DE Seminar: Rileigh Mansfield
UMBC Undergraduate Student
Location
Mathematics/Psychology : 401
Date & Time
December 2, 2024, 11:00 am – 12:00 pm
Description
Title: Understanding
and Tuning Earthquake Models with Data Assimilation
Speaker: Rileigh Mansfield
Abstract: Every year
fault-lying lands have to combat frequent earthquakes and their damaging
consequences. Although there are GPS stations used to measure the displacement
of the Earth on the surface, it is difficult to measure the Earth’s
displacement and stress field directly and densely below the surface. This
makes it hard to understand and predict the effects of earthquakes. We address
this issue by making use of a viscoelastic history-dependent partial
differential equation model of the Earth’s displacement. We included an
internal variable (history-dependence) in our model because the history of
the stress and strain on the material affects how it deforms. Internal
variables are often used to model time-dependent complex material behaviors due
to their ability to incorporate memory effects. Models are imperfect, so we
utilize data assimilation to correct our model using displacement measurements
on the Earth’s surface. More specifically, we utilize a stochastic data
assimilation method called particle filter, a method that uses Bayesian methods
to assign more importance to model trajectories that best match the data, to
recover the deformation field in a simplified viscoelastic model without
knowing the deformation history. Our preliminary results can be extended to
construct predictive viscoelastic models for continuous monitoring and
predictions of the effects of earthquake events, helping to contribute to the
effort of combatting damages from an earthquake’s aftermath.
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