Analysis of radiation patterns for optimized full waveform inversion in fluid-saturated porous media

The study of radiation patterns in poroelastic media allows us to visually explore the possibility of reconstructing crucial model properties describing reservoir rocks, and to examine the coupling effects between different parameters during full-waveform inversion (FWI). In this paper, we derive analytical formulae for the radiation patterns of single parameter perturbations in fluid-saturated porous media by deriving scattered wavefields based on plane-wave theory and the far-field approximation. We illustrate these scattered wavefields via their radiation patterns expressed as a function of the angle between the incident and scattered waves. To simplify the algebra, we consider poroelastic waves at seismic (low) frequencies, where the fast compressional wave and shear wave are propagating modes but the slow compressional wave is severely dispersive. To verify our derivation of the analytical radiation patterns, we also compute them numerically by perturbing one parameter at a single point, keeping the other parameters fixed at their background values. We find that all the analytical radiation patterns match the wavefronts of the numerically computed scattered wavefields, well indicating that our derivations are correct. Parameters such as the solid density, fluid density, viscosity of the fluid, and intrinsic permeability, have similar radiation patterns and thus show strong coupling effects. Therefore, we anticipate difficulties in recovering these parameters in a multi-parameter FWI procedure. In an attempt to mitigate these trade-offs, we analyze different parameterizations which result in different radiation patterns. As the patterns that we observe are similar to those of the elastic case, we anticipate that parameter separation might be easier when inverting for velocities than for moduli.