FDTD simulation and analysis of the collar wave propagation in acoustic logging while drilling

It is still an outstanding problem in acoustic logging while drilling (LWD) technique of the large-amplitude collar wave covering the formation waves, thus cognition of the characteristics of the collar wave is essential for eliminating or effectively reducing that wave. The seismoelectric LWD that records the electromagnetic fields induced by acoustic waves in the formation is expected to solve this problem thoroughly. In this study, a finite-difference time-domain algorithm is implemented to simulate the acoustic LWD waves in various collars and borehole models. Based on the propagation characteristics of the collar wave excited by a monopole source, the reason is addressed of the electric field accompanying the collar wave in seismoelectric LWD. It is found that the collar wave radiates energy into the outer media continually when propagating along the collar. Part of the energy with an apparent collar-wave velocity goes into the formation through the borehole wall, which induces electric fields like the formation compressional and shear waves thus can cause a signal of with collar-wave velocity in the seismoelectric LWD. In addition, there are two collar wave groups in the high-frequency acoustic LWD full waveforms. The high-order one having smaller amplitude cuts off in low frequency and it is slightly slower than the compressional wave in the collar. The low-order one having larger amplitude exists in the whole frequency range and it is even slower than the shear wave in the collar. The dispersion and multiple modes are the characteristics of guided waves in cylindrically-layered open wave guide structures.