{"@context":{"@vocab":"https://cir.nii.ac.jp/schema/1.0/","rdfs":"http://www.w3.org/2000/01/rdf-schema#","dc":"http://purl.org/dc/elements/1.1/","dcterms":"http://purl.org/dc/terms/","foaf":"http://xmlns.com/foaf/0.1/","prism":"http://prismstandard.org/namespaces/basic/2.0/","cinii":"http://ci.nii.ac.jp/ns/1.0/","datacite":"https://schema.datacite.org/meta/kernel-4/","ndl":"http://ndl.go.jp/dcndl/terms/","jpcoar":"https://github.com/JPCOAR/schema/blob/master/2.0/"},"@id":"https://cir.nii.ac.jp/crid/1362262943923004416.json","@type":"Article","productIdentifier":[{"identifier":{"@type":"DOI","@value":"10.1093/gji/ggw063"}},{"identifier":{"@type":"URI","@value":"http://academic.oup.com/gji/article-pdf/205/2/971/39584902/gji_205_2_971.pdf"}}],"dc:title":[{"@value":"Exploring equivalence domain in nonlinear inverse problems using Covariance Matrix Adaption Evolution Strategy (CMAES) and random sampling"}],"description":[{"type":"abstract","notation":[{"@value":"<jats:title>Abstract</jats:title>\n               <jats:p>This paper presents a methodology to sample equivalence domain (ED) in nonlinear partial differential equation (PDE)-constrained inverse problems. For this purpose, we first applied state-of-the-art stochastic optimization algorithm called Covariance Matrix Adaptation Evolution Strategy (CMAES) to identify low-misfit regions of the model space. These regions were then randomly sampled to create an ensemble of equivalent models and quantify uncertainty. CMAES is aimed at exploring model space globally and is robust on very ill-conditioned problems. We show that the number of iterations required to converge grows at a moderate rate with respect to number of unknowns and the algorithm is embarrassingly parallel. We formulated the problem by using the generalized Gaussian distribution. This enabled us to seamlessly use arbitrary norms for residual and regularization terms. We show that various regularization norms facilitate studying different classes of equivalent solutions. We further show how performance of the standard Metropolis–Hastings Markov chain Monte Carlo algorithm can be substantially improved by using information CMAES provides. This methodology was tested by using individual and joint inversions of magneotelluric, controlled-source electromagnetic (EM) and global EM induction data.</jats:p>"}]}],"creator":[{"@id":"https://cir.nii.ac.jp/crid/1382262943923004544","@type":"Researcher","foaf:name":[{"@value":"Alexander V. Grayver"}],"jpcoar:affiliationName":[{"@value":"Institute of Geophysics, ETH Zürich, Sonneggstrasse 5, 8092 Zürich, Switzerland. E-mail: agrayver@erdw.ethz.ch"}]},{"@id":"https://cir.nii.ac.jp/crid/1382262943923004545","@type":"Researcher","foaf:name":[{"@value":"Alexey V. Kuvshinov"}],"jpcoar:affiliationName":[{"@value":"Institute of Geophysics, ETH Zürich, Sonneggstrasse 5, 8092 Zürich, Switzerland. E-mail: agrayver@erdw.ethz.ch"}]}],"publication":{"publicationIdentifier":[{"@type":"EISSN","@value":"1365246X"},{"@type":"PISSN","@value":"0956540X"}],"prism:publicationName":[{"@value":"Geophysical Journal International"}],"dc:publisher":[{"@value":"Oxford University Press (OUP)"}],"prism:publicationDate":"2016-02-11","prism:volume":"205","prism:number":"2","prism:startingPage":"971","prism:endingPage":"987"},"reviewed":"false","url":[{"@id":"http://academic.oup.com/gji/article-pdf/205/2/971/39584902/gji_205_2_971.pdf"}],"createdAt":"2016-02-12","modifiedAt":"2021-08-05","relatedProduct":[{"@id":"https://cir.nii.ac.jp/crid/1360003449883468416","@type":"Article","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Design of acoustic metamaterials using the covariance matrix adaptation evolutionary strategy"}]},{"@id":"https://cir.nii.ac.jp/crid/1360580232138931968","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Multimodal Rayleigh and Love Wave Joint Inversion for S‐Wave Velocity Structures in Kanto Basin, Japan"}]},{"@id":"https://cir.nii.ac.jp/crid/2050870367053035520","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Regularized magnetotelluric inversion based on a minimum support gradient stabilizing functional"}]}],"dataSourceIdentifier":[{"@type":"CROSSREF","@value":"10.1093/gji/ggw063"},{"@type":"CROSSREF","@value":"10.7567/apex.10.037301_references_DOI_35h0CINq3jBOWc9pmikWu5Qob6"},{"@type":"CROSSREF","@value":"10.1186/s40623-017-0743-y_references_DOI_35h0CINq3jBOWc9pmikWu5Qob6"},{"@type":"CROSSREF","@value":"10.1029/2022jb025017_references_DOI_35h0CINq3jBOWc9pmikWu5Qob6"}]}