GEOPHYSICS, VOL. 68, NO. 2 (MARCH-APRIL 2003); P. 566–573, 9 FIGS., 3 TABLES.
10.1190/1.1567226
Seismic mapping and modeling of near-surface sediments
in polar areas
Tor Arne Johansen∗ , Per Digranes‡ , Mark van Schaack∗∗ , and Ida Lønne§
ABSTRACT
from the delta front. To our knowledge, this is the first
attempt to study pore-fluid freezing from such data.
Our study indicates that the P- and S-wave velocities may increase as much as 80–90% when fully, or
almost fully, water-saturated unconsolidated sediments
freeze. Since a small amount of frozen water in the voids
of a porous rock can lead to large velocity increases,
the freezing of sediments reduces seismic resolution;
thus, the optimum resolution is obtained at locations
where the sediments appear unfrozen. The reflectivity
from boundaries separating sediments of slightly different porosity may depend more strongly on the actual saturation rather than changes in granular characteristics.
For fully water-saturated sediments, the P-wave reflectivity decreases sharply with freezing, while the reflectivity
becomes less affected as the water saturation is lowered.
Thus, a combination of velocity and reflectivity information may reveal saturation and freezing conditions.
A knowledge of permafrost conditions is important
for planning the foundation of buildings and engineering activities at high latitudes and for geological mapping of sediment thicknesses and architecture. The freezing of sediments is known to greatly affect their seismic
velocities. In polar regions the actual velocities of the
upper sediments may therefore potentially reveal water saturation and extent of freezing. We apply various
strategies for modeling seismic velocities and reflectivity properties of unconsolidated granular materials as
a function of water saturation and freezing conditions.
The modeling results are used to interpret a set of highresolution seismic data collected from a glaciomarine
delta at Spitsbergen, the Norwegian Arctic, where the
upper subsurface sediments are assumed to be in transition from unfrozen to frozen along a transect landward
INTRODUCTION
applicable for modeling the elasticity and seismic properties of
fully or partly frozen sediments are given by Zimmermann and
King (1986), Jacoby et al. (1996), Ecker et al. (1998), Dvorkin
et al. (1999), and Jakobsen et al. (2000).
A high-resolution seismic experiment was conducted at
the active glaciomarine Adventdelta at Spitsbergen [78◦ N
(Figure 1)] as part of the educational and research program at
the University Courses on Svalbard (UNIS). The thickness of
continuous permafrost in this region is generally 100–450 m
(Liestøl, 1977). However, areas with rapid sediment input,
such as deltas, are likely to exhibit a gradual transition from
permafrost to unfrozen ground. A 5-km-long seismic line was
shot in early spring when the ground was frozen and covered
by a thin snow layer. The profile extended upvalley from the
delta front, oriented parallel with the direction of sediment
In arctic areas, seismic data may yield key information about
the permafrost conditions because seismic velocities strongly
vary with the degree of freezing of the pore fluids in porous
rocks (Zimmermann and King, 1986; Dvorkin et al., 1999).
For instance, the spatial distribution of permafrost is important to know when exploiting hydrocarbons and other mineral
resources in such regions. The reflectivity properties of the sediment boundaries, and hence the interpretation of the nearsurface features, are strongly dependent on the content and
state of any ice–water mixtures within the pore volume in these
regions. The study of velocities of porous sediments containing
frozen pore fluids has received increased interest as seismic exploration for gas hydrates has become more relevant. Theories
Manuscript received by the Editor March 20, 2001; revised manuscript received September 23, 2002.
∗
University of Bergen, Institute of Solid Earth Physics, N-5020 Bergen, Norway. E-mail: torarne.johansen@ifjf.uib.no.
‡Statoil, N-5020 Bergen, Norway. E-mail: perdig@statoil.com.
∗∗
Formerly University of Bergen, Institute of Solid Earth Physics, N-5020 Bergen, Norway; presently Schlumberger Offshore Services, N-5257
Kokstad, Norway.
§University Courses on Svalbard, N-9170 Longyearbyen, Norway.
°
c 2003 Society of Exploration Geophysicists. All rights reserved.
