On the Implications of A Priori Constraints in Transdimensional Bayesian Inversion for Continental Lithospheric Layering. Issue 12 (13th December 2017) - Roy, C.; Romanowicz, B. A.
Abstract: Monte Carlo methods are powerful approaches to solve nonlinear problems and are becoming very popular in Earth sciences. One reason being that, at first glance, no constraints or explicit regularization of model parameters are required. At second glance, one might realize that regularization is done through a prior. The choice of this prior, however, is subjective, and with its choice, unintended or undesired extra information can be injected into the problem. The principal criticism of Bayesian methods is that the prior can be "tuned" in order to get the expected solution. Consequently, detractors of the Bayesian method could easily argue that the solution is influenced by the form of the prior distribution, which choice is subjective. Hence, models obtained with Monte Carlo methods are still highly debated. Here we investigate the influence of a priori constraints (i.e., fixed crustal discontinuities) on the posterior probability distributions of estimated parameters, that is, vertical polarized shear velocity V SV and radial anisotropy ξ, in a transdimensional Bayesian inversion for continental lithospheric structure. We follow upon the work of Calò et al. (2016), who jointly inverted converted phases ( P to S ) without deconvolution and surface wave dispersion data, to obtain 1‐D radial anisotropic shear wave velocity profiles in the North American craton. We aim at verifying whether the strong lithospheric layering found in the stable part of the craton is robust with respect to artifacts that might be caused by the methodology used. We test the hypothesis that the observed midlithospheric discontinuities result from (1) fixed crustal discontinuities in the reference model and (2) a fixed V p / V s ratio. The synthetic tests on two Earth models show that a fixed V p / V s ratio does not introduce artificial layering, even if the assumed value is slightly wrong. This is an important finding for real data inversion where the true value is not always available or accurate. However, fixing crustal discontinuities can lead to the introduction of spurious layering, and this is not recommended. Additionally, allowing the V p / V s ratio to vary does not help preventing that. Applying the modified approach resulting from these tests to two stations (FRB and FCC) in the North American craton, we confirm the presence of at least one midlithospheric low‐velocity layer. We also confirm the difficulty of consistently detecting the lithosphere‐asthenosphere boundary in the craton. Key Points: Fixing crustal discontinuities can lead to erroneous results in modeling upper mantle structure Treating the V p / V s as an unknown does not improve results and cannot prevent the appearance of spurious layers We confirm the presence of a sharp MLD at 70 km atop a ∼50 km thick low shear velocity layer in the middle of the NA craton