A B

(3X HORIZONTAL

EXAGGERATION)

Core NGHP–01–10B–08Y

Data collected at 100 bar

0.1

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.1 1.2 1.3 1.4 1.5 1.6 1.7

0.0

0.2

SECTION DEPTH, IN METERS

GAMMA DENSITY

(g/cc)

X-RAY IMAGE

2

, 2

1, 1

U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2009–5141

Anisotropic Velocities of Gas Hydrate-Bearing

Sediments in Fractured Reservoirs

Anisotropic Velocities of Gas HydrateBearing Sediments in Fractured Reservoirs

By Myung W. Lee

Scientific Investigations Report 2009–5141

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

KEN SALAZAR, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia: 2009

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Suggested citation:

Lee, M.W., 2009, Anisotropic velocities of gas hydrate-bearing sediments in fractured reservoirs: U.S. Geological 

Survey Scientific Investigations Report 2009–5141, 13 p.
iii

Contents

Abstract...........................................................................................................................................................1

Introduction.....................................................................................................................................................1

Theory .............................................................................................................................................................3

Isotropic Velocities...............................................................................................................................3

Anisotropic Velocities ..........................................................................................................................3

Modeling..........................................................................................................................................................5

Fractures in High-Porosity Shale .......................................................................................................5

Fractures in Sandstone........................................................................................................................7

Gas Hydrate Saturations ..............................................................................................................................9

Discussion.....................................................................................................................................................10

Conclusions...................................................................................................................................................11

Acknowledgments.......................................................................................................................................12

References Cited..........................................................................................................................................12

Figures

1. NGHP Expedition 01 site map .............................................................................................................2

2. X-ray image of gas hydrate-bearing sediments and schematic diagram showing

laminated two-component sediment package ................................................................................4

3. Isotropic velocities of gas hydrate-bearing sediments and anisotropic velocities

for horizontal fracture in shale ...........................................................................................................6

4. Modeling elastic velocities for fractures in shale ..........................................................................7

5. Group and phase velocities for a horizontal fracture.....................................................................8

6. Isotropic velocities of gas hydrate-bearing sediment and anisotropic velocities

for horizontal fractures in sandstone ................................................................................................8

7. Modeling elastic velocities for fractures in sandstone..................................................................9

8. Measured logging-while-drilling P-wave velocities and P- and S-wave velocities ...............10

9. Gas hydrate saturations estimated from wireline velocities.......................................................11

Table

1. Constants used for modeling ..............................................................................................................6

Abstract

During the Indian National Gas Hydrate Program 

Expedition 01 (NGHP–01), one of the richest marine 

gas hydrate accumulations was discovered at drill site 

NGHP–01–10 in the Krishna-Godavari Basin, offshore of 

southeast India. The occurrence of concentrated gas hydrate 

at this site is primarily controlled by the presence of fractures. Gas hydrate saturations estimated from P- and S-wave 

velocities, assuming that gas hydrate-bearing sediments 

(GHBS) are isotropic, are much higher than those estimated 

from the pressure cores. To reconcile this difference, an anisotropic GHBS model is developed and applied to estimate gas 

hydrate saturations. Gas hydrate saturations estimated from 

the P-wave velocities, assuming high-angle fractures, agree 

well with saturations estimated from the cores. An anisotropic 

GHBS model assuming two-component laminated media—

one component is fracture filled with 100-percent gas hydrate, 

and the other component is the isotropic water-saturated 

sediment—adequately predicts anisotropic velocities at the 

research site.

Introduction

Gas hydrates are a type of clathrate in which water molecules surround gas molecules to form an ice-like crystalline 

solid. In situ physical characteristics of gas hydrate-bearing 

sediments (GHBS) have been investigated extensively because 

of their widespread occurrence in most of the world oceans, as 

well as in permafrost regions (Kvenvolden, 1993), and their 

recognition as a negative feedback control on global temperature fluctuations (Archer, 2007), as a potential energy resource 

(Ruppel, 2007), and as a factor in sea-floor stability and safety 

issues (Nixon and Grozic, 2007).

As part of the Indian energy resource program, the Indian 

National Gas Hydrate Program Expedition 01 (NGHP–01) 

in 2006 was designed to investigate the geologic and geochemical controls on gas hydrate occurrences offshore of the 

Indian Peninsula and along the Andaman convergent margin. 

A general description on geological and geophysical studies 

related to the gas hydrate occurrence in the offshore regions 

of India is well documented in Rao (2001). A total of 39 holes 

were drilled at 21 sites (fig. 1), some of which were cored as 

part of the expedition. One of the richest marine gas hydrate 

accumulations was discovered at drill site NGHP–01–10 in the 

Krishna-Godavari Basin (Collett and others, 2008). The initial 

site report used logging data and infrared images of recovered 

cores to infer the presence of gas hydrate within the depth 

interval from ≈25 to ≈160 m below the sea floor (mbsf). The 

gas hydrate existed as solid nodules, as fracture fill in highangle and subhorizontal veins, and was disseminated throughout the cores.

The gas hydrate saturations estimated from the loggingwhile-drilling (LWD) resistivity log reached as much as 

80 percent of the pore space (Collett and others, 2008), 

whereas the highest saturations estimated from the pressure 

core at the nearby wells are about 26 percent of the pore space. 