566
Mapping Shallow Sediments in Polar Areas
transport (Figure 1b). The objectives of the experiment were
to map the thicknesses and architecture of the near-surface
sediments and to study the change in reflectivity properties
with increase of pore ice in a transect from the unfrozen delta
front and upvalley.
We focus on seismic characteristics of the uppermost reflections of the profile and discuss our observations in the light of
the micromechanical models of cemented unconsolidated sediments as proposed by Dvorkin et al. (1999). We start by briefly
introducing the study area and the seismic data, followed by
a description of our strategy for modeling seismic velocities
of partly or fully water-saturated unconsolidated sediments,
where the saturating fluid is frozen or unfrozen. Finally, we
combine micromechanical and seismic modeling to interpret
our data and draw conclusions.
THE STUDY AREA
The Svalbard archipelago (Figure 1) is situated between
74◦ and 81◦ north and between 10◦ and 35◦ east. The islands cover an area of 62 700 km2 , of which approximately
60% of the total land surface is covered by glaciers. The
mean annual temperature at Svalbard Airport is −6.7◦ C
(Førland et al., 1997), and the region is underlain by continuous
permafrost.
567
Svalbard was glaciated during the Late Weichselian (approximately 18–20 kybp), and the glaciers extended to the shelf
edge (Landvik et al., 1998). Glacial settings and processes described from this region are often used as a modern analog for
the glacial periods and processes at the lower latitudes. However, the dynamics of sediment transport at this latitude are
not well understood. As a result of the deglaciation of The
Little Ice Age that terminated at the end of the 19th century,
a large number of the small glaciers on Svalbard are, or are
turning into, cold-based ice masses (Dowdeswell et al., 1995).
The subglacial erosion and deposition are therefore reduced
and replaced by a fluvial reshaping of the landscape because of
larger volumes of glacial meltwater released to the proglacial
area. Our knowledge of the thicknesses of the upper sediment
on Svalbard comes mainly from the fjord basins, with very little data from the land areas. The study reported here is the
first attempt to use a high-resolution seismic snow streamer
for obtaining such information.
THE SEISMIC DATA
The 5-km seismic profile was recorded from the head of the
fjord into the valley (Figure 1b). The mean temperature during the five days of field work was about −25◦ C. An important
advantage of the test site, aside from its close vicinity to
FIG. 1. (a) The Adventdalen basin study area in central Spitsbergen, (b) Location of seismic line A–A0 (the black dots represent
shotpoints), extending 5 km upvalley from the delta front.
568
Johansen et al.
Longyearbyen, is the plane and horizontal surface which requires no static corrections of surface seismic data. Furthermore, the surface layer is quite homogeneous with respect to
snow conditions, making it well suited for repeatable seismic
experiments using surface explosives. The snow layer was about
20 cm thick during the acquisition period.
The recording cable was a 24-channel snow streamer. Geophone take-out distance was 5 m. Each geophone position had
a single gimballed SG-1 geophone with a 14-Hz natural frequency. Detonating cord, equivalent to 40 g TNT per meter
and burning at a velocity of 7000 m/s, was used as the seismic
source. Several detonations of either 25 or 50 g were stacked
at each shotpoint (10 m offset). The seismic profile was obtained using 0.5-ms sampling rate and was given the shot and
geophone spacings, yielding a maximum of six common midpoint (CMP) traces. The frequency filtering during recording
was designed for 10- to 500-Hz passband with 24-dB/octave
slope.
The main processing steps were trace editing, true amplitude recovery, frequency filtering, velocity analysis, front and
tail mute, stacking, and a weighted nine-trace mix. Because of
the very limited offset window, the layer velocities obtained
from the stacking velocities were not considered to be very
precise. The stack is shown in Figure 2, while some NMOcorrected CDP supergathers along the profile are shown in
Figure 3. The recorded seismic energy lies within a frequency
band from 10 to 500 Hz, yielding a high-resolution power.
By using the velocity of the direct wave (found to be about
3500 m/s) and a center frequency of 250 Hz, the corresponding seismic resolution (i.e., the quarter wavelength) is about
3 m. At this time of the year, the upper active layer (i.e., the
layer becoming unfrozen 2–3 months during the summertime)
is frozen; thus, the arrival times of the direct wave are fairly
constant.
