Limits on inferring an effective lithospheric rheology from geodetic observations of the earthquake cycle

Abstract The relationship between stress and deformation of the solid Earth at various temporal and spatial scales can be described using a variety of constitutive relations. Although our knowledge of the elastic component of these constitutive relations is relatively well-constrained by seismological observations, there are limited opportunities to probe the inelastic component of plausible constitutive relations. Focusing on viscoelastic rheologies, the exact formulation of the viscous component of the rheology of the crust–mantle system is not uniquely constrained, i.e. multiple formulations (linear Burgers and power-law) are able to recreate geodetic observations of the earthquake cycle. Here, we show that it is possible to discriminate between these commonly adopted rheological models under certain conditions, even with the limited observational time span of geodetic networks. We first run a set of numerical simulations of periodic earthquake cycles as well as 2-event sequences for a two-dimensional strike–slip plate boundary, assuming a 20-km-thick frictional fault in an elastic layer overlying a 30-km-thick viscoelastic channel, to predict the resulting surface displacement time series over a 20-year time window. We use a rate-dependent friction law for the fault and a combined diffusion and dislocation creep viscous flow law with laboratory-derived rheological parameters to describe the non-elastic properties of the medium. We invert the synthetic surface displacements to obtain best-fit parameters for a simplified boundary element representation of each rheological model, assuming all viscous strain is localized beneath the fault, and compare the misfits. Linear Burgers and power-law rheologies are nearly indistinguishable when considering periodic events, but they can be distinguished using data from earthquake sequences when events are sufficiently different in magnitude (at least 0.2 units in magnitude) and occur with adequate temporal separation ( $$\sim $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>∼</mml:mo> </mml:math> 1–10 years). However, when the true parameters represent a power-law rheology, it is not possible to uniquely recover all the rheological parameters. Graphical abstract