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

Inferring from seismological data the spatio-temporal distribution of slip during earthquakes remains a challenge due to the large size, non-uniqueness and ill-posedness of the inverse problem. Consequently, finite source inversion usually relies on simplifying assumptions. Moreover, in the absence of ground truth source data, the evaluation of the performance of source inversion is only possible through synthetic tests.

To address these concerns and test the viability of the inversion methods used for natural earthquakes, laboratory earthquakes offer a valuable alternative. They enable us to work with "simulated real data" and provide a relatively well-constrained solution. Here, we employ a biaxial apparatus capable of reproducing shear rupture along a rectangular fault separating two PMMA blocks. Both normal and shear stresses are initially increased up to the target normal stress using external pressure pumps, assuming a fixed shear to normal stress ratio of 0.3. Subsequently, the shear stress is increased until instabilities occur at a peak friction of 0.4. During each seismic rupture, we measure the acceleration at 20 receivers along the fault. The acceleration data are integrated twice into displacements, and then used to invert for the slip history, which is compared to direct measurements using laser sensors placed through the fault. For a static inversion of final slip, predictions are computed using Okada's formulation and the posterior probability density function of the slip history is obtained using a Metropolis algorithm. We will also report on results of quasi-static inversion. The adoption of a probabilistic approach provided a range of solutions, essential for assessing the uncertainty in our results and addressing the issue of non-uniqueness. Ultimately, the obtained results will offer insights into inversion methods, presenting their strengths and limitations more realistically than when using artificially generated synthetic datasets.