the predictions of fluid flow behavior based on these approximations are more often than not
unsuccessful. There is thus a strong need for a method,
which can generate a reliable subsurface model of hydraulic conductivity. Recent Ground Pene-
Ž .
trating Radar GPR work has demonstrated the feasibility of surface and borehole radar to de-
Ž tect fluid movement Brewster and Annan, 1994;
. Lane et al., 1996 . Research conducted in time-
dependent monitoring of oil and gas reservoirs, using multiple instances of 3D seismic data sets,
has demonstrated the feasibility of extracting a time- and space-dependent model of subsurface
fluid flow. From this a model of subsurface, hydrogeological
properties can
be derived
Ž .
Anderson et al., 1991, 1994 . Thus, four-di- Ž
. mensional 4D or time-lapse 3D GPR could be
the method to provide models of hydrogeologi- cal properties. The extraction of these models
from the 4D data and the visualization of 4D radar data are the topic of this paper.
2. 4D-seismic and 4D-GPR
4D-seismic visualization and analysis tech- niques were pioneered by the 4D Technologies
Research Group at the Lamont-Doherty Earth Ž
Observatory of Columbia University Anderson .
et al., 1991, 1994 and have by now become well adapted in the oil industry. 4D-seismic
technology uses multiple 3D seismic data sets with
the aim
of monitoring
changes in
impedance caused by drainage and migration of hydrocarbons and other subsurface fluids. The
goal of this effort is to enhance reservoir man- agement.
The principle of 4D-GPR is the same as that of 4D-seismic: the same survey is repeated at
different times, and as the solid fraction of the earth will not change noticeably between mea-
surements, the change between data must be a result of changes in the subsurface fluid phase.
The motivation behind 4D GPR is in a way similar to that of 4D seismic: we want to ob-
serve the results of contaminant migration or the effectiveness of remediation methods.
If we want to use 4D seismic or GPR, an imported component of these methods is the
verification, using numerical models, that what is observed actually corresponds to a fluid mi-
gration. Through a collaborative effort with Rice University, we currently have access to a two-
Ž .
dimensional 2D finite-difference time-domain Ž
. FDTD-TE modeling code with similar charac-
teristics as the code described by Xu and Ž
. McMechan 1997 . This code allows arbitrary
electrical conductivity, permittivity and mag- netic permeability variations on a grid, and has
an option to include relaxation mechanisms. This code is a modification of a code written by
Ž .
Bergmann et al. 1996
which is in itself a modification of a visco-elastic modeling code
Ž .
Robertsson et al., 1994 . The code has absorb- ing boundaries, is second-order in time and
fourth-order in space and in its current incarna- tion uses a Ricker source wavelet whose center
frequency can be specified at run time.
This code was used in its current incarnation Ž
. in which it has a uniform radiation pattern to
simulate a simplified 4D experiment in which a Ž
. saline tracer ´ s 81, s s 1000 mSrm is re-
r
Ž leased in a low conductivity medium ´ s 5.58,
r
. s s 0.01 mSrm . Note that only a 2D medium
is modeled, so the term 4D is not really appro- priate here. The tracer is modeled as a point
source, which spreads out first both laterally and in depth, and subsequently spreads out only
laterally. Twenty-one time-steps were modeled, with the first time-step being the simulated pre-
spill data. The spill occurs 110 cm beneath the surface, and spreads 5 cm in each direction per
time-step. For each time-step, 21 zero-offset traces were calculated with a spacing of 5 cm
centered around our spill point. Consequently, an area of 2 m is covered with the spill point at
the center. Fig. 1 shows the result for the first 10 time steps. This modeling effort shows that
in this case, the tracer could be clearly identi- fied.
Ž . Ž .
Fig. 1. Ten time steps a to j of numerical modeling of a time-lapse radar simulation. A spill of saline tracer is simulated as seen by a 300-MHz GPR antenna.
These results indicate that from real 4D data, we could in theory, determine information re-
lated to the fluid phase and to the controlling Ž
hydrogeological parameters hydraulic conduc- .
tivity, permeability . Implementing this, and ac- tually extracting information on subsurface fluid
Ž flow from GPR data is fairly complex Sander,
. 1994; Sander and Olhoeft, 1995 . Some of this
complexity arises
because collecting
the ‘‘same’’ geophysical survey is less trivial than
it sounds. Depending on the method used, a positioning
Ž .
accuracy in real-time on the order of centime- ters is required. In situations when individual
3D surveys are repeated in the order of weeks to months, an additional complication occurs. This
complicating factor is that significant changes in the near-surface zone may occur. This will ob-
scure the signal difference and we thus may need to do elaborate processing steps to separate
near-surface effects from ‘‘at-depth’’ effects. Additional complicating factors are line and
trace spacing requirements needed for the com- parison of features in 4D. Ideally, the line spac-
ing should be of the order of the trace spacing to allow for optimum visualization of subsur-
face structures in 3D, but in reality, the trace spacing is mostly much smaller than the line
spacing. For a 200-MHz GPR survey with a cross-line dip of 208 and a subsurface velocity
of 0.07 mrns, we need cross-line spacing of 60 cm to avoid spatial aliasing. As for most 4D
surveys, these kinds of parameters are not at- tainable and will degrade the data analysis.
The main complexity of analyzing 4D radar data is of course the processing and visualiza-
tion. These are discussed using the 200-MHz and 500-MHz Borden data sets.