The large difference of gas hydrate estimations is speculated 

to be caused by the anisotropic nature of the reservoir due to 

fractures at this site (Lee and Collett, 2009).

Well logs have been extensively used to characterize the 

in situ gas hydrate-bearing sediments including their saturations (for example, Collett, 2000, 2002; Guerin and others, 

1999; Helgerud and others, 1999; Hyndman and others, 2001; 

Lee and Collett, 2005). The majority of investigations have 

been focused on the unfractured sandstone reservoirs and 

dispersed gas hydrate in the shale, but few investigations 

analyzed well logs acquired within the fractured reservoirs.

The purpose of this report is to derive a realistic fracture 

model to predict P- and S-wave velocities and to compare gas 

hydrate saturations estimated from the P- and S-wave velocities with those estimated from pressure cores by incorporating anisotropic properties of fractured reservoir. Transverse 

isotropic theory for laminated media (for example, Backus, 

1962; Postma, 1955; White and Angona, 1955) and anisotropy 

theory by Thomsen (1986, 1995) are used to describe elastic 

velocities for the fractured reservoir, and gas hydrate saturations are estimated from P- and S-wave velocities assuming 

isotropic and anisotropic GHBS.

Anisotropic Velocities of Gas Hydrate-Bearing Sediments 

in Fractured Reservoirs

By Myung W. Lee
2 Anisotropic Velocities of Gas Hydrate-Bearing Sediments in Fractured Reservoirs

Figure 1. A, NGHP Expedition 01 site map depicting the location of the research drill sites established during 

the expedition. B, Insert map of the NGHP Expedition 01 drill sites in the Krishna-Godavari Basin. Modified from 

Collett and others (2008).

16°

17°

5°

10°

15°

20°

65° 70° 75° 80° 85° 90° 95° 100°

81° 82° 83° 84°

0 200 400 KILOMETERS

0 10 20 30 40 KILOMETERS

Site NGHP–01–01

Site NGHP–01–08

Site NGHP–01–09

Site NGHP–01–17

Site NGHP–01–18

Site NGHP–01–19

Site NGHP–01–02

Site NGHP–01–03 Site NGHP–01–04

Site NGHP–01–05

Site NGHP–01–06

Site NGHP-01-07

Sites NGHP–01–10,

 12, and 13

Site NGHP–01–11

Site NGHP–01–14 Site NGHP–01–15

Site NGHP-01-16

Site NGHP–01–20 Site NGHP–01–21

B

A

B
Theory 3

Theory

Isotropic Velocities

Velocities of isotropic GHBS, whereby the gas hydrate 

fills the sediment’s pore space, are calculated using the 

three-phase Biot equation (Lee, 2007). Lee (2008) derived 

the following bulk (k) and shear moduli (μ) of the GHBS 

applicable for low-frequency well-log and seismic data:

k Kma p p av K

ma s

= − +

= −

( )

( )

1

1

2  

   (1)

with

1

1

1

K K K K av

p

ma

w

w

h

h

p

as

as

= − + +

= +

+

( )

( )

( )

   

  



,

  

 p

as

as

= +

+

( )

( )

1

1 ,

and

  

 s

as

as

= +

+

( )

( )

1

1

where α is the consolidation parameter (Pride and others, 2004; 

Lee, 2005) with 



 = +

+

1 2

1 ; as = w + εh

, w = (1 – Ch ), and 

h = Ch. Kma, Kw, and Kh are the bulk moduli of grain, water, 

and gas hydrate respectively; μma is shear modulus of the grain.

The parameter ε accounts for the reduced impact of 

hydrate formation relative to compaction in terms of stiffening the host-sediment framework, and Lee and Waite (2008) 

recommended ε = 0.12 for modeling velocities of GHBS.

The P-wave (Vp ) and S-wave velocities (Vs) of the GHBS 

are given by:

V k p

b

= + 4 3 



/ and Vs

b

= 



(2)

where

	 rb is the bulk density of GHBS given by 

rb = rs(1 –  ) + rw (1 – Ch ) + rhCh.

The use of equations 1 and 2 for computing velocities 

of GHBS is referred to as the simplified three-phase equation 

(STPE) in this report. For water-saturated sediments, STPE is 

the same as the Gassmann equation.

The consolidation parameter α depends on the effective 

pressure and degree of consolidation. Mindlin (1949) showed 

that the bulk and shear moduli depend on the one-third power 

of the effective pressure. On the basis of the theory by Mindlin 

(1949), the depth (or effective pressure) dependent α is proposed by the following equation using the exponent n:

αi = α0(p0 / pi) n ≈ α0(d0 / di) n (3)

where

α0 is the consolidation parameter at the effective pressure 

p0 or depth d0,

and

αi is the consolidation parameter at the effective pressure 

pi or depth di.

The use of n =1/3 in equation (3) is similar to the Mindlin relation.

Anisotropic Velocities

Out of 21 holes drilled in the Indian Ocean during 

NGHP–01, Collett and others (2008) identified four gas hydrate 

accumulations within the fractured shale. Figure 2A shows an 

X-ray image for recovered core at drill site NGHP–01–10B at 

the depth of 50.1 mbsf. The light color in the image denotes the 

presence of gas hydrate, and figure 2A shows five or six layers 

of gas hydrate and wispy subvertical veins within a relatively 

homogeneous matrix (Collett and others, 2008). Figure 2B

shows a schematic diagram for modeling the fractured reservoir.

