We quantified mathematical constraints of Backus averaging.

 

Our quantification is based on approximation theory, and examines intrinsic approximations of Backus averaging, such as the average of a product expressed as product of averages.

 

Presently, seismologists can quantify the reliability of their interpretation based Backus averaging, which is a ubiquitous method of applied geophysics.

Dalton, D.R., Meehan, T.B., Slawinski, M.A. (2018)   On Backus average in modelling guided waves.  arXiv:1801.05464

 

Bos, L.P., Danek T., Slawinski, M.A., Stanoev, T.   (2017)   Statistical and numerical considerations of  Backus-average product approximation.   Journal of Elasticity

 

Bos, L.P., Dalton, D.R., Slawinski, M.A., Stanoev, T.   (2017)   On Backus average for generally anisotropic layers .   Journal of Elasticity. 127(2), 179-196

 

Bos, L.P., Dalton, D.R., Slawinski, M.A. (2017)   On  commutativity and near commutativity of translational and rotational averages: Analytical proofs and numerical examination. arXiv: 1704.05541

Dalton D.R., Slawinski, M.A.   (2016)   On commutativity of Backus average and Gazis et al. average . arXiv: 1601.02969

Dalton, D.R., Slawinski, M.A.   (2016)   On Backus average for oblique incidence .  arXiv:1601.02966

 

Dalton, D.R., Slawinski, M.A.   (2016)   Numerical examination of commutativity between Backus and Gazis et al. averages.  arXiv: 1609.01034

 

Danek, T., Slawinski, M.A.   (2016)   Backus average under random perturbations of layered media.   SIAM Journal on Applied Mathematics 76(4), 1239-1249

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