On the Implications of A Priori Constraints in Transdimensional Bayesian Inversion for Continental Lithospheric Layering

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 VSV 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 Vp/Vs ratio. The synthetic tests on two Earth models show that a fixed Vp/Vs 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 Vp/Vs 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.

Stochastic Inversion of P‐to‐S Converted Waves for Mantle Composition and Thermal Structure: Methodology and Application

“…Crustal velocities are assumed to increase as a function of depth ( ) with S wave velocity below the Moho determined by the mantle compositional and thermal structure (see section ). As discussed by Roy and Romanowicz (), the choice of crustal V p /V s ratio does not significantly affect the recovery of crustal velocity models. Therefore, crustal P wave velocities and densities are computed using V p /V s and ρ /V s ratios taken from PREM (Dziewonski & Anderson, ).…”

“…) with S wave velocity below the Moho V Moho s determined by the mantle compositional and thermal structure (see section 2.1). As discussed by Roy and Romanowicz (2017), the choice of crustal V p ∕V s ratio does not significantly affect the recovery of crustal velocity models. Therefore, crustal P wave velocities and densities are computed using V p ∕V s and ∕V s ratios taken from PREM (Dziewonski & Anderson, 1981).…”

Shear Velocity Model of Alaska Via Joint Inversion of Rayleigh Wave Ellipticity, Phase Velocities, and Receiver Functions Across the Alaska Transportable Array

“…The initial Bayesian MCMC inversion benefits from full exploration of the parameter space and is unlikely to be trapped in a local minimum while simultaneously quantifying model uncertainty (Roy & Romanowicz, 2017;Shen et al, 2012). The MCMC model space of our study consists of three layers from the surface to a total depth of 145 km, including a top linear sedimentary layer, a crustal layer described by four cubic B-splines, and a mantle layer described by five cubic B-splines, a total of 13 free parameters (see Table 1).…”

Transdimensional Electrical Resistivity Tomography

“…This is particularly beneficial in cases where forward modeling calculations are computationally expensive so that considerable computing time may be spent on a single Markov chain iteration. Examples of applications of parallel tempering to geophysical inverse problems include the inversion of controlled source electromagnetic data (Ray et al, ), finite fault (Dettmer et al, ) and direct seismogram (Dettmer et al, ) inversion, the inversion of surface wave dispersion and receiver function data (Roy & Romanowicz, ), seismic body wave (Bottero et al, ) and ambient noise (Valentová et al, ) tomography, inversion of airborne electromagnetic data (Hawkins et al, ), and full waveform inversion of marine seismic data (Ray et al, ).…”