**HYDROGEOLOGICAL PROPERTY ESTIMATION USING TOMOGRAPHIC**

**DATA AT THE BOISE HYDROGEOPHYSICAL RESEARCH SITE**

John E. Peterson, Jr, Ernest L. Majer, and Michael D. Knoll

ABSTRACT

Crosswell seismic and radar data were acquired at the Boise
Hydrogeophysical Research Site (BHRS). The data were acquired as part of
an effort to characterize the permeability distribution in a
heterogeneous alluvial acquifer. The tomographic data were acquired
between three wells located in a triangular pattern. The radar data were
acquired using 200 MHz antennas for all three well pairs and 100 MHz
across one of the well pairs to study the effects of the radar frequency
on resolution. The seismic data were acquired at a frequency of about 4
kHz. The electromagnetic wave velocity and amplitude attenuation values
obtained from inversion of the radar data, as well as the seismic P-Wave
velocity values obtained from inversion of the seismic data, reveal
similar spatial patterns. These coincident patterns suggest that the
geophysical attributes are all sensitive to lithological and/or
hydrogeological variations. The radar travel time data were inverted for
velocity while the radar amplitude data were inverted for attenuation.
Petrophysical relationships can also be used to construct images of
porosity which can then be compared to estimates from neutron logs
collected in the wells.

INTRODUCTION

The Boise Hydrogeophysical Research Site (BHRS) is being developed in
Boise, Idaho for hydrologic and geophysical research in a shallow
alluvial aquifer comprised of unconsolidated sands and clays. The water
table is located at approximately 2.5 meters below ground surface. A
goal of the research is to use this site to develop and test hydrologic
and geophysical methods for characterizing the distribution of
permeability in heterogeneous alluvial aquifers. As part of this
research, Lawrence Berkeley National Laboratory (LBNL) acquired high
resolution crosswell seismic and radar data in October, 1997. The data
were collected to characterize the acoustic and electromagnetic velocity
and attenuation structure of the site and to study differences in the
information that these two geophysical methods offer. Correlation of
these seismic and radar attributes with borehole log data permits
elucidation of the relationships between geophysical and hydrological
parameters at this site. Some of the radar data were acquired at a lower
frequency to study the effects of frequency content on the resolution of
structural features. The geophysical data can be used with the developed
petrophysical relationships to provide high-resolution,
multi-dimensional estimates of hydrologic parameters. The development of
these relationships is in progress. Here, we present examples of the
high-resolution radar and seismic data and illustrate how we will use
these data to both delineate structural features and to map porosity
variations.

ACQUISITION AND ANALYSIS OF RADAR TOMOGRAPHY
DATA![](media/image1.emf){width="3.452777777777778in"
height="4.051388888888889in"}

Three radar tomographic profiles, B1-B2, B1-C1, and B2-C1 were collected
between three wells which form a triangle with sides of 3.41, 5.21 and
4.70 meters, respectively (Figure 1). The radar tomography data were
acquired using the Sensors and Software pulseEKKO 100 ground penetrating
radar system. Radar profiles were collected with 200 MHz antennas and
profile B1-C1 was additionally acquired using 100 MHz antennas to study
resolution variations as a function of acquisition frequencies. The
radar data were collected with 0.25 meter source and receiver spacing
between the depths of 1 to 18 meters below ground surface to obtain
radar tomographic coverage over angles of approximately 0 to 70 degrees.
In addition to acquiring the full tomographic data, Zero Offset Profiles
(ZOP) data were collected before and after each survey to determine the
drift in zero time which is necessary for data processing as described
in Peterson and Williams (1997).

Good signal quality was obtained for all offsets of each well pair. A
typical frequency content of the signals received for the 200 MHz
antennas is shown in Figure 2a which illustrates that the peak energy is
at about 80 MHz. The 100 MHz signal produces peak energy at about 40 MHz
(Figure 2b). These central frequencies are independent of the three
borehole separation distances. The data quality at these distances and
angular offsets suggests that radar data may be acquired at 12 to 15
meter well separations using 200 MHz antennas and at 15 to 20 meters
using 100 Mhz antennas at the BHRS. The first arrival times of the
electromagnetic energy were picked for each survey, producing about 3000
to 4000 travel times for each data set. An Algebraic Reconstruction
Technique (ART; Peterson, et al., 1985) was used for obtaining the
velocity field by inverting the electromagnetic wave travel time data.
The program assumes that the energy is traveling as straight ray paths
between source and receiver in the inversion. In addition, radar source
and receiver statics were determined for each source and receiver
location. Such travel time shifts compensate for variations in the
borehole, very small-scale structures immediately adjacent to the
borehole, and antenna-borehole coupling effects. The algorithm produced
a grid composed of 0.20 meter square pixels of constant velocity, or a
two-dimensional velocity image of the intra-borehole area in the
saturated section.

