Nowadays, acoustic logging technology is widely used in oil exploration, engineering geophysics and some other well-logging field. However, the formation out of a borehole is usually radially inhomogeneous due to mud invasion caused by drilling operations. So in order to discover the sound propagation law and set up a better sound field simulation for future research, Zhang Bixing of CAS Institute of Acoustics, in collaboration with the researchers of Harbin Institute of Technology conducted a series of studies and set up a simulation of acoustic well-logging wave field in a radially multilayered fluid-saturated porous formation.

In their study, they assume the formation consists of radially multilayered porous layers, and adopt a transfer matrix method to simulated acoustic well-logging waveforms. They notice that the real and imaginary parts of slow compressional wave number are both very large when there is a thick annulus layer out of the borehole at a high frequency, so that the Hankel function is prone to overflow with large arguments.

To solve this problem, they introduce the normalized Hankel functions to the wave field expressions. The generalized reflection and transmission coefficient method is extended to calculate the wave field in radially multilayered porous formations. Recursive formulae for wave field in radially multilayered porous formations. Recursive formulae for wave amplitude coefficients are deduced. As an example, acoustic full waveforms are calculated to simulate logging responses in a radially multilayered porous formation with an invaded zone.