Figures 2 and 3 clearly reveal that the data quality becomes
poorer with increased distance from the delta front because
of ground roll interference. In segment U (Figure 2), a series
of coherent reflection events are seen, allowing a detailed interpretation. In segment F, these events become less coherent
FIG. 2. The seismic section along A–A0 given in two-way traveltime. The three ellipses below U, T, and F indicate areas where
the continuity and frequency content of the reflected energy
changes from continuous and well-defined events (U) to barely
visible events (F) via a gradual transition zone (T). We suggest
this is related to changes in the elastic parameters caused by a
gradual transition from unfrozen to frozen sediments. (Arrows
point to reflections marked in the CDP data of Figure 3.)
and the reflections are more scattered. Also note the higher
average velocity in F relative to U, evidenced by decreased
two-way reflection times for comparable events. The reflectors
are slightly updipping in segment T, which defines a transition
from U and F. The systematic and rapid change in the apparent
layered structure may be caused by a change in the sediment
thicknesses, the freezing conditions, or both. Because of the
coherent updipping of the reflectors in segment T, we believe
this occurs as a result of the subsurface freezing conditions just
below the active surface layer.
VELOCITY MODELING OF FROZEN AND
UNFROZEN SEDIMENTS
In this section we outline the concepts applied when predicting seismic velocity modifications in the upper unconsolidated
sediments as a result of varying water content and freezing conditions. The upper fluvial sediments in the study area are mainly
deposited by the meltwater. We consider them to be coarse
grained and poorly sorted and thus to behave elastically like
granular materials. There was no borehole information along
the profile, but data from shallow boreholes at the southern
flank of the valley showed grains up to gravel size (>5 mm in
diameter) (EBA, 1998).
For modeling elastic and seismic properties, we start by applying contact theory (CT) (Mindlin, 1949) to estimate the
composite elasticity of unconsolidated grain packings as a function of grain elasticity and hydrostatic pressure. Later extensions (Dvorkin et al., 1991, 1994), referred to as contact cementation theory (CCT), include the effects of cementation at grain
contacts and grain boundaries. These theories are restricted to
granular materials where the void space contains only a small
fraction (<15%) of cement. For modeling a larger cement fraction, Dvorkin et al. (1999) propose a hybrid approach where
CCT is combined with an effective medium theory (EMT).
We combine these three approaches for modeling the seismic
properties of the upper sediments in our survey. We assume the
FIG. 3. CDP supergathers taken at 500-m intervals along the
line. Shallow reflectors become weaker and the data quality becomes poorer with increasing distance to the fjord head. CDP
numbers are given above the gathers. (Arrows point to reflections indicated in the stacked section of Figure 2.)
Mapping Shallow Sediments in Polar Areas
sediments occur as unconsolidated grain packings—dry, partially, or fully saturated—with frozen, unfrozen, and/or partly
frozen pore water.
Given the effective values of the bulk modulus K ∗ , shear
modulus G ∗ , and density ρ ∗ of an isotropic composite, the Pwave velocity (V p ) and S-wave velocity (Vs ) are
µ
Vp =
∗
∗
K + 4G /3
ρ∗
µ
Vs =
G∗
ρ∗
¶1/2
¶1/2
(1)
When the voids are dry and uncemented, the effective elastic
properties are found by applying the CT approach (Dvorkin
and Nur, 1996). The effective bulk modulus K ∗ = K CT is
n 2 (1 − φ0 )2 G 2G
18π 2 (1 − νG )2
#1
3
P
,
(2)
while the effective shear modulus G ∗ = G C T is
G CT
"
3n 2 (1 − φ0 )2 G 2G
2π 2 (1 − νG )2
#1
3
P
,
(3)
where n is the average number of contacts per grain, P is the
hydrostatic differential pressure, and νG is the Poisson ratio of
the grains.
Voids partially or fully saturated with water
When the pore space is fully water saturated, the effective bulk modulus K satW is found by applying the theories of
Gassmann (1951) or Biot (1956) by considering the dry rock
(frame) elasticity given by K CT and G CT . The effective bulk
modulus K ∗ = K satW is
K satW = K G
(5)
Voids partially or fully saturated with ice
.
