Bayesian transdimensional seismic full-waveform inversion with a dipping layer parameterization

Abstract

Seismic full-waveform inversion (FWI) has become a popular tool for estimating subsurface models using the amplitude and phase of seismograms. Unlike the conventional gradient-based approach, Bayesian inference using Markov chain Monte Carlo (MCMC) sampling can remove dependence on starting models and can quantify uncertainty. We have developed a Bayesian transdimensional (trans-d) MCMC seismic FWI method for estimating dipping-layer velocity models, in which the number of layers is unknown. A time-domain staggered-grid finite-difference wave equation solver is used for forward modeling. The FWI and MCMC methods are known to be computationally expensive. Two strategies are used to get practical computational performance. A layer-stripping strategy is used to accelerate sampler convergence, and a parsimonious dipping layer parameterization is used so that the MCMC algorithm can search broadly with fewer iterations. The parameters for each layer are velocity, thickness, and lower interface dip angle. We find that this parameterization has sufficient flexibility to invert for narrow 2D velocity models using small offset data. Model stitching is then used to bring several such inversions together to create larger 2D models. In turn, these can be used as starting models for gradient-based adjoint FWI to image complicated geologic settings. Two synthetic 2D numerical examples, including the Marmousi model, are considered, using seismic data dominated by reflections. Creation of good starting models traditionally requires significant human effort. We determine how much of that effort can be substituted with computation.