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On commutativity of Backus and Gazis averages

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David R. Dalton, Michael A. Slawinski

Geophysics · Submitted 12 Jan 2016

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show that the Backus (1962) equivalent-medium average, which is an average over a spatial variable, and the Gazis et al. (1963) effective-medium average, which is an average over a symmetry group, do not commute, in general.

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arXiv ID1601.02969 (version 1)
Pith IDFYJO35N4, Pith's permanent record of this paper and its review
CitationDavid R. Dalton, Michael A. Slawinski. "On commutativity of Backus and Gazis averages." arXiv:1601.02969 (2016). https://pith.science/paper/FYJO35N4
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,295 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.45 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.59 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We show that the Backus (1962) equivalent-medium average, which is an average over a spatial variable, and the Gazis et al. (1963) effective-medium average, which is an average over a symmetry group, do not commute, in general. They commute in special cases, which we exemplify.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We show that the Backus (1962) equivalent-medium average, which is an average over a spatial variable, and the Gazis et al. (1963) effective-medium average, which is an average over a symmetry group, do not commute, in general. result 0.97 0.89 0.95 asserted 1.00
s1 They commute in special cases, which we exemplify. result 0.97 0.86 0.08 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.98.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We show that the Backus (1962) equivalent-medium average, which is an average over a spatial variable, and the Gazis et al. (1963) effective-medium average, which is an average over a symmetry group, do not commute, in general. They commute in special cases, which we exemplify.

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