Elastic anisotropy due to aligned cracks in porous rock 

has been investigated extensively (for example, Eshelby, 

1957; Walsh, 1969; Watt and others, 1976; Hudson, 1980; 

Thomsen, 1995). Because it is assumed that the fracture is 

filled with 100-percent gas hydrate, the fractured reservoir can 

be modeled as a laminated elastic media (White and Angona, 

1955) rather than saturated aligned cracks embedded in porous 

media (for example, see Thomsen, 1995). In this report, a 

fractured reservoir is modeled as a layered media composed of 

two components as shown in figure 2B. The first component is 

fractures filled with 100-percent gas hydrate, and its characteristics are given by P-wave velocity (VP1), S-wave velocity 

(Vs1), and density (1); the second component is isotropic 

medium with P-wave velocity (VP2), S-wave velocity (Vs2), 

and density (2). Anisotropic P- and S-wave velocities can be 

computed using equations shown in White (1965). Because 

the fracture is filled with 100-percent gas hydrate, the elastic 

constants for the fracture are identical to those of the pure 

gas hydrate.

Let’s define 1 and 2 to be the volume fraction of 

component 1 and volume fraction of component 2, respectively. 

Phase velocities of transverse isotropic media caused from fractures can be computed using the following definition:

< > ≡ +

< > ≡ + ⎛

⎝

⎜

⎞

⎠

⎟ −

−

G G G

G

G G

 

 

1 1 2 2

1 1

1

2

2

1

where

G is any elastic constant such as density of the 

component 1 and component 2.
4 Anisotropic Velocities of Gas Hydrate-Bearing Sediments in Fractured Reservoirs

The P- and S-wave velocities of transverse isotropic media 

can be calculated from the following equations using the Lamé 

constants  and μ (White, 1965):

A y = <

+

( + ) > + < ( + )

> < ( + )>

4 −

2

1

2 2

   1 2

     

( ) (4)

C = < ( + )>

1 −

2

1

 

F = < ( + )> < ( + )>

1 −

2 2

1

 



 

L = < >

1 −1



N = < > 

  = < >

V A C L Q P = ⎛ + + +

⎝

⎜

⎞

⎠

⎟

sin cos / 2 2 1 2

2

 



V A C L Q S

V = ⎛ + + +

⎝

⎜

⎞

⎠

⎟

sin cos / 2 2 1 2

2

 



V N L S

H = ⎛ +

⎝

⎜

⎞

⎠

⎟

sin cos / 2 2 1 2

 



Q A L C L = − − − + + [( )sin ( ) cos ] ( ) sin cos F L 2 2 2 2 2 2   4  

where

 is the angle between the wavefront normal and the 

vertical axis (perpendicular to the layering);

VP is the anisotropic P-wave velocity,

VS

H is the horizontally polarized S-wave (SH) velocity,

and

VS

V is the vertically polarized S-wave (SV) velocity.

Generally, transverse isotropic elastic media is described 

using Thomsen’s parameters. Thomsen (1986, 1995) described 

an anisotropic elastic media using the three parameters γ, , 

and ε. Using these parameters, velocities are given by:

Figure 2. A, X-ray image of gas hydrate-bearing sediments at the depth of 

50.1 meters below sea floor at the drill site NGHP–01–10B (modified from Collett 

and others, 2008). B, Schematic diagram showing laminated two-component 

sediment package. Parameter 1 is the volume fraction of component 1, 2 is 

the volume fraction of component 2, and  is porosity.

A B

(3X HORIZONTAL

EXAGGERATION)

Core NGHP–01–10B–08Y

Data collected at 100 bar

0.1

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.1 1.2 1.3 1.4 1.5 1.6 1.7

0.0

0.2

SECTION DEPTH, IN METERS

GAMMA DENSITY

(g/cc)

X-RAY IMAGE

2

, 2

1, 1
Modeling 5

V

V

V

p o

S

H

o

S

V

o

2 2 2 4

2 2 2

2 2

1 2 2

1 2

1

= + +

= +

=

    

  



( sin sin )

( ) ( sin )

( ) +

⎡ −

⎣

⎢ ⎤

⎦

⎥ 2 2 2 2

2

    



o

o

( )sin cos

(5)

where 0 and 0 are the P- and S-wave velocities at  = 0 or in 

the symmetry direction.

Thomsen’s parameters are related to White’s equation by 

the following equations (Thomsen, 1986):







= −

= + − −

−

= −

N L

L

F L C L

C C L

A C

C

2

2

2

2 2 ( ) ( )

( )

(6)

The velocities shown in equations 4 and 5 are phase velocities. Unless incident angle is 0° or 90°, the phase and group 

velocities are different. If the dip of the fracture is not 0° or 90°, 

the group velocities should be used to calculate the saturations.

