Seismic data are used to generate high resolution subsurface images, which require detailed velocity models. Full Waveform Inversion (FWI), has recently gathered immense popularity in inverting for the elastic wave velocities from the seismic data. FWI is a non-linear and non-unique inverse problem that uses complete time and amplitude information for estimating the elastic properties. Typically FWI is performed using local optimization methods in which the subsurface model is described by using a large number of grids. The number of model parameters is determined a priori. In addition, the convergence of the algorithm to the globally optimum answer is largely dictated by the choice of a starting model. Here, we apply a trans-dimensional approach, which is based on a Bayesian framework to solve the waveform inversion problem. In our approach, the number of model parameters is also treated as a variable, which we hope to estimate. We use Voronoi cells and represent our 2D velocity model using certain nuclei points and employ a recently developed method called the Reversible Jump Hamiltonian Monte Carlo (RJHMC). RJHMC is an effective tool for model exploration and uncertainty quantification. It combines the reversible jump MCMC with the gradient based Hamiltonian Monte Carlo (HMC). We solve our forward problem using time-domain finite difference method while ad-joint method is used to compute the gradient vector required at the HMC stage. We demonstrate our algorithm with noisy synthetic data for the well known Marmousi model. Convergence of the chain is attained in about 3000 iterations; marginal posterior density plots of velocity models demonstrate uncertainty in the obtained velocity models.
Presentation Date: Monday, September 25, 2017
Start Time: 2:15 PM
Presentation Type: ORAL