For the moderate- to coarse- textured materials at this site, and for
the high excitation frequencies utilized, the radar velocity is
dependent on the dielectric constant of the material through the
equation:

$v = \frac{c}{\sqrt{k}}$
(1)![](media/image2.emf){width="3.1416666666666666in"
height="6.46875in"}

where c is the velocity of electromagnetic waves through air and κ is
the bulk dielectric constant. As the dielectric constant of air is 1 and
the dielectric constant of water is 80, saturated and higher porosity
material will have a higher dielectric constant than the corresponding
unsaturated or lower porosity material. The velocity fields for each of
the three well pairs obtained from the inversion procedure were
converted to dielectric constant using (1).

The measured bulk dielectric constant has been expressed using a time
propagation model, which for a two phase saturated system is given by:

κ ≈ \[(1-θ)√κ~m~ + θ√κ~m~\]^2^ (2)

where θ is porosity, subscripts m and w refer to matrix and water
respectively. We assume here that the dielectric constant of the matrix
sand and gravel material at the BHRS is fairly constant. With this
assumption and under the saturated conditions, equation (2) suggests
that any changes in bulk dielectric constant is a function of variations
in porosity. For a matrix dielectric constant of approximately 4 and a
water dielectric constant of 80, equation (2) reduces to:

κ ≈ 4 + 12.88 θ + 41.47 θ^2^ (3)

Using (3), the dielectric constant were converted into porosity images
(Figure 3). Each image displays a similar porosity structure with two
well-defined zones of high porosity at approximate depths of 6 and 12.4.
A deeper high porosity zone at 15 meters is not as well-defined as the
upper two zones. Another high porosity feature is observed on the B1-C1
and B2-C1 tomograms at a depth of about 5 meters.

Neutron logs, available from all three wells, were used to calculate
porosity. These values were plotted to the left and right of the
tomograms in Figure 3. (A value of 0.03 was added to the neutron
porosities to fall in the same range as the tomogram velocities). The
logs from each borehole are significantly different from each other. The
porosity variations observed in the B2 and C1 logs are quite consistent
with the co-located values in the porosity tomograms shown in Figure 3;
the higher porosity zones on the logs to the left and right of the
tomograms correspond to higher porosity zones in the tomograms as
predicted by Equations (2) and (3). For example, high porosity regions
coincide at depths of 6, 12 and 15 meters in well B2 (the B1-C1 and
B2-C2 tomograms). The high porosity feature at a depth of 6 meters in
the B2 porosity log appears to shift to a depth of 5 meters on the
borehole C1 porosity log. The B2-C1 tomogram (Figure 3), however,
indicates that this is not a continuous dipping feature as would be
interpreted using log correlation, but two distinctive layers, neither
of which extend the length of the tomogram. A high porosity zone at the
15 meter depth is more extensive on the C1 porosity log than on the B2
log; this is also observed on tomogram B2-C1. The porosity log from
borehole B1 is more oscillatory than the others, with less well-defined
high- and low- porosity zones. The B1-B2 and the B1-C1 tomograms,
however, indicate distinct zones of high and low porosity above depths
of 13 meters and do not display the oscillatory pattern observed on the
B1 porosity log. This suggests that the B1 neutron response is not
indicative of variations in porosity, but the response is more likely is
due to local borehole conditions caused by drilling or grouting.

Radar attenuation information can also be obtained from the radar data.
The amplitudes are measured by taking the root mean squared value of
approximately the half cycle of the first arrival. The attenuation is
calculated by inverting the waveform amplitudes using the same
algorithm, geometry, and input values as were used for the velocity
tomograms. In low-attenuating media (from 0.02 to 10 dB/m) and at the
high excitation frequencies used for this experiment, the attenuation is
related to the conductivity of the material through the equation (Davis
and Annan, 1989):

σ\[S/m\] ≈ α\[dB/m\] √κ / 1640 (4)

The attenuation tomograms were converted to electrical conductivity
tomograms using this relation and are shown in Figure 4. These
conductivity tomograms are coincident with the attenuation tomograms;
the dielectric constant had little effect on the conductivity, because
the relative range in dielectric constant values was small relative to
the range in attenuation values. Also shown, to the left and right of
the crosswell image, are the measured borehole electrical conductivities
obtained from borehole induction logs which have been arithmetically
averaged over 20 cm depth intervals so that log and radar tomogram
sampling intervals are equivalent. The conductivity images show
anomalies in the same regions as the porosity anomalies (Figure 3). For
example, a low conductivity zone is coincident with the high porosity
zone at a depth of 6 meters, and on either side of this layer are high
conductivity zones which are especially strong in the B1-C1 and B2-C1
tomograms. A low conductivity zone observed in all the tomograms at a
depth of 12 meters is also coincident with the high porosity zone at
that depth. This layer is also associated with a high conductivity zones
immediately below. There is no coinciding conductivity anomaly near the
high porosity zone observed in all tomograms at a depth of 15 meters,
and the area between the two low conductivity layers appears more
heterogeneous than was observed in the porosity tomograms.

