  Stochastic reservoir characterization, a critical aspect of subsurface
exploration for oil and gas reservoirs, relies on stochastic methods to model
and understand subsurface properties using seismic data. This paper addresses
the computational challenges associated with Bayesian reservoir inversion
methods, focusing on two key obstacles: the demanding forward model and the
high dimensionality of Gaussian random fields. Leveraging the generalized
Bayesian approach, we replace the intricate forward function with a
computationally efficient multivariate adaptive regression splines method,
resulting in a 34 acceleration in computational efficiency. For handling
high-dimensional Gaussian random fields, we employ a fast Fourier transform
(FFT) technique. Additionally, we explore the preconditioned Crank-Nicolson
method for sampling, providing a more efficient exploration of high-dimensional
parameter spaces. The practicality and efficacy of our approach are tested
extensively in simulations and its validity is demonstrated in application to
the Alvheim field data.