Thomsen (1986) derived the relation between group and 

phase velocities for transversely isotropic media. Let g be the 

angle between the ray direction and the vertical axis and GVp, 

GVS

H, and GVSV be the group velocities of P-wave, horizontally 

polarized shear-wave, and vertically polarized S-wave velocities, respectively. Then

V GV

V GV

V GV

p p g

S

H

S

H

g

S

V

S

V

g

( ) ( )

( ) ( )

( ) ( )

 

 

 

=

=

=

(7)

Note that equation 7 does not mean that group velocity equals 

phase velocity. Equation 7 indicates that if the corresponding 

wavefront normal angle  is calculated using the following 

formula for a given ray angle g, then equation 7 is applicable 

to compute group velocity:

tan

tan

tan











g

V

dV

d

V

dV

d

=

+ ⎛

⎝

⎜

⎞

⎠

⎟

− ⎛

⎝

⎜

⎞

⎠

⎟

1

1

(8)

For weakly anisotropic media, group velocities are 

(Thomsen, 1986):

For P-wave: tang = tan[1 + 2 + 4(ε – )sin2]

For SH-wave: tang = tan[1 + 2] (9)

For SV-wave: tang = tan 1 2 1 2 2 2

2 +

⎡ − −

⎣

⎢ ⎤

⎦

⎥    



o

o

( )( sin

For more details for the group and phase velocities, consult 

Thomsen (1986).

Modeling

Fractures in High-Porosity Shale

Figure 3 shows modeled P- and S-wave velocities for 

a fractured shale reservoir using the elastic constants shown 

in table 1. The model parameters for the fracture filled with 

100-percent gas hydrate are VP1 = 3.744 km/s, VS1 = 1.946 km/s, 

and 1 = 0.926 g/cm3; parameters for 100-percent watersaturated sediment are VP2 = 1.503 km/s, VS2 = 0.166 km/s, 

and 2 = 1.563 g/cm3; 2 = 0.65 and CV2 = 0.6, where Cv is 

clay volume fraction. Velocities of water-saturated sediments 

were calculated using the STPE with  = 100. Velocities of 

shale in this fracture model represent the velocities of shallow 

marine sediments.

Figure 3 shows a polar plot of P- and S-wave phase 

velocities with respect to the phase angle for a horizontal 

fracture whose volume fraction is 15 percent of the sediment 

volume, or the volume of a fracture filled with 100-percent 

gas hydrate is 15 percent of the total sediment volume. The 

P-wave velocity at the phase angle of 0° or equivalent for a 

horizontal fracture is 1.64 km/s, whereas the P-wave velocity 

at the phase angle of 90° or equivalent for vertical fractures 

is 1.83 km/s (about an 11-percent increase). The minimum 

SH-wave velocity of 0.186 km/s occurs at the phase angle of 

0°, whereas the maximum SH-wave velocity of 0.621 km/s 

occurs at the phase angle of 90° (about a 200-percent 

increase). These anisotropic velocities can be calculated using 

Thomsen’s parameters using equation 5, and these parameters 

are  = 5.09,  = –0.0729, and ε = 0.1169, which are calculated 

from equation 6. The magnitude of these parameters increases 

with increasing fracture density (or gas hydrate volume).

For comparison, velocities for isotropic GHBS (gas 

hydrate accumulates in the pore space of the sediments) having 

15-percent gas hydrate volume content are shown in figure 3. 

Velocities are computed using the STPE with a constant  = 100

and the same parameters for the water-saturated sediments for 

the fracture model. Depending on the phase angle, the isotropic 

velocities are smaller or larger than the anisotropic velocities.

Figure 4 shows calculated velocities for isotropic GHBS 

along with transversely isotropic velocities for the fractured 

reservoir with respect to volume fraction of gas hydrate. 

Isotropic velocities of GHBS are calculated from the STPE 

with  = 100 and CV = 0.6, which are the same as those for 

water-saturated sediment of the fracture model. For isotropic 

medium, the volume fraction of gas hydrate (Vh) is given by 

Vh = Sh, where Sh is the gas hydrate saturation in the pore 

space and is given by the volume fraction of fractures for a 

fractured reservoir. In the case that there is no gas hydrate 

either in the pore or fracture, the two velocities are the same. 

Because the maximum volume fraction for the isotropic 

medium is limited by porosity, maximum volume fraction 

for the isotropic GHBS is 0.65. For 100-percent gas hydrate 

saturation in the fracture, the velocities are velocities of pure 

methane gas hydrate.
6 Anisotropic Velocities of Gas Hydrate-Bearing Sediments in Fractured Reservoirs

As shown in figure 4A, the effect of anisotropy is much 

more pronounced on the S-wave velocities as expected from 

figure 3. When the fracture orientation is perpendicular to the 

direction of measurement (incident angle is 0°), the S-wave 

velocities are almost constant except at very high volumes of 

gas hydrate saturations above 80 percent. On the other hand, 

in the case that the fracture is parallel to the direction of measurement, the S-wave velocities increase rapidly at low saturation and increase monotonically as gas hydrate saturation 

further increases. For all ranges of fracture volume, velocities 

modeled for isotropic GHBS lie between two velocities modeled for anisotropic GHBS.

Figure 4B shows the relation between modeled anisotropic P- and S-wave velocities along with the measured 

relation at drill site NGHP–01–10D. Based on the theoretical 

curves for P- and S-wave velocities by angle of incidence, the 

measured data do not exhibit isotropic behavior. A series of 

theoretical curves were calculated to determine the fracture 

orientation representative of the measured data. Assuming a 

fracture dip of 85°, or ray angle of 85°, the modeled P- and 

S-wave velocity relation is similar to the measured data, especially within the shaded area.

