse‐grained aggregates, heterogeneous formation of spinel aggregates contributes to high ‐values. Conversely, in fine‐grained aggregates, homogeneous formation of spinel grains at the grain boundaries results in lower ‐values. Therefore, the homogeneity (or heterogeneity) of spinel formation could be one of the factors controlling the ‐values of deep‐focus earthquakes.