Finite Difference Methods for Acoustic and Acousto-gravity Wavefields: Application to Low Frequency Infrasound Propagation

A finite difference (FD) method is derived for the frequency-domain acoustic and acousto-gravity equations as expressed in cylindrical coordinates. First, it is shown analytically that for an isovelocity atmosphere in which the density decreases exponentially with altitude, the acoustic wave equations (i.e., neglecting gravity) indicate that (1) the pressure varies with the square root of the density and (2) the acoustic wavelength depends not only on the frequency and velocity but also on the rate of exponential decrease of the density with altitude. Discretization of the linear equations relating acoustic particle velocities and pressures is straightforward except near the source. At r = 0, a singularity exists for the acoustic wave equation as expressed in cylindrical coordinates. In this case, l’Hopital’s rule is used to transform the singularity at r = 0 into a determinate form. The FD equations must be solved simultaneously, which requires the solution of a very large, sparse matrix equation, which is accomplished using a quasi-minimum residual method. The resulting FD algorithms can be used to solve for sound intensities in arbitrarily complex models that may include high material contrasts and arbitrary topography. The FD method is also extended to handle the effects of gravity on the acoustic wavefields. It is shown that the acousto-gravity equations require the simultaneous solution of the pressure and density perturbations caused by the passage of a sound wave. Acousto-gravity waves are relevant at very low frequencies, especially in the upper atmosphere where densities are very low. 28th Seismic Research Review: Ground-Based Nuclear Explosion Monitoring Technologies