Dry voids
5 − 4νG
=
5 (2 − νG )
(K ∗ + 4G C T /3)−1 = SW (K satW + 4G C T /3)−1 + (1 − SW )
× (K C T + 4G C T /3)−1 .
ρ ∗ = (1 − φ0 )ρG + φ0 SW ρW + φ0 S I ρ I .
K CT =
Partial saturation herein means that some voids are fully
water saturated while some are dry. This is often referred to
as patchy saturation. The effective bulk modulus may be estimated from the elasticities of the material, in dry and fully
water-saturated states, using the Hill average (Hill, 1963):
,
The bulk moduli, shear moduli, and densities of grains and
ice are given by K G , G G , ρG , K I , G I , and ρ I , respectively. The
water properties are given by the bulk modulus K W and the
density ρW . Let φ0 denote the volume fraction of the void space
(porosity) without ice (as cementation material), while S D , S I ,
and SW denote the fractions of the void space which are dry,
ice filled, and water filled, respectively. The effective density is,
accordingly,
"
569
φ0 K C T − (1 + φ0 )K W K C T /K G + K W
, (4)
(1 − φ0 )K W + φ0 K G − K W K C T /K G
while the shear modulus is unaffected by the presence of a
nonviscous fluid, i.e., G ∗ = G CT .
For small concentrations of ice, we use the contact cementation theory of Dvorkin et al. (1994) in a manner similar to
Ecker et al. (1998) to model effects of relatively small concentrations of hydrate cementation of grains. The effective bulk
modulus K ∗ = K CCT becomes
K CCT =
n(1 − φ0 )
M I Sn ,
6
(6)
and the effective shear modulus G ∗ = G CCT is
G CCT =
1
3n(1 − φ0 )
K CCT +
G I Sτ ,
5
20
(7)
where Sn and Sτ are parameters which depend on the elastic
moduli of the grains and ice and the fraction of void space cemented with ice (SCI ). Complete formulas for Sn and Sτ are
given in Dvorkin et al. (1994), while simpler (statistical) evaluation formulas are found in Ecker et al. (1998). The ice compressional modulus is M I (= K I + 4G I /3).
For larger concentrations of ice, we apply the approach of
Dvorkin et al. (1999) by combining CCT with an EMT. The conceptual steps of their modeling procedure is as follows. First,
compute the elastic properties (K CCT (SCI ), G CCT (SCI )) of the
granular material with a small portion of ice (SCI = 0.1 − 0.15)
cementing the grain contacts by use of CCT. Second, define a
continuous host material, having the (yet unknown) bulk modulus K H and shear modulus G H , which contains a volume fraction φ = φ0 (1 − SCI ) of dry spherical voids. Solve for the host
elastic properties by considering the effective medium modeled bulk modulus K EMT (φ) and shear modulus G EMT (φ) to
be equal to the CCT moduli, i.e.,
K EMT (φ) = K CCT (SCI ); G EMT (φ) = G CCT (SCI ).
(8)
Third, find the effect of any ice concentration (S I > SCI ) using
an EMT considering the host medium to contain a volume
fraction φ I = φ0 (S I − SCI ) of ice inclusions and φ D = φ0 (1− S I )
of dry inclusions, or (φ = φ D + φ I ).
We now define the effective elastic moduli by K EMT (φ D , φ I )
and G EMT (φ D , φ I ). When the host elastic properties K H and
G H are known (to be derived below), the effective properties
K ∗ = K EMT (φ I , φ D ) and G ∗ = G EMT (φ I , φ D ) of the sediment
containing volume fractions φ I (noncementing ice) and φ D (air)
may then be derived by solving the system
[K H − K EMT (φ I , φ D )](1 − φ)PH
+ [K I − K EMT (φ I , φ D )]φ I PI
+ K EMT (φ I , φ D )φ D PD = 0,
(9)
570
Johansen et al.
