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Model parameterizations in the time domain multi parameter acoustic least squares reverse time migration

Zhang Wei, Gao Jinghuai

Acta Geophysica

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2021

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Vol. 69, no. 2

441--458

EN

Acoustic least-squares reverse time migration (LSRTM) can retrieve the improved refection images. However, the most existing acoustic LSRTM approaches generally ignore the density variation of the subsurface. The multi-parameter acoustic LSRTM approach in the presence of a density parameter can overcome this weakness. However, diferent model parameterizations in such an acoustic LSRTM approach can lead to diferent migration artifacts and infuence the rate of convergence. In this paper, we mainly investigate and analyze the refectivity images of diferent model parameterizations in the multi-parameter acoustic LSRTM approach, in which the velocity–density parameterization can provide reliable refection images. According to Green’s representation theory, we derive the gradients of the objective function with regard to the multi-parameter refectivity images in detail, in which both the migration image of density in the velocity–density model parameterization and the migration image of impedance in the impedance–velocity model parameterization are free from the low-frequency artifacts. Through numerical examples using the layered and fault models, we have proved that the multiparameter acoustic LSRTM approach with the velocity–density model parameterization can provide the migration images with higher resolution and improved amplitudes. Meanwhile, a correlation-based objective function is less sensitive to amplitude errors than the conventional waveform-matching objective function in the multi-parameter acoustic LSRTM approach.

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Solutions for network games and symmetric group representations

Sánchez-Pérez Joss

Operations Research and Decisions

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2019

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Vol. 29, No. 4

95--123

EN

We present the relationship between network games and representation theory of the group of permutations of the set of players (nodes), and also offer a different perspective to study solutions for this kind of problems. We then provide several applications of this approach to the cases with three and four players.

3

An application of the representations of symmetric groups to characterizing solutions of games in partition function form

Sánchez-Pérez J.

Operations Research and Decisions

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2014

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Vol. 24, No. 2

97--122

EN

A different perspective from the more “traditional” approaches to studying solutions of games in partition function form has been presented. We provide a decomposition of the space of such games under the action of the symmetric group, for the cases with three and four players. In particular, we identify all the irreducible subspaces that are relevant to the study of linear symmetric solutions. We then use such a decomposition to derive a characterization of the class of linear and symmetric solutions, as well as of the class of linear, symmetric and efficient solutions.

4

An Incidence Algebra Approach to Knowledge Granulation in Pawlak Information Systems

Wolski M., Gomolińska A.

Fundamenta Informaticae

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2013

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Vol. 128, nr 1-2

223--238

EN

Representation theory is a branch of mathematics whose original purpose was to represent information about abstract algebraic structures by means of methods of linear algebra (usually, by linear transformations and matrices). G.-C. Rota in his famous Foundations defined a representation of a locally finite partially ordered set (locally finite poset) P in terms of a module over a ring \mathbbA, which can further be extended by the addition of a convolution operation to an associative \mathbbA-algebra called an incidence algebra of P. He applied this construction to solve a number of important problems in combinatorics. Our goal in this paper is to discuss the concept of an incidence algebra as a representation of a Pawlak information system. We shall analyse both incidence algebras and information systems in the context of granular computing, a paradigm which has recently received a lot of attention in computer science. We discuss therefore the concept of an incidence algebra on two levels: the level of objects which form a preordered set and the level of information granules which form a poset. Since incidence algebras induced on these two levels are Morita equivalent, we may focus our attention on the incidence algebra of information granules. We take the lattice of closed ideals of this algebra, where the maximal elements serve as a representation of information granules. The poset of maximal closed ideals obtained in this way is isomorphic to the set of information granules of the Pawlak information system equipped with a natural information order.