Bayesian Framework to Wavelet Estimation and Linearized Acoustic Inversion

In this letter, we show how a seismic inversion method based on a Bayesian framework can be applied on poststack seismic data to estimate the wavelet, the seismic noise level, and the subsurface acoustic impedance. We propose a different linearized forward model and discuss in detail how some stochastic quantities are defined in a geophysical interpretation. The forward model and the Gaussian assumption for the likelihood distributions enable to obtain the conditional distributions. The method is divided into two sequential steps: the wavelet and noise level estimation, in which the posterior distribution is obtained via the Gibbs sampling algorithm, and the acoustic inversion, which uses the proposal forward model and the results of the first step. In the second step, the posterior distribution for acoustic impedance is analytically obtained. Therefore, the maximum a posteriori impedance can be calculated, yielding a very fast inversion algorithm. Results of tests on real data are compared with the deterministic constrained sparse-spike inversion, indicating that our proposal is viable and reliable.