[G H − G EMT (φ I , φ D )](1 − φ)Q H
+ [G I − G EMT (φ I , φ D )]φ I Q I
+ G EMT (φ I , φ D )φ D Q D = 0,
(10)
where Pi and Q i (i = H, I, D) are tensors which depend on
the elastic properties of the host (H ) and the inclusion material (I = ice, D = dry), the inclusion shape (Berryman,
1980a,b).
The effective moduli are found by iteration, with
K EMT (φ I , φ D )initial = K H and G EMT (φ I , φ D )initial = G H . The
host properties are then found using the above technique, assuming a two-phase material containing dry spherical inclusions (φ I = 0, φ D = φ) having the effective medium properties
constrained as in equation (8). The values K H and G H are then
obtained from
1
K CCT (SCI ) + 4G CCT (SCI )/3
φ
1−φ
+
,
=
K H + 4G CCT (SCI )/3 4G CCT (SCI )/3
1
1−φ
φ
=
+
,
G CCT (SCI )/3 + Z H
GH + ZH
ZH
(11)
using K satP instead of K satW using the patchy saturation model
given by equation (5).
When the ice–water mixture behaves as a solid (G P > 0),
it has cementation properties. If its pore volume fraction is
sufficiently small, the overall properties are found using CCT
by letting K I = K P and G I = G P in equations (6) and (7). For a
larger pore volume fraction, the same parameter substitutions
are performed in the combined CCT and EMT model. If the
partially frozen ice–water mixture fully saturates the sediment,
only the first two terms of equations (9) and (10) contribute,
since φ D = 0. The CCT-EMT model can thus be applied to any
proportion of a solid ice–water mixture and air.
Figure 5 summarizes the complete strategy for the velocity
modeling, when the void space varies from (1) dry to fully water
Table 1.
Quartz
Water
Ice
Physical properties of consituents used in the
modeling.
Bulk modulus
(GPa)
Shear modulus
(GPa)
Density
(g/cm3 )
37.0
2.4
8.4
44.0
0.0
3.6
2.7
1.0
0.92
(12)
with Z H defined as in Dvorkin et al. (1999).
Voids saturated with partially frozen water
If the temperature is just about the freezing point of water, the pore fluid may be partially frozen. In such a case, we
also have to model the effective elastic properties of the ice–
water composite because these will vary with the actual mixing
conditions. For this modeling we again apply the self-consistent
approximation of Berryman (1980a,b) to account for the phase
transition from solid ice to an ice–water suspension as the ice–
water ratio decreases.
The composite properties of the ice–water mixed phase are
determined by iteratively solving the system
[K I − K P (SW , S I )] S I PI + [K W − K P (SW , S I )] SW PW = 0,
FIG. 4. Modeled bulk and shear moduli of a mixture of ice and
water (partially frozen water) as a function of the ice–water
fraction using the SC approach with spherical (S) and ellipsoidal inclusions (E).
(13)
[G I − G P (SW , S I )] S I Q I −G P (SW , S I )SW Q W = 0.
(14)
Figure 4 shows the modeled properties of an ice–water composite for both spherical inclusions and ellipsoidal inclusions
of aspect ratio 0.1. The physical constants of ice and water
are given in Table 1. The critical ice–water fraction for which
the mixture transforms from a fluid to a solid is between 0.4
(spheres) to 0.33 (ellipsoids). The reduced suspension limit for
the ellipsoidal model results from the random distribution of
the ellipsoids in contact for a relatively lower concentration
than the spheres. The net effect between the elastic properties
of the ice–water mixture for the two inclusion models is small.
When the ice–water mixture behaves as a fluid (G P = 0)
and fully saturates the sediment, the bulk modulus K satP is
found using the Gassmann model [substituting K P with K W in
equation (4)]. If the ice–water mixture does not fully saturate
the sediment, the effective bulk modulus may be estimated
FIG. 5. Strategy for modeling the properties of dry and partly or
fully, frozen or unfrozen, water-saturated unconsolidated sediments. If the material is partly saturated with partially frozen
water and air, the properties are estimated using a patchy saturation model, with end members defined from the properties
of a dry composite and a fully partially frozen water saturated
composite.
Mapping Shallow Sediments in Polar Areas
saturated (A-B), (2) dry to fully ice saturated (A-C), and (3)
fully (partially) water to fully (partially) ice saturated (e.g.,
partially frozen pore fluid) (B-C).