The velocity at the ray angle of 85° is the group velocity, 

not the phase velocity shown in figure 3. Because energy is 

transmitted with the group velocity, the group velocity should 

be used to analyze measured velocities. As shown in equation 9, 

the relation between the ray angle and phase angle depends on 

Thomsen’s parameters, which depend on the fracture volume 

and elastic properties of sediments encasing the fracture. Consequently, for a given ray angle, the phase angle to be used in 

calculating the group velocity varies with gas hydrate saturation. 

Assuming the fracture volume is 15 percent of the sediment 

(same as for figure 3), group and phase velocities using equations 7 and 8 are calculated and are shown in figure 5.

Because the P-wave velocity has only a small amount 

of anisotropy, the phase and group velocities are similar to 

those shown in figure 5A. In other words, the phase angle 

can be interchanged into the ray angle without significant 

error in the P-wave velocity. However, group and phase 

velocities for the horizontally polarized shear wave are quite 

different as shown in figure 5B. For ray angles less than about 

60°, the group velocities are almost the same. A greater change 

of group velocity occurs for ray angles greater than 60°. In 

other words, the SH-wave velocities are insensitive to the 

Table 1. Constants used for modeling.

[Subscript s, h, c, and w are sand, gas hydrate, clay, and water, respectively; 

K, μ, and  are bulk modulus, shear modulus, and density, respectively. The 

bulk and shear moduli of gas hydrate are calculated at 11°C and 1 MPa from 

Helgerud and others (2009) and others are from Lee (2005). The bulk and 

shear moduli of gas hydrate yield the P- and S-wave velocities of pure gas 

hydrate as 3.744 km/s and 1.946 km/s, respectively. MPa; Mega Pascals, GPa, 

Giga Pascals]

Bulk modulus Shear modulus Density

Ks = 38 GPa μs = 44 GPa s = 2,650 kg/m3

Kc = 20.9 GPa μc = 6.85 GPa c = 2,580 kg/m3

Kh = 8.27 GPa μh

 = 3.49 GPa h = 922 kg/m3

Kw = 2.29 GPa μw = 0 w = 1,000 kg/m3

Figure 3. Isotropic velocities of gas hydrate-bearing sediment and anisotropic velocities for horizontal fracture 

having a 15-percent bulk volume of gas hydrate with respect to the angle of incident. The model represents fractures 

in high-porosity shale. A, P-wave velocity. B, Horizontally polarized (VS

H) and vertically polarized S-wave velocity (VSV).

A P-WAVE B S-WAVE

120

90

60

30

0

330

300

270

240

210

180

150

120

90

60

30

0

330

300

270

240

210

180

150

VELOCITY,

IN KILOMETERS PER SECOND

VELOCITY,

IN KILOMETERS PER SECOND

2

1

2

0.8

0.4

0.0

0.4

0.8

Bulk volume of gas hydrate = 15%

Anisotropic P-wave velocity

Isotropic P-wave velocity

Bulk volume of gas hydrate = 15%

Anisotropic SH-wave velocity

Anisotropic SV-wave velocity

Isotropic S-wave velocity

EXPLANATION EXPLANATION
Modeling 7

dip of the fracture, if the dip is less than ≈60°. However, this 

observation for SH-waves cannot be generalized, because the 

relation between ray angle and SH-velocity is a complicated 

function of porosity and fracture density.

Fractures in Sandstone

Figure 6 shows modeled P- and S-wave velocities for a 

fractured reservoir in sandstone using elastic constants shown 

in table 1. The model parameters for the fracture filled with 

100-percent gas hydrate in sandstone are identical to those 

for the fracture in shale. Parameters for 100-percent watersaturated sandstone are VP2 = 1.950 km/s, VS2 = 0.650 km/s, 

2 = 1.986 g/cm3, 2 = 0.4 , and CV2 = 0.1. Velocities of 

sandstone in this fracture model represent the velocities of 

host sediments at depths of around 600–800 m, typical host 

sediments of GHBS at the Alaska North Slope (Lee, 2005).

Figure 6 show a polar plot of P- and S-wave velocities 

with respect to the angle of incidence for a horizontal fracture 

whose volume fraction is 15 percent. The P-wave velocity at 

the incident angle of 0° is 2.108 km/s, whereas the P-wave 

velocity at the incident angle of 90° is 2.144 km/s (less than 

2-percent increase). The SH-wave velocity at the incident 

angle of 0° is 0.720 km/s, whereas the SH-wave velocity at 

the incident angle of 90° is 0.826 km/s (about a 16-percent 

increase). These anisotropic velocities can be calculated using 

Thomsen’s parameters using equation 5, and these parameters 

are calculated using equation 6 as  = 0.01573,  = –0.0340, 

and ε = 0.0204.

For comparison, velocities for isotropic GHBS having 

15-percent gas hydrate volume content are shown in figure 6. 

