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Hamiltonian Nullspace Shuttles
Author(s) -
Fichtner Andreas,
Zunino Andrea
Publication year - 2019
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/2018gl080931
Subject(s) - monte carlo method , hybrid monte carlo , hamiltonian (control theory) , hamiltonian system , nonlinear system , probabilistic logic , hamiltonian mechanics , mathematics , physics , statistical physics , mathematical analysis , mathematical optimization , markov chain monte carlo , phase space , statistics , quantum mechanics , thermodynamics
We present a method to explore the effective nullspace of nonlinear inverse problems without Monte Carlo sampling. This is based on the construction of an artificial Hamiltonian system where a model is treated as a high‐dimensional particle. Depending on its initial momentum and mass matrix, the particle evolves along a trajectory that traverses the effective nullspace, thereby producing a series of alternative models that are consistent with observations and their uncertainties. Variants of the nullspace shuttle enable hypothesis testing, for example, by adding features or by producing smoother or rougher models. Furthermore, the Hamiltonian nullspace shuttle can serve as a tunable hybrid between deterministic and probabilistic inversion methods: Choosing random initial momenta, it resembles Hamiltonian Monte Carlo; requiring misfits to decrease along a trajectory, it transforms into gradient descent. We illustrate the concept with a low‐dimensional toy example and with high‐dimensional nonlinear inversions of seismic traveltimes and magnetic data, respectively.