def rayleigh_vel(longitudinal_vel, transverse_vel):
    """
    Approximate Rayleigh velocitiy.

    Parameters
    ----------
    longitudinal_vel : float
    transverse_vel : float

    Returns
    -------
    rayleigh_vel : float

    Notes
    -----
    [Freund98] Freund, L. B.. 1998. `Dynamic Fracture Mechanics`.
    Cambridge University Press. p. 83. ISBN 978-0521629225.


    """
    poisson = (longitudinal_vel ** 2 - 2 * transverse_vel ** 2) / (
        2 * (longitudinal_vel ** 2 - transverse_vel ** 2)
    )
    if poisson <= 0:
        raise ValueError
    return transverse_vel * (0.862 + 1.14 * poisson) / (1 + poisson)