Finite element modeling of borehole acoustics

Abstract

The sonic wave propagation of a fluid‐filled cylindrical borehole in a solid formation was modeled by the finite element method. The excitation was a point source located on the axis, hence the problem was assumed to be axially symmetric. The transient waveforms at the receivers in the borehole were generated by the finite element method using the explicit time integration with lumped mass simplification. The fine time step requirement of data processing ensured the numerical stability of the explicit scheme. For a homogeneous formation the finite element generated receiver waveforms compared very well with those obtained from the real axis integration method [L. Tsang and D. Rader, Geophys. 44, 1706–1720 (1979)]. Numerical dispersion and convergence in regard to grid sizes were investigated. Synthetic waveforms for the case having two solid formations with a horizontal interface, which were still not solvable by analytical means, were generated and studied.