Topographic and 3D elastic variations: when to account for it in fault slip estimates?

Inference of subsurface fault slip is primarily constrained by measures of deformation at the surface of the Earth, but is also severely impacted by our description of the Earth's response to this deformation. Our understanding of the structure of the Earth's interior being uncertain, our parameterization of the Earth's response will remain an approximation of the reality, and thus will always be susceptible to include biases in inferred source properties. Yet, biases in slip estimates can be, at least in part, overcome; by building realistic replicates of the known, and by explicitly accounting for the imperfections of the poorly known. The elevation of the Earth's surface is well known almost everywhere on the globe, and can have a significant impact on inferred source properties. In contrast, most characteristics of the surface and sub-surface, such as crustal properties or fault geometry, fall in the poorly-known category. Yet, topography is often overlooked, and when it is not, its impact on subsurface fault slip is usually amalgamated with the effect of crustal structure. In the presence of which geomorphological features, and in which context, do we need to implement topography when solving for subsurface fault slip - or else encounter large biases? Similarly, do we need to implement the effect of 3D crustal heterogeneity and related uncertainties- in any context to ensure robust results?The aim of this study to provide generic guidelines on when to neglect, or when to account for, 3D elastic and topographic variations, to obtain robust slip estimates with the most efficient modeling strategy. We design a series of toy models, mainly in subduction context, to investigate the interplay between the structure of the Earths interior and surface, data distribution, slip location and robustness of the slip estimates.