Mathematical constraints of Backus averaging

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., Slawinski, M.A. (2019) On Backus average in modelling guided waves. Journal of Applied Geophysics 170(103815)


Bos, L., Slawinski, M.A., Stanoev, T. (2019) On the Backus average of layers with randomly oriented elasticity tensors. Zeitschrift für angewandte Mathematik und Physik 70(84)


Bos, L., Dalton, D.R., Slawinski, M.A. (2019) On commutativity and near commutativity of translational and rotational averages: Analytical proofs and numerical examinations. Journal of Elasticity 136, 189–206


Bos, L., Danek, T., Slawinski, M.A., Stanoev, T. (2018) Statistical and numerical considerations of Backus-average product approximation. Journal of Elasticity 132(1), 141–159


Adamus, F.P., Slawinski, M.A., Stanoev, T. (2018) On effects of inhomogeneity on anisotropy in Backus average, 1802.04075 [physics.geo-ph]

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

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

The Geomechanics Project