Abstract
This paper is concerned with the estimation of a parametric probabilistic model of the random displacement source field at the origin of seaquakes in a given region. The observation of the physical effects induced by statistically independent realizations of the seaquake random process is inherent with uncertainty in the measurements and a stochastic inverse method is proposed to identify each realization of the source field. A statistical reduction is performed to drastically lower the dimension of the space in which the random field is sought and one is left with a random vector to identify. An approximation of the vector components is determined using a polynomial chaos decomposition, solution of an optimality system to identify an optimal representation. A second order gradient-based optimization technique is used to efficiently estimate this statistical representation of the unknown source while accounting for the non-linear constraints in the model parameters. This methodology allows the uncertainty associated with the estimates to be quantified and avoids the need for repeatedly solving the forward model.
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Mathelin, L., Desceliers, C. & Hussaini, M.Y. Stochastic data assimilation of the random shallow water model loads with uncertain experimental measurements. Comput Mech 47, 603–616 (2011). https://doi.org/10.1007/s00466-010-0560-7
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DOI: https://doi.org/10.1007/s00466-010-0560-7