NUMERICAL MODELING AND SEISMIC INTERPRETATION
In this section, we show results of the above modeling strategy and discuss their relevance to the interpretation of the
seismic data in Figures 2 and 3. Table 2 defines the properties
of three granular materials, denoted M1, M2, and M3, having different porosities (φ0 ) and average number of contact
points per grain (n). The physical properties of the various
constituents composing the materials are found in Table 1.
We consider that reduced porosity is associated with denser
grain packing, so that n increases with reduced porosity. The
model parameters were chosen in accordance with Dvorkin
and Brevik (1999), where n for high-porosity (36–40%) sandstones is in the range of 8–9. Furthermore, Jacoby et al. (1996)
report n to about 8.5 for unconsolidated high-porosity sands,
while Dvorkin and Nur (1996) use n = 9 when φ0 = 0.36.
Note that the reduction in porosity is just 2% from M1 to M2
and from M2 to M3. For modeling the dry and unconsolidated
case, the differential pressure was set to 5 MPa, correspondTable 2.
Layer
M1
M2
M3
Model parameters.
Thickness
(m)
Critical porosity
(φ0 )
No. of contact points
(n)
100
10
—
0.40
0.38
0.36
8.2
8.6
9.0
571
ing to a depth of 200 m and considering an average density of
2.5 g/cm3 .
Figure 6 shows the modeled P- and S-wave velocities of the
materials with porosities 0.36 (M3) and 0.38 (M2) as they transition between unfrozen to frozen for water saturations of 100%,
75%, and 25% (B-C, Figure 5). Some numerical artifacts occurred close to the ice–water suspension limit (60–70%), i.e.,
when the shear modulus of the ice cement vanishes. The reported data were at these points extrapolated from higher ice
concentrations. The P-wave velocity increases gently with the
degree of freezing when the mixture behaves as a suspension,
though we observe some water saturation effect. The corresponding S-wave velocities are unaffected by freezing but reflect the amount of water since higher saturation increases
density and reduces velocity. When the water becomes frozen
(G p > 0), both the P- and S-wave velocities increase strongly
with further freezing.
Figure 7 shows the P- and S-wave velocities when the two materials change from being dry to fully water saturated (Figure 5,
trend A-B) and dry to fully ice saturated (Figure 5, trend AC). Again, modeling indicates the strong impact of only a small
amount of ice cement. We set the maximum amount of ice cement (SC I ) to 15% for the transition from CCT to EMT theory.
For both unfrozen water saturations and low ice saturations, the
results are as expected (i.e., increased porosity reduces the velocities). As the fluid transitions to mostly or fully ice saturated,
the P- and S-wave velocities of the material of highest porosity (M2) slightly exceed those of the one with lower porosity
(M3). A closer inspection of the numerical results shows that
though both the bulk and shear moduli of M2 and M3 converge as ice saturation increases, the dominant relative velocity effect is the lower density of M2 relative to M3. The same
FIG. 6. Modeled P- and S-velocities for (a) sediment M2 and (b) sediment M3 as a function of the ice–water fraction (degree of
freezing) for water saturation levels of 1.00, 0.75, and 0.25 (Figure 5, trend B-C).
572
Johansen et al.
trend was found by comparing results for M1, M2, and M3 (see
Table 3).
The above results appear to agree with the seismic data in
Figure 2. A distinctive increase in velocity as the seismic line
enters into the assumed permafrozen area is clearly observed.
Segment T, where the reflectors updip slightly may define a
transition zone from unfrozen to frozen pore fluid. In segment U, we observe several relatively weak reflectors which
are more-or-less absent in segment F. If the layer boundaries
are planar from U to F, this effect may then be attributed to a
reduced reflectivity between the sediment layers. We evaluate
this hypothesis by testing several simple seismic models using
the parameters in Tables 1 and 2, under different assumptions
of partial saturation, using 25% and 75% ice–water mixtures
as the pore fluids.
The normal incidence PP-wave reflection coefficients for
the M2-M3 interface are shown as a function of freezing for the
various saturation models in Figure 8. The plots show that the
reflectivity can diminish as the pore fluid freezes. The freezing
effects on the seismic data are further supported in Figure 9.
