Uncertainty quantification for inhomogeneous frictional features in a slow-slipping fault based on a large-scale four-dimensional variational data assimilation
Abstract
Dynamics of slipping motion of a fault largely depends on spatial inhomogeneous frictional features on the fault. Thus, it is important to estimate the spatial frictional features from the observations of the slipping motion and to identify essential parts of frictional features that contribute to the main motion of the slipping by quantifying uncertainties involved in the estimated frictional features.
Data assimilation (DA) is a numerical technique that integrates numerical simulation models and observational data based on the Bayesian statistics, and it enables us to estimate unobservable quantities such as spatial frictional features together with their uncertainties by evaluating a posterior probability density function (PDF). However, evaluating the posterior PDF easily becomes impossible when applying conventional DAs to large-scale simulation models used in the solid Earth science because "curse of dimensionality" causes an exponential explosion of computational complexity. To solve this problem, we proposed a DA method based on a four-dimensional variational method that enables us to obtain estimates together with their uncertainties within a practical computational time and resources. Our method, in which a second-order adjoint method is implemented, does not depend on the number of degrees of freedom (NDF) involved in a given simulation model to obtain estimates together with their uncertainties, whereas the conventional DAs needs computational cost proportional to an exponential order of NDF. This study applies our new DA method to a fault model that mimics slow-slipping region along the Bungo Channel. The fault model employs a rate-and-state dependent friction law, of which the frictional parameters are spatially dependent. Due to this feature, NDF of this fault model is so large that the conventional DAs cannot be applied. Through applying our new DA method to the fault model using synthetic data of slip velocity on the fault, we investigate the estimates of frictional features and their uncertainties, and subsequently, we quantify the relation between the slow-slipping motion and the uncertainties of frictional features. Such quantification provides valuable information to optimize observational design.- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2019
- Bibcode:
- 2019AGUFM.T43G0400I
- Keywords:
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- 1242 Seismic cycle related deformations;
- GEODESY AND GRAVITY;
- 7223 Earthquake interaction;
- forecasting;
- and prediction;
- SEISMOLOGY;
- 8118 Dynamics and mechanics of faulting;
- TECTONOPHYSICS;
- 8163 Rheology and friction of fault zones;
- TECTONOPHYSICS