Inverse Problem Theory

By A. Morelli. 2010

796 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/4784e4ddf5a861fce8a691f841c515713e203394

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Citations in the corpus

Data Assimilation: A Mathematical Introduction (2015, methodology): “14) as the starting point, rather than starting from a minimization principle; it is then very closely related to the method of krigging from the geosciences [108].”
Data Assimilation for Numerical Weather Prediction: A Review (2009, background): “…yo −H(xb) ] (2) Related theoretical material related to the set-up that led to modern data assimilation may be found in the “Inverse Problem Theory” of Tarantola (1987), the optimal control book of Lions (1971), the “Perspectives in Flow Control and Optimization” by Max Gunzburger (2003) along…”
B‐preconditioned minimization algorithms for variational data assimilation with the dual formulation (2014, background): “This approach has its origin in maximum likelihood estimation under a Gaussian assumption (Tarantola, 2005, pp 24–32).”
Non-Gaussian statistical inverse problems. Part I: Posterior distributions (2012, methodology): “Statistical inverse theory became a popular method for solving geophysical problems in 1980’s [121, 122], and has since spread into many other fields (see [65, 120]).”
Misfit functions for full waveform inversion based on instantaneous phase and envelope measurements (2011, background): “…is based on differences between observed and synthetic waveforms combining amplitude together with phase information, and is defined as (e.g. Tarantola 1984, 1987, 1988; Nolet 1987) χ (m) = 1 2 N∑ r=1 ∫ T 0 ‖d(xr , t) − s(xr , t, m)‖2 dt, (35) C© 2011 The Authors, GJI, 185, 845–870…”
Survey of multifidelity methods in uncertainty propagation, inference, and optimization (2018, background): “In statistical inference [195, 194, 110, 192], the unknown input is modeled as a random variable and one is interested in sampling the distribution of this random variable to assess the uncertainty associated with the input estimation.”
An improved neighborhood algorithm: Parameter conditions and dynamic scaling (2008, methodology): “Inversion tools include linearized methods [Nolet, 1981; Tarantola, 1987] and direct search techniques [Sen and Stoffa, 1991; Lomax and Snieder, 1994] that gained success during the nineties parallel to the development of the power of desk computers.”
Bayesian Gaussian Mixture Linear Inversion for Geophysical Inverse Problems (2017, background): “Bayesian inversion methods are commonly used in geophysics and petroleum engineering for solving inverse problems and estimating an unknown model from measured data in the subsurface (Tarantola, 2005).”