Synthetic seismic sections have been modeled using normal
incidence rays in the plane layer model and with different saturation scenarios. Freezing acts (1) to give a pull-up of the
reflector and (2) to reduce the apparent reflection coefficient.
The reduction in reflectivity depends on the actual saturation.
In principle, this shows that by combining velocity and reflectivity properties, the degree of saturation may be revealed. The
freezing of the pore fluid increases the velocities and decreases
the seismic resolution. This further means that reflections from
closely spaced reflectors will more strongly interfere as the pore
fluid turns from unfrozen to frozen.
DISCUSSION AND CONCLUSIONS
Most research discussing velocity effects resulting from
frozen pore fluids are concerned with analysis of laboratory
Table 3.
Layer
M1
M2
M3
Modeled layer velocities (km/s) with dry and icesaturated pore volume.
V p – dry
Vs – dry
V p – ice
Vs – ice
2.47
2.50
2.54
1.35
1.38
1.40
4.33
4.30
4.28
2.95
2.93
2.91
measurements. The scope of our work has been to discuss a
modeling strategy for obtaining the seismic velocities and the
reflectivity properties of dry and water-filled unconsolidated
sediments, where the water may be partly or completely frozen.
Such modeling is relevant to seismic investigation of the upper
sediments at high latitudes, which may transition from discontinuously to continuously frozen ground. We have discussed
seismic effects interpreted as possible signatures of freezing
conditions, although alternative explanations may be possible
for certain observations. We consider the transition from unfrozen to frozen ground only as a function of distance upvalley from the fjord head, though there are certainly both vertical and horizontal heterogeneities in the subsurface drainage
system. Nevertheless, this conceptual model for describing
shallow seismic reflection data acquired in such environments should still help interpretation efforts in high-latitude
surveys.
Numerical modeling shows that both P- and S-wave velocities may increase as much as 80–90% when a fully watersaturated sediment turns from being unfrozen to frozen. The
difference in the bulk moduli of two unconsolidated sediments
of different porosity is reduced as the void space becomes
ice saturated. The lower effective density of the sediment of
highest porosity may account, under full ice saturation, for the
P-wave velocity increase (at least for the porosity range 0.3–
0.4). The shear modulus and the S-wave velocity show a similar
behavior.
The strong effect on velocities because of freezing may also
affect the reflectivity from the boundaries separating sediment layers of different porosity. Our modeling shows that
the reflectivity in sediments that are fully water saturated is
strongly reduced when they become frozen. The reduction decreases as the water saturation decreases. For a water saturation of about 25%, there is no longer a dominant effect on
the reflectivity. The significant increase in velocity with freezing produces a loss in seismic resolution (increase in wavelength); thus, the freezing of sediments reduces the ability to
map subsurface features. The optimum seismic resolution is
accordingly obtained at locations where the sediments appear
unfrozen.
Our modeling strategy provides physical insight on how
pore-fluid saturation and freezing will affect the seismic velocities and reflectivity properties of near-surface sediments. The
high-resolution seismic data presented clearly show the general
reflection features inferred by the modeling. The modeling and
FIG. 7. Modeled P- and S-velocities for M2 and M3 as a function of water saturation (W M2 and W M3) (Figure 5, trend A-B) and
ice saturation (I M2 and I M3) (Figure 5, A-C).
Mapping Shallow Sediments in Polar Areas
573
data should also point to the ability of using seismic techniques
for mapping spatial distributions of permanent frozen ground.
ACKNOWLEDGMENTS
We appreciate the assistance of the seismic crew: Helge
Johnsen, Alf Nilsen, Karstein Rød, Arne Sjursen, and the students of AG-205 Seismic Exploration, Spring 1999.
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FIG. 8. Modeled normal-incidence P-wave reflection coefficients as a function of freezing conditions for interface 2
(M2-M3) for the three saturation models.
FIG. 9. Normal-incidence seismic sections obtained for various
saturation models, with (a) 100%, (b) 75%, and (c) 25% water,
as the water gradually turns from unfrozen to frozen. [Zero
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