Adjoint-based uncertainty quantification for inhomogeneous friction on a slow-slipping fault

Abstract

SUMMARY Long-term slow-slip events (LSSEs) usually occur on a fault existing at the deep, shallow parts of subducting plates and substantially relate to adjacent megathrust fault motions. The dynamics of the LSSE largely depend on the inhomogeneity of friction that occurs between the fault interfaces. Thus, it is crucial to estimate the spatial-dependent frictional features from the observations of the slip motion and subsequently identify essential parts that contribute to the principal slip motion by quantifying uncertainties involved in the estimates. Although quantifying the uncertainties of the frictional feature fields in high resolution is necessary to solve the task, conventional techniques of quantifying slow earthquake frictional features have not yet achieved such uncertainty quantification (UQ) due to the complexity of LSSE models such as the large dimensionality. We, therefore, propose a method of UQ for spatially inhomogeneous frictional features from slip motion based on a 4-D variational data assimilation technique using a second-order adjoint method. The proposed method enables us to conduct an accurate UQ even when the dimensionality is large. By combining a fault motion model that mimics slow-slip motion on an LSSE fault–megathrust fault complex in southwestern Japan and the data assimilation technique, we successfully quantified the spatial distribution of the uncertainty of the frictional features in high-resolution. The evaluated spatial distribution in high-resolution reveals the correlation between the dynamics of the slow-slip motion and the important components of the frictional features, which is a valuable information for designing observation systems. Findings from this study are expected to advance the theoretical foundation of applied seismic motion prediction techniques using slow-slip frictional features as stress metres for megaquakes, as well as to improve the understanding of the relationship between the slow-slip motion and frictional parameters of a fault.