Geophysical data acquisition - OGS

Phase velocities
of the five wave
modes
propagating in
partially frozen
Berea sandstone
versus water
proportion.
Phase velocity (km/s)
5
4
3
2
1
0
P1
S1
P2
S2
P3
(a)
0.05 0.1 0.15 0.2
Water proportion
Snapshot of the rock-frame
vertical particle velocity
corresponding to the wave
modes illustrated
in the previous figure.
The compressional waves
are labeled P1, P2 and P3,
and the shear waves
are labeled S1 and S2.
Finally investigation on dynamics of frozen porous media has been conducted. The
knowledge of the physical properties of frozen soils is essential, in polar areas, for
the exploitation of mineral resources and for the construction of highways and
pipelines. A three-phase Biot-type theory has been developed to describe a seismic
wave propagating in a porous rock filled with ice and water. The model predicts
three compressional waves and two shear waves, and takes into account energy
dissipation and wave dispersion as observed in rocks. Attenuation is introduced
with exponential relaxation functions, which allow a differential fomulation based
on memory variables. The wavefield is computed with a grid method based on the
Fourier differential operator in space and a Runge-Kutta time-integration
algorithm. The presence of slow quasi static modes makes the differential
equations stiff and hence numerically untractable as such. But a splitting timeintegration
algorithm has allowed to solve the stiff part analytically. The algorithm
is second-order accurate with respect to time and has spectral accuracy in the
computation of the spatial derivatives.
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