## 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.

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.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