Solution of coupled acoustic–elastic wave propagation problems with anelastic attenuation using automatic hp-adaptivity

The paper presents a frequency-domain hp-adaptive finite element (FE) method for a class of coupled (visco-)acoustics/anelasticity problems with application to modeling of sonic tools in the borehole environment. The paper extends methodology, software, and results presented in [1]. A new FE code enables solution a wider class of problems, including modeling of logging-while-drilling (LWD) tools, viscous damping in fluids and solids, well- and poor-bonded cased boreholes, and more complicated axially-symmetrical geometries of the formation. Solutions of non-trivial examples involving modeling of fast and slow formations, a formation with a soft layer, and an LWD tool, are presented. Results of the hp-FE simulations are post-processed to obtain time-domain solutions.