Ensemble smoother (ES) has been widely used in high-dimensional inversemodeling. However, its application is limited to problems where uncertainparameters approximately follow Gaussian distributions. For problems withmultimodal distributions, using ES directly would be problematic. One solutionis to use a clustering algorithm to identify each mode, which is not veryefficient when the dimension is high or the number of modes is large.Alternatively, we propose in this paper a very simple and efficient algorithm,i.e., the iterative local updating ensemble smoother (ILUES), to exploremultimodal distributions in high-dimensional problems. This algorithm is basedon updating local ensembles of each sample in ES to explore possible multimodaldistributions. To achieve satisfactory data matches in nonlinear problems, weadopt an iterative form of ES to assimilate the measurement multiple times.Five numerical case studies are tested to show the performance of the proposedmethod. The first example is a low-dimensional problem that has infinite modesin the posterior distribution, which is used to illustrate the basic ideas ofthe proposed method. The second example is similar to the first one, but it isin a high-dimensional setting. To show its applicability in practical problems,we test the ILUES algorithm with three inverse problems in hydrologicalmodeling that have multimodal prior distribution, multimodal posteriordistribution and a large number of unknown parameters, respectively.
展开▼
