Time-lapse uncertainty quantification using state of the art Hamiltonian Monte Carlo method

Abstract:

Sampling based uncertainty quantification (UQ) methods are ideal because they make no assumptions about the distributions of the underlying uncertainty. This characteristic is particularly useful in seismic imaging, where the structure of velocity model distributions is typically unknown. Most commonly used sampling algorithms, such as Metropolis Hastings, are slow to converge and can only handle a small number of dimensions. To overcome these challenges we use a more advanced UQ method, Hamiltonian Monte Carlo (HMC). Through long distance updates to the parameter space HMC allows for faster convergence while maintaining high acceptance rates. HMC explores a target distribution by incorporating information about its differential geometry into the search proposal process via gradient calculations. While adjoint state methods typically allow for fast gradient calculations, UQ estimates of seismic velocity models can still be computationally intensive due to the large number of model parameters and thousands of evaluations needed to approximate the distribution. To address these challenges, we exploit the localized nature of typical time-lapse problems by using a local domain. The use of the local domain considerably reduces the computational cost of the wavefield simulation, and allows us to construct a feasible and computationally efficient time-lapse HMC framework. Through our numerical example we show how one can easily set up the algorithm and tune the parameters that are necessary for a successful performance. All computations were performed using a Docker container, allowing for easy reproducibility.