Apparent attenuation and dispersion arising in seismic body-wave velocity retrieval
Abstract
The fact that seismologists often make measurements, using natural seismic solicitations,
of properties of the Earth on rather large scales (laterally and in terms of depth) has led to
interrogations as to whether attenuation of body waves is dispersive and even significant. The
present study, whose aim is to clarify these complicated issues, via a controlled thought mea-
surement, concerns the retrieval of a single, real body wave velocity of a simple geophysical
configuration (involving two homogeneous, isotropic, non-dissipative media, one occupying the
layer, the other the substratum, from its simulated response to pulsed plane wave probe ra-
diation. This inverse problem is solved, at all frequencies within the bandwidth of the pulse.
Due to discordance between the models associated with the assumed and trial responses, the
imaginary part of the retrieved velocity turns out to be non-nil even when both the layer and
substratum are non-lossy, and, in fact, to be all the greater, the larger is the discordance. The
reason for this cannot be due to intrinsic attenuation, scattering, or geometrical spreading since
these phenomena are absent in the chosen thought experiment, but rather to uncertainty in the
measurement model.