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

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 $b$-values of the Gutenberg-Richter law for transformational faulting, deformation experiments reveal that $b$-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 $b$-values. We conducted deformation experiments on germanate olivine (${\text{Mg}}_2{\text{GeO}}_4$), an analog to silicate olivine, with various grain sizes to reveal the effect of grain size on $b$-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. $b$-values in the fine-grained aggregates (a few $\mu m$) are smaller than those in the coarse-grained aggregates (hundreds of $\mu m$) at the same deformation conditions. In coarse-grained aggregates, heterogeneous formation of spinel aggregates contributes to high $b$-values. Conversely, in fine-grained aggregates, homogeneous formation of spinel grains at the grain boundaries results in lower $b$-values. Therefore, the homogeneity (or heterogeneity) of spinel formation could be one of the factors controlling the $b$-values of deep-focus earthquakes.