Mode analyses in a fluid‐filled borehole surrounded by a concentrically layered formation

Acoustic wave modes including normal modes and leaky modes in a fluid‐filled borehole surrounded by a concentrically layered medium are analyzed. Dispersions and excitation spectra of various modes related to monopole, dipole, including hexapole, octepole, and decapole sources, are calculated for typical well logging environments. The numerical results demonstrate that the cutoff frequencies of nonsymmetrical modes vary greatly with the orders. A Stoneley mode has no cutoff frequency in a fast formation, while at a very slow formation, it possesses a cutoff frequency. Multiple pseudo‐Rayleigh modes, flexural modes, and the other higher modes have their correspondent cutoff frequencies. As frequency decreases from the cutoff frequencies, these modes correspond to the complex pole on the other Riemann sheets and become leaky modes. Also, followed by our previous work (Wang et al., 1994, 1995), it is shown that head compressional and shear arrivals cannot be totally described by contributions of vertical bra...