Velocities of isotropic GHBS are computed using the STPE 

with  = 30 and the same parameters for the water-saturated 

sediments used for the fracture model (that is 2 = 1.986 g/cm3, 

2 = 0.4, and CV2 = 0.1). The isotropic P-wave velocity is 

2.347 km/s and S-wave velocity is 0.871 km/s, which are larger 

than the maximum anisotropic P- and S-wave velocities. Unlike 

velocities for the fractured shale reservoir, velocities of anisotropic velocities in sandstone are insensitive to the orientation 

of fractures.

Figure 7A shows calculated velocities for isotropic 

GHBS along with transversely isotropic velocities for the 

fracture reservoir in sandstone with respect to volume fraction 

Figure 4. Modeling elastic velocities for anisotropic gas hydrate-bearing sediments (GHBS) caused by 

fracture in high-porosity shale and for isotropic GHBS. A, Relation between gas hydrate saturation and bulk 

volume of gas hydrate in sediments. B, Relation between S-wave velocity and P-wave velocity. 

VOLUME FRACTION OF GAS HYDRATE S-WAVE VELOCITY, IN KILOMETERS PER SECOND

0.0 0.2 0.4 0.6 0.8 1.0 0.0

1

2

3

4

1

0

2

3

4

0.5 1.0 1.5 2.0

VELOCITY, IN KILOMETERS PER SECOND

P-WAVE VELOCITY, IN KILOMETERS PER SECOND

Pure

hydrate

A B

Incident angle of 0° (horizontal fracture)

Incident angle of 90° (vertical fracture)

Isotropic GHBS

Incident angle of 0° (horizontal fracture)

Incident angle of 90° (vertical fracture)

Incident angle of 85°

Isotropic GHBS

Measured at site NGHP−01−10D

EXPLANATION EXPLANATION

Water-saturated

sediment

P-wave

S-wave
8 Anisotropic Velocities of Gas Hydrate-Bearing Sediments in Fractured Reservoirs

Figure 6. Isotropic velocities of gas hydrate-bearing sediment and anisotropic velocities for horizontal fracture 

having a 15-percent bulk volume of gas hydrate with respect to the angle of incidence. The model represents 

fractures in clean sandstone. A, P-wave velocity. B, Horizontally polarized (VS

H) and vertically polarized S-wave 

velocity (VS

V

).

Figure 5. Group and phase velocities for a horizontal fracture having 15-percent bulk volume of gas hydrate (or 

fracture volume) with respect to phase and ray angles. A, P-wave velocity. B, SH-wave velocity.

A P-WAVE B SH-WAVE

VELOCITY,

IN KILOMETERS PER SECOND

2

1

2

120

90

60

30

0

330

300

270

240

210

180

150

VELOCITY,

IN KILOMETERS PER SECOND

0.8

0.4

0.0

0.4

0.8

120

90

60

30

0

330

300

270

240

210

180

150

Bulk volume of gas hydrate = 15%

Phase velocity

Group velocity

Bulk volume of gas hydrate = 15%

Phase velocity

Group velocity

EXPLANATION EXPLANATION

1.2

0.6

0.0

0.6

1.2

A P-WAVE B S-WAVE

90

60

30

0

330

300

270

240

210

180

150

120

90

60

30

0

330

300

270

240

210

180

150

120

VELOCITY,

IN KILOMETERS PER SECOND

VELOCITY,

IN KILOMETERS PER SECOND

3

2

1

0

1

2

3

Bulk volume of gas hydrate = 15%

Anisotropic velocity

Isotropic velocity

Bulk volume of gas hydrate = 15%

Anisotropic SH-velocity

Anisotropic SV-velocity

Isotropic velocity

EXPLANATION EXPLANATION
Gas Hydrate Saturations 9

Figure 7. Modeling elastic velocities for anisotropic gas hydrate-bearing sediments (GHBS) caused 

by fracture in clean sandstone and for isotropic GHBS. A, Relation between gas hydrate saturation and 

bulk volume of gas hydrate in sediments. B, Relation between S-wave velocity and P-wave velocity.

of gas hydrate. Because the maximum volume fraction 

for the isotropic medium is limited by porosity, maximum 

volume fraction for the isotropic GHBS is 0.4. For a given 

gas hydrate content, the isotropic velocities are always 

larger than anisotropic velocities, and the orientation of fractures is insensitive to the amount of gas hydrate. For a given 

velocity, gas hydrate saturations estimated from the isotropic 

GHBS model are much less than those estimated from the 

anisotropic GHBS model.

Figure 7B shows the relation between P- and S-wave 

velocities of GHBS. The modeled relations using the isotropic 

and anisotropic GHBS are similar. Consequently, the relation 

between P- and S-wave velocities is not a good indicator for 

identifying fractured reservoirs in sandstone.

Because the fast and slow velocities of S-waves are 

almost identical, the presence of fractures in sandstone is difficult to detect on the basis of elastic velocities. The relation 

between velocity and saturation that is estimated independently from the velocity, such as saturations estimated from 

the nuclear magnetic resonance (NMR) log, can be used to 

identify the presence of fractures, although the orientation of 

the fractures may not be determined.

Gas Hydrate Saturations 

The modeled velocities shown in figure 4 can be used 

to estimate gas hydrate saturations from measured velocities. 

