Solution of coupled poroelastic/acoustic/elastic wave propagation problems using automatic hphp-adaptivity

The paper presents a frequency-domain hphp-adaptive Finite Element (FE) Method for a class of coupled acoustics/elasticity/poroelasticity problems with application to modeling of acoustic logging measurements in complex borehole environments. The paper extends methodology, software, and results presented in Matuszyk et al. (2012). We derive for poroelastic media a mixed weak formulation, which is closely related to the enhanced (u,p) formulation developed by Atalla et al. (2001). The formulation is extended to the transversely anisotropic (VTI) case, and makes use of the viscodynamic operator, which enables more accurate calculations for higher frequencies. In this approach, a special split of the differential operator results in boundary and coupling conditions that can be easily implemented within the FE framework. The appropriate PML technique is employed to truncate the computational domain. Accordingly, the original hphp-FE code is modified by the implementation of the appropriate scaling of the independent variables to make efficient the automatic adaptation algorithm. Solutions of non-trivial examples involving formations with permeable layers are presented. They positively verify the consistency and accuracy of the presented method.