Rapid spatially coupled AVO inversion in the Fourier domain

Spatial coupling of the model parameters in an inversion problem provides lateral consistency and robust solutions. We have defined the inversion problem in a Bayesian framework, where the solution is represented by a posterior distribution obtained from a prior distribution and a likelihood model for the recorded data. The spatial coupling of the model parameters is imposed via the prior distribution by a spatial correlation function. In the Fourier domain, the spatially correlated model parameters can be decoupled, and the inversion problem can be solved independently for each frequency component. For a spatial model parameter represented on n grid nodes, the computing time for the inversion in the Fourier domain follows a linear function of the number of grid nodes, while the computing time for the fast Fourier transform follows an n log n function. We have developed a 3D linearized amplitude variation with offset (AVO) inversion method with spatially coupled model parameters, where the objective is to obtain posterior distributions for P-wave velocity, S-wave velocity, and density. The inversion algorithm has been tested on a 3D dataset from Sleipner field with 4 million grid nodes, each with three unknown model parameters. The computing time was less than 3 minutes on the inversion in the Fourier domain, while each 3D Fourier transform used about 30 s on a single 400-MHz Mips R12000 CPU.