1. Subject : “Quantitative 4D seismic in complex media using 2D full-waveform
inversion”
2. Supervisors : Jean Virieux (HDR), S. Garambois1, P. Thore2
1. LGIT, Université Joseph Fourier 38041 Grenoble Cedex 9.
2. TOTAL, Pau, France
Email:Jean.Virieux@obs.ujf-grenoble.fr; Stephane.Garambois@ujf-grenoble.fr;
Pierre.Thore@total.com
The PhD thesis will be included in a collaboration between LGIT and TOTAL and will be supported
via a CIFRE scholarship. The PhD work will be will be performed in both laboratories (LGIT
and TOTAL), according to periods to define. Adequate computer and scientific environment
will be provided to the student; access to synthetic and real data will also be ensured by
TOTAL.
3. Geophysics, modelling
4. Subject. Since the middle of the nineteen, oil industry undertook the time monitoring of
oil field with repeated 3D seismic imaging of oil fields (4D imaging) in order to assess the
evolution of petro-elastic properties of these fields from an initial acquisition (denoted the
base, often performed before any hydrocarbon production) and so to ameliorate their
productiveness. The obtained differential images constitute an important source of
information on the evolution of the characteristics of a given field. For an optimum and
quantitative interpretation, they must be as correct and precise possible. To achieve this goal,
these four steps are classically followed:
1. Perform a similar processing for all the seismic vintages;
2. Estimate the variation in phase and amplitude due to the production (change in local
velocity due to fluid substitution, or compaction, or …..) between processed base and
monitor datasets;
3. Deduce from the 4D changes the variations in petro-elastic properties;
4. Interpret the variations in petro-elastic properties in terms of fluid displacement and
substitution.
In recent works, Williamson et al., have merged the steps 2 & 3 into an inverse problem
where time-shifts and related amplitude variations are jointly used to estimate a change in
local velocity. An important restriction of this approach lies in its limitation to 1D problems
(1D propagation in a 1D medium), where a trace by trace approach can be used. In complex
media, where the dipping of layers is larger than 10%, or when significant lateral variations in
the velocity field are present, the wave propagation becomes more complex. Even after
elaborated processing steps (time or depth migration), the resulting seismic events along a
given trace can have travelled along different paths, which makes the 1D approach, previously
described, no longer suitable. Moreover, any significant change in the velocity field between
the base and the monitor surveys will make the process much more complex and its impact
spread out in a relatively large domain. A straightforward solution would be to process
independently base and monitor in depth, including velocity field estimation for both of them,
followed by depth migration in order to produce results in a common depth referential
domain. Even if such an approach should not be ignored, it is anticipated that any technique
which does not take advantage of the specificity of the 4D seismic (propagation medium is
supposed to have only slightly changed between base and monitor acquisition) will not be the
most suitable and that the 4D signal would probably be drawn in the uncertainties associated
with the processing.
Aim of the PhD subject. Although many other phenomena can be at the origin of a 4D
signal, such as compaction, changes in fractures behaviour, etc …, a first approach will be
concentrated on the effect due to change in velocity (and possibly density) within reservoirs
embedded into a 3D complex medium. In elastic media, a 2D full-waveform inversion scheme
has been recently developed (Brossier et al, 2008) to rebuild the 2D P and S wave velocity
fields (or of their variations if applied to differential seismograms using same sources and
receivers). The aim of the PhD thesis if to adapt and to apply this inversion procedure i) to
synthetic data whose solution is well known and ii) to existing real 3D data (using different
2D seismograms), which benefits to the presence of boreholes, which also independently
monitored the petro-physical changes due to production. The obtained differences in velocity
will be converted into petro-physical changes using classical analytical relations of
Gassmann. Depending on the obtained results, this approach can be extended – if possible during the PhD thesis to i) a 3D full-waveform inversion of a small region localized around
the production and ii) a 2D full-waveform in poroelastic media, an approach developed at
LGIT (PhD thesis of Bastien Dupuy).