Duputel, Zacharie and Agram, Piyush S. and Simons, Mark,(2014),
*Accounting for prediction uncertainty when inferring subsurface fault slip.*
, Geophys. J. Int. (2014) 197, 464–482, UNSPECIFIED

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## Abstract

This study lays the groundwork for a new generation of earthquake source models based on
a general formalism that rigorously quantiﬁes and incorporates the impact of uncertainties in
fault slip inverse problems. We distinguish two sources of uncertainty when considering the
discrepancy between data and forward model predictions. The ﬁrst class of error is induced
by imperfect measurements and is often referred to as observational error. The second source
of uncertainty is generally neglected and corresponds to the prediction error, that is the
uncertainty due to imperfect forward modelling. Yet the prediction error can be shown to
scale approximately with the size of earthquakes and thus can dwarf the observational error,
particularly for large events. Both sources of uncertainty can be formulated using the misﬁt
covariance matrix, Cχ, which combines a covariance matrix for observation errors, C and a
covariance matrix for prediction errors, C, associated with inaccurate model predictions. We
develop a physically based stochastic forward model to treat the model prediction uncertainty
and show how Cp p
can be constructed to explicitly account for some of the inaccuracies
in the earth model. Based on a ﬁrst-order perturbation approach, our formalism relates C
to uncertainties on the elastic parameters of different regions (e.g. crust, mantle, etc.). We
demonstrate the importance of including C
using a simple example of an inﬁnite strike-slip
fault in the quasi-static approximation. In this toy model, we treat only uncertainties in the
1-D depth distribution of the shear modulus. We discuss how this can be extended to general
3-D cases and applied to other parameters (e.g. fault geometry) using our formalism for Cp.
The improved modelling of C
is expected to lead to more reliable images of the earthquake
rupture, that are more resistant to overﬁtting of data and include more realistic estimates of
uncertainty on inferred model parameters.

Keywords : | Inverse theory; Probability distributions; Earthquake source observations., UNSPECIFIED |
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Journal or Publication Title: | Geophys. J. Int. (2014) 197, 464–482 |

Volume: | 197 |

Number: | UNSPECIFIED |

Item Type: | Article |

Subjects: | Akuntansi |

Depositing User: | Gunawan Gunawan |

Date Deposited: | 23 Dec 2019 07:04 |

Last Modified: | 23 Dec 2019 07:04 |

URI: | https://repofeb.undip.ac.id/id/eprint/716 |