Compaction driven fluid flow is inherently unstable such that an
obstruction to upward fluid flow (i.e. a shock) may induce fluid-filled
waves of porosity, propagated by dilational deformation due to an
effective pressure gradient within the wave. Viscous porosity waves have
attracted attention as a mechanism for melt transport, but are also a
mechanism for both the transport and trapping of fluids released by
diagenetic and metamorphic reactions. We introduce a mathematical
formulation applicable to compaction driven flow for the entire range of
rheological behaviors realized in the lithosphere. We then examine three
first-order factors that influence the character of fluid flow: (1)
thermally activated creep, (2) dependence of bulk viscosity on porosity,
and (3) fluid flow in the limit of zero initial connected porosity. For
normal geothermal gradients, thermally activated creep stabilizes
horizontal waves, a geometry that was thought to be unstable on the
basis of constant viscosity models. Implications of this stabilization
are that: (1) the vertical length scale for compaction driven flow is
generally constrained by the activation energy for viscous deformation
rather than the viscous compaction length, and (2) lateral fluid flow in
viscous regimes may occur on greater length scales than anticipated from
earlier estimates of compaction length scales. In viscous rock, inverted
geothermal gradients stabilize vertically elongated waves or vertical
channels. Decreasing temperature toward the earth's surface can induce
an abrupt transition from viscous to elastic deformation-propagated
fluid flow. Below the transition, fluid flow is accomplished by short
wavelength, large amplitude waves; above the transition flow is by high
velocity, low amplitude surges. The resulting transient flow patterns
vary strongly in space and time. Solitary porosity waves may nucleate in
viscous, viscoplastic, and viscoelastic rheologies. The amplitude of
these waves is effectively unlimited for physically realistic models
with dependence of bulk viscosity on porosity. In the limit of zero
initial connected porosity, arguably the only model relevant for melt
extraction, travelling waves are only possible in a viscoelastic matrix.
Such waves are truly self-propagating in that the fluid and the wave
phase velocities are identical; thus, if no chemical processes occur
during propagation, the waves have the capacity to transmit geochemical
signatures indefinitely. In addition to solitary waves, we find that
periodic solutions to the compaction equations are common though
previously unrecognized. The transition between the solutions depends on
the pore volume carried by the wave and the Darcyian velocity of the
background fluid flux. Periodic solutions are possible for all
velocities, whereas solitary solutions require large volumes and low
velocities. (C) Elsevier, Paris.