Comparing the Gradual Deformation with the Probability Perturbation Method for Solving Inverse Problems

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Geological realism in hydrogeological and geophysical inverse modeling: A review (2015, methodology): “The probability perturbation method (PPM) is similar to the gradual deformation method in principle but offers a different perspective [15,17].”
Bayesian inverse problem and optimization with iterative spatial resampling (2010, methodology): “[22] Among data‐driven methods, we mention the gradual deformation method (GDM) [Caers, 2007; Hu and Le Ravalec‐Dupin, 2004; Le Ravalec‐Dupin and Noetinger, 2002; Liu and Oliver, 2004], the quasi‐linear method [Kitanidis, 1995; Zanini and Kitanidis, 2009], and the regularized pilot points method…”
Blocking Moving Window algorithm: Conditioning multiple‐point simulations to hydrogeological data (2010, methodology): “A second difficulty is inherent to the use of the tau model, because the posterior distribution (conditioned to state variables) depends on the value of the coefficient used in the tau model [Caers, 2007].”
A New Differentiable Parameterization Based on Principal Component Analysis for the Low-Dimensional Representation of Complex Geological Models (2014, methodology): “Other data assimilation procedures, which do not require gradients, include the gradual deformation method (Hu et al. 2001) and the probability perturbation method (Caers 2007).”