Because the measured porosity m is assumed to be an averaged value of the porosity of the water-saturated part of sediments and the porosity of the fracture filled with gas hydrate, 

the porosity of the water-saturated sediment is dependent on 

the amount of fracture (or gas hydrate). Therefore, an appropriate porosity for component 2 used to calculate velocities of 

water-saturated sediment is:

  2 1 = −

−

m h

h

V

V (10)

Equation 10 indicates that the porosity of water-saturated sediment is the same as the measured porosity of sediment in the 

absence of gas hydrate. As the volume of gas hydrate increases, 

the porosity of water-saturated sediment decreases to account 

for the presence of fractures.

The density porosity calculated from the density log 

assumes that the densities of gas hydrate and water are the 

same. Because the density of gas hydrate is less than that 

0.0 0.2 0.4 0.6 0.8 1.0 0.5 1.0 1.5 2.0 2.5

VOLUME FRACTION

OF GAS HYDRATE

S-WAVE VELOCITY,

IN KILOMETERS PER SECOND

5

4

3

2

1

0

4

3

2

VELOCITY,

IN KILOMETERS PER SECOND

P-WAVE VELOCITY,

IN KILOMETERS PER SECOND

P-wave

S-wave

EXPLANATION EXPLANATION

Incidence angle 0° (horizontal fracture)

Incidence angle 90° (vertical fracture)

Isotropic GHBS

Incidence angle 0° (horizontal fracture)

Incidence angle 90° (vertical fracture)

Isotropic GHBS

A B
10 Anisotropic Velocities of Gas Hydrate-Bearing Sediments in Fractured Reservoirs

of water, the calculated density porosity is not accurate for 

high-porosity sediments at high gas hydrate saturations. To 

compute accurate density porosity, the gas hydrate saturations 

are required. Consequently, estimating gas hydrate saturation 

and calculating density porosity are iterative processes, and 

the density porosity is updated using the estimated Sh as:

   

   new m

w ma

w h h h ma S S = −

− + −

⎡

⎣

⎢ ⎤

⎦

⎥ ( ) 1 (11)

where w, h, and ma are density of water, gas hydrate, and grains, 

respectively. The updated new is used for m in equation 10.

Figure 8 shows wireline P- and S-wave velocities measured at drill site NGHP–10–10D along with logging-whiledrilling (LWD) P-wave velocity at site NGHP–01–10A. 

Wireline velocities were measured only for the gas hydrate 

interval. Figure 9 shows the gas hydrate saturations estimated assuming isotropic GHBS and anisotropic GHBS from 

wireline P- and S-wave velocities. The STPE parameters used 

for the estimation of gas hydrate assuming isotropic GHBS is 

 = 70(200 / di)1/3 and Cv calculated from the gamma log. The 

gas hydrate saturation estimated from the fracture model is an 

average value of fracture reservoir and water-saturated sediments and is calculated as Sh

 = Vh/new. As implied in figure 4, 

the gas hydrate saturations estimated assuming isotropic 

GHBS are between the two gas hydrate estimates: one assuming that the fracture is vertical and one assuming that the fracture is horizontal. Also shown as solid dots are the gas hydrate 

saturations estimated from the pressure cores. In this report, 

saturations estimated from the pressure cores are considered 

as reference saturations because pressure cores capture all the 

mass in samples. Gas hydrate saturations are estimated from 

the P-wave velocities by assuming vertical fractures agree better with those estimated from the pressure cores. However, the 

estimations from the pressure cores differ significantly from 

those estimated using the S-wave velocities assuming either 

isotropic or anisotropic GHBS. If the fractures are vertical, 

the orientation of the P-wave sensor does not matter for the 

velocity, because the particle motion of the P-wave is parallel 

to the fractures. On the other hand, the direction of particle 

motion of the S-wave is critical to estimate the velocities. 

Generally, it is not possible to accurately estimate gas hydrate 

saturation from the S-wave velocities without knowing the 

orientation of the S-wave sensor relative to the fracture. 

Because the orientation of the dipole sonic imager (DSI) tool 

is not available, it is assumed that the motion of the wireline 

S-wave is parallel to the fracture plane. That is, VS

H shown in 

equation 4 is used as the theoretical S-wave velocity. Overall, 

the gas hydrate saturations assuming horizontal fracture agree 

well with those estimated assuming isotropic GHBS and agree 

well with that estimate from the pressure cores except the core 

at ≈74 mbsf.

Figure 8. Measured logging-while-drilling (LWD) P-wave 

velocities at drill site NGHP–01–10A and wireline P- and 

S-wave velocities at drill site NGHP–01–10D. Calculated 

baseline velocities are shown in red.

Discussion

The model results indicate that the elastic characteristics 

of fractures in shale differ significantly from those in sandstone. The primary reason is that the elastic properties of pure 

methane are much higher than those of high-porosity shales, 

which are the most common host sediments for shallow 

marine GHBS, such as GHBS at drill site NGHP–01–10. On 

the other hand, the elastic velocities of sandstone reservoirs at 

moderate depths, such as GHBS at the Alaska North Slope, are 

much higher than those of shale at shallow depth; anisotropic 

effects of fractures in sandstone are not significant. However, 

to analyze the anisotropic elastic velocities due to fractures, 

the velocities of host sediments at a given locality should be 

accurately incorporated.

