On possible issues of Backus average

TL;DR

This paper examines potential issues with the Backus average approximation in seismology, analyzing specific scenarios where it may fail despite its general stability, through theoretical and case study approaches.

Contribution

It investigates the conditions under which the Backus average may produce inaccuracies in seismological models, extending prior work with new case studies and analysis.

Findings

Potential issues identified in specific seismological scenarios

Backus average stability conditions may not always hold

Case study in oceanic crust highlights possible inaccuracies

Abstract

In this paper, we continue the study of Bos et al. (2018) regarding statistical and numerical considerations of the Backus (1962) product approximation. While the approximation is typically quite good for seismological scenarios, Bos et al. (2018) demonstrate a physical scenario that could, in spite of the stability conditions for isotropic media, lead to an issue within the Backus average. Using the Preliminary Reference Earth Model of Dziewo\'nski and Anderson (1981) and a case study in the upper oceanic crust, we investigate whether this issue is likely to occur in the context of seismology.