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.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
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