PyMDS, a Bayesian inversion algorithm for chlorine 36 dating based on the last No-UTurn Sampler (NUTS)

Abstract

Markov Chain Monte Carlo (MCMC) algorithms are sampling approaches relying on Bayesian inference, theorized in the late 1940s and used in many applications (multi-dimensional integral computations, probability law explorations, inversion problems, etc.). MCMC methods are computationally expensive and many variants have been proposed to optimize them Today, MCMC algorithms are used as inversion tools in different contexts: from receiver functions in seismology . The success and efficiency of those methodologies depends on: the complexity of the forward function, the efficiency of the MCMC strategy and the implementation language. The last MCMC sampler is the No U-Turn Sampler or NUTS (Hoffman and Gelman, 2011), an evolution of the Metropolis Hastings (HMC). Estimating seismic history along fault scarps from 36Cl profiles is a typical inversion problem. Thus, previous studies have proposed MCMC routines to the forward function described in (Schlagenhauf et al., 2011), to invert 36Cl data and to infer seismic histories on fault scarps  (Beck et al., 2018; Mechernich et al., 2023; Tesson and Benedetti, 2019). The complexity of the forward function implies the necessity of a powerful MCMC sampler such as NUTS (Liesenfeld and Richard, 2008). Here, we discuss these different approaches and present a new approach, termed as PyMDS, which relies on the NUTS algorithm. We implemented the code in python and performed synthetic tests to evaluate the algorithm ability to retrieve seismic histories.The results for three earthquakes synthetics tests will be presented and show that the algorithm is capable of finding the seismic scenario (ages, slips and slip rate) with a precision of few hundred years on the ages, 10 to 30 cm on the slips and inferior 0.05 mm/yr on the slip rate with a runtime of 4 hours (faster than the previous Fortran code published by Tesson & Benedetti (2019) that required 3 days to complete). We will also present preliminary results obtained on the five sites located on the Velino-Magnola fault system and the implication on seismic cycle. Finally, we will discuss potential improvement and development perspectives, such as the optimization of the forward function, the necessity to invert slips and the parametrization of the NUTS algorithm.