A crosswell survey was also performed from B1-C1 at a frequency of 100
MHz instead of 200 MHz to study the effects of excitation frequency on
spatial resolution and hydraulic parameter estimation. The station
spacing and inversion parameters were the same as for the 200 MHz
surveys. The resulting dielectric constant image is shown in Figure 5.
The same three zones of high dielectric constant (high porosity) are
still observed in this image, but the zones are less distinct and the
absolute dielectric constant values are not as high. More importantly,
the smaller high dielectric constant zone at a depth of 5 meters, which
was observed on the 200 MHz profile, is not as easily observed and
cannot be spatially distinguished from the 6 meter zone. Also, the high
frequency tomogram resolved some structure in the generally homogeneous
region from 6 to 12 meters, whereas the low frequency tomogram did not.
The lower resolution obtained with the 100 MHz data are due to the
increased wavelengths; the wavelengths are twice as long as the
wavelength of the 200 MHz data, so larger amounts of material are
sampled and effectively averaged with the 100 MHz data than with the 200
MHz data.

ACQUISITION AND ANALYSIS OF SEISMIC TOMOGRAPHY DATA

Seismic tomographic data were also acquired between the same boreholes
as the radar data (Figure 1). The data for the well pair with shorter
separation (B2-B1) was of much better quality than the other well pairs.
While there was a marked decrease in amplitudes for the data with the
farther borehole separation, the poor quality of this data was primarily
due to a problem in the acquisition equipment. The peak frequency of the
seismic data was at 4000 Hz. Based on this data and prior experience
with this system, good quality data should be achieved for well
separations up to 8 to 10 meters.

The seismic data were inverted in the same manner as the radar data; the
resulting seismic velocity image is shown in Figure 6. The velocity
structure appears to offer similar resolution as that obtained from the
radar velocity (porosity) structure for the B1-B2 well pair (Figure 3).
Attenuation tomograms could not be produced at this time due to errors
in recording the gain applied at acquisition. Observations of the data
show that the signals are almost entirely attenuated in the low velocity
feature at 6 meters, but not at the 12 meter low velocity zone.
Comparison of the seismic and radar data suggests that the radar data
can be collected at farther offsets and supply similar resolution
information as the seismic data. Lower frequency seismic data will
produce farther acquisition offsets, but as shown in the radar data,
there can be a significant loss of information with any drop in
frequency.

CONCLUSIONS

High-resolution images of dielectric constant, electromagnetic wave
attenuation, and seismic velocity were obtained using radar and seismic
borehole tomography methods. Radar frequencies of 200 MHz and seismic
frequencies of 4000 Hz appear to provide similar resolution of features,
with a wavelength of approximately 0.6 meters, and high quality radar
data could be acquired at farther offsets than seismic data. Preliminary
analysis of borehole neutron and induction logs and seismic and radar
tomography data suggests that:

1\) The higher resolution offered by the 200 MHz radar data delineate
the interwell variability more clearly than the coincident 100 MHz data,

2\) There is a direct correspondence between porosity and dielectric
constant,

3\) The estimated porosities, obtained form the dielectric constant
estimates and the time propagation petrophysical model, compare
favorably with the porosities obtained from the neutron probe.

4\) Electrical conductivity from borehole induction logs correspond with
conductivity estimated using radar tomography travel time and amplitude
information.

The information produced by the well and tomography data, as well as
laboratory core data, will enable development of petrophysical
relationships which will then be used with to provide multi-dimensional
profiles of porosity and lithology with a 0.20 meter resolution.

ACKNOWLEDGEMENTS

This project is supported by U.S. Army Research Office grant
DAAH04-96-1-0318. Cooperative arrangements with the Idaho Transportation
Department, the U.S. Bureau of Reclamation, and Ada County allow
development and use of the BHRS and are gratefully acknowledged.

REFERENCES

Davis, J.L. and A.P. Annan, Ground-penetrating radar for high-resolution
mapping of soil and rock stratigraphy, *Geophysical Prospecting*, 37,
531-551, 1989.

Peterson, J.E., Jr. and K.H. Williams, Ground Penetrating Radar Results
at the Box Canyon Site: 1996 Survey as part of Infiltration Test,
*LBNL-Report-40915*, 1997.

Peterson, J. E., B. N. P. Paulsson and T. V. McEvilly, Applications of
algebraic reconstruction techniques to crosshole seismic data,
*Geophysics,* 50, 1566-1580, 1985.