High-resolution tomographic imaging of the shallow subsurface is becoming
increasingly important for a wide range of environmental, hydrological
and engineering applications. Because of their superior resolution
power, their sensitivity to pertinent petrophysical parameters, and
their far reaching complementarities, both seismic and georadar crosshole
imaging are of particular importance. To date, corresponding approaches
have largely relied on asymptotic, ray-based approaches, which only
account for a very small part of the observed wavefields, inherently
suffer from a limited resolution, and in complex environments may
prove to be inadequate. These problems can potentially be alleviated
through waveform inversion. We have developed an acoustic waveform
inversion approach for crosshole seismic data whose kernel is based
on a finite-difference time-domain (FDTD) solution of the 2-D acoustic
wave equations. This algorithm is tested on and applied to synthetic
data from seismic velocity models of increasing complexity and realism
and the results are compared to those obtained using state-of-the-art
ray-based traveltime tomography. Regardless of the heterogeneity
of the underlying models, the waveform inversion approach has the
potential of reliably resolving both the geometry and the acoustic
properties of features of the size of less than half a dominant wavelength.
Our results do, however, also indicate that, within their inherent
resolution limits, ray-based approaches provide an effective and
efficient means to obtain satisfactory tomographic reconstructions
of the seismic velocity structure in the presence of mild to moderate
heterogeneity and in absence of strong scattering. Conversely, the
excess effort of waveform inversion provides the greatest benefits
for the most heterogeneous, and arguably most realistic, environments
where multiple scattering effects tend to be prevalent and ray-based
methods lose most of their effectiveness.