Transdimensional Bayesian Joint Inversion of Complementary Seismic Observables with Realistic Data Uncertainties

Due to their different and complementary sensitivities to structure, multiple seismic observables are often combined to image the Earth’s deep interior. We use a reversible jump Markov chain Monte Carlo (rjMCMC) algorithm to incorporate surface wave dispersion, particle motion ellipticity (HZ ratio), and receiver functions into transdimensional, Bayesian inversion for the profiles of shear velocity (Vs), compressional velocity (Vp), and density beneath a seismic station. While traditional inversion approaches seek a single best-fit model, a Bayesian approach yields an ensemble of models, allowing us to fully quantify uncertainty and trade-offs between model parameters. Furthermore, we show that by treating the number model parameters as an unknown to be estimated from the data, we both eliminate the need for a fixed parameterization based on prior information, and obtain better model estimates with reduced trade-offs.

Optimal weighting of disparate datasets is paramount for maximizing the resolving power of joint inversions. In a Bayesian framework, data uncertainty directly determines the variance of the model posterior probability distribution; therefore, characteristics of the uncertainties on the observables become even more important in the inversion (Bodin et al., 2011). To properly account for the noise characteristics of the different seismic observables, we compute covariance matrices of data errors for each data type by generating realistic synthetic noise using noise covariance matrices computed from thousands of noise samples, and then measuring the seismic observables of interest from synthetic waveforms contaminated by many different realizations of noise. We find large non-diagonal terms in the covariance matrices for different data types, indicating that typical assumptions of uncorrelated data errors are unjustified. We quantify how the use of realistic data covariance matrices in the joint inversion affects the retrieval of seismic structure under different noise conditions, and demonstrate the need for accurate data uncertainty representation in seismic inversions.