Gas hydrates at drill site NGHP–01–10 were inferred 

from LWD and wireline logs, and from recovered cores using 

X-ray images, cold spots, chlorinity anomaly, and moussey 

and soupy textures (Collett and others, 2008). The gas hydrate 

existed as solid nodules, high-angle and subhorizontal veins as 

fracture fill, and was disseminated throughout the cores. However, large differences exist among the various gas hydrate 

saturations. For example, the maximum gas hydrate saturation estimated from the pressure core is about 25.4 percent at 

DEPTH BELOW SEA FLOOR,

IN METERS

0 50 100 150 200

VELOCITY,

IN KILOMETERS PER SECOND

3

2

1

0

S-wave

P-wave

EXPLANATION

LWD P-wave velocity at site 10A

Wireline velocity at site 10D

Modeled baseline velocity
Conclusions 11

Figure 9. Gas hydrate saturations estimated from wireline velocities at drill site NGHP–01–10D assuming 

both anisotropic (vertical and horizontal fractures) and isotropic gas hydrate-bearing sediments (GHBS). A, 

From P-wave velocity. B, From S-wave velocity.

the depth of 117.4 mbsf at drill site NGHP–01–10B, which is 

shown in figure 9. The highest gas hydrate saturation assuming isotropic GHBS is about 80 percent, which was estimated 

from the LWD resistivity log as indicated in the initial report 

(Collett and others, 2008) or from S-wave velocities shown in 

figure 9.

Gas hydrate saturations estimated from the pressure cores 

depend only on the bulk volume of gas hydrate irrespective of 

whether gas hydrate fills the fractures or is dispersed throughout the sediments. The cumulative random measurement error 

in gas hydrate saturations from the pressure cores at drill site 

NGHP–01–10 is estimated slightly less than 5 percent (95-percent confidence interval) (M. Holland, written commun., 2009). 

The largest contributions of error are from porosity and ambient 

pressure. However, the loss of pressure and mass during core 

recovery occurred in only one sample at drill site NGHP–01–10 

(Collett and others, 2008). Also, porosity was accurately 

measured. Therefore, these estimates can be used as reference 

saturations. Gas hydrate saturations from wireline P-wave 

velocities, assuming high-angle fractures, generally agree with 

those estimated from the pressure core, but are not consistent to 

those estimated from S-wave velocities due to uncertainties in 

the particle motion relative to the fracture orientation.

Conclusions

The anisotropic elastic velocities caused by fractures filled 

with 100-percent gas hydrate are modeled using laminated 

media and are applied to analyze velocities measured at drill site 

NGHP–01–10. From this study, the following conclusions can 

be drawn.

Fractures in shale at shallow depth filled with 100-percent 

gas hydrate significantly affect elastic velocities, particularly 

S-wave velocity, relative to the orientation of the fractures. On the 

other hand, velocities for fractured sandstone gas hydrate reservoirs are insensitive to the fracture orientation. However, to analyze the elastic velocities for fractured reservoirs, the velocities of 

host sediment at a given locality should be accurately modeled.

Assuming that velocities for gas hydrate-bearing sediments (GHBS) are isotropic could overestimate gas hydrate 

saturations for the fractured reservoirs, and the overestimation 

generally increases as the dip of the fracture increases. 

An anisotropic GHBS model assuming two-component 

laminated media—one component is a fracture filled with 

100-percent gas hydrate, and the other component is the isotropic water-saturated sediment—adequately predicts anisotropic velocities at drill site NGHP–01–10.

DEPTH BELOW SEA FLOOR, IN METERS DEPTH BELOW SEA FLOOR, IN METERS

50 100 150 50 100 150

GAS HYDRATE SATURATIONGAS HYDRATE SATURATION

0.8

0.6

0.4

0.2

0.0 0.0

0.2

0.4

0.6

0.8

A P-WAVE B S-WAVE

EXPLANATION

Assuming isotropic GHBS

Assuming vertical fracture

Assuming horizontal fracture

Pressure core at site 10B

Pressure core at site 10D
12 Anisotropic Velocities of Gas Hydrate-Bearing Sediments in Fractured Reservoirs

Acknowledgments

I would like to thank the Science Team of the Indian NGHP 

Expedition 01 and the Indian Governments for the release of 

the data. I thank T.S. Collett for his continuous support and 

encouragement throughout this investigation and W.F. Agena and 

L. Burke for their many helpful comments and suggestions. This 

study was partially funded by the U.S. Geological Survey, Energy 

Resources program and the U.S. Department Energy under the 

Interagency Agreement No. DE–A126–05NT42496.

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Publishing support provided by:

Denver Publishing Service Center, Denver, Colorado

Manuscript approved for publication, April 2, 2009

Edited by Tom Judkins

Graphics and layout by Joy Monson

For more information concerning this publication, contact:

Team Chief Scientist, USGS Central Energy Resources

Box 25046, Mail Stop 939

Denver, CO 80225

(303) 236-1647

Or visit the Central Energy Resources Team Web site at:

http://energy.cr.usgs.gov/

This publication is available online at:

http://pubs.usgs.gov/sir/2009/5141/

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Lee—Anisotropic Velocities of Gas Hydrate-Bearing Sediments in Fractured Reservoirs—Scientific Investigations