Static and Quasi-Static Inversion of Fault Slip During Laboratory Earthquakes

Inferring the spatio-temporal distribution of fault slip during earthquakes from seismological data is challenging due to the non-uniqueness, ill-posed nature, and high dimensionality of the inverse problem. Finite source inversion often relies on simplifying assumptions, and in the absence of ground truth observations it is difficult to assess the reliability of the resulting slip history. Therefore, evaluation of the inversion performance is typically limited to synthetic tests.

Laboratory earthquakes provide an alternative approach to address these challenges by providing "simulated real data" under controlled conditions with relatively well-constrained solutions. In this study, we are analyzing frictional ruptures obtained using a biaxial apparatus. The setup uses three independent vertical pistons to apply heterogeneous normal loads, and one horizontal piston to apply shear load along a 40 cm long fault interface. During each rupture, acceleration is recorded at 20 receivers positioned horizontally or vertically along the fault. These acceleration measurements are integrated twice to obtain displacements, which are then used to invert the slip history.

One of the critical aspects of slip inversion is the accurate definition of Green's function, which depends on numerous assumptions, including source geometry, medium properties and computational constraints, etc. To test the influence of Green’s functions, we first conduct a static inversion of the final slip using two distinct solutions: (1) the analytical Okada solution for a semi-infinite half-space and (2) finite-element simulations using COMSOL, which incorporate detailed information about our setup.

To perform the inversion, we use the Metropolis sampling algorithm, which provides a range of solutions, essential for assessing the uncertainty in our results and addressing the issue of non-uniqueness.

Our results demonstrate that while both solutions provide a good fit of the observed data, only the Green’s function obtained considering the geometry of the fault system and the loading conditions allows to obtain a solution that is consistent with the ground truth, measured individually during the experiments using laser sensors.

Using COMSOL-generated Green’s functions, our quasi-static inversion are able to reconstruct the evolution of the rupture, even for complex ruptures involving deceleration and subsequent acceleration, which are measured independently using high-speed photoelastic measurements. Our results demonstrate the robustness of our inversion procedure, and that accelerometers can be used to invert the evolution of fault slip along the fault, even during complex propagation sequences.