A method includes receiving observed seismic data, determining an envelope or magnitude of the observed seismic data as a first observed value, generating a variable noise term based in part upon the first observed value, and utilizing the variable noise term to determine a likelihood function of a stochastic inversion operation. The method also includes utilizing the likelihood function to generate a posterior probability distribution in conjunction with the stochastic inversion operation and applying the posterior probability distribution to characterize a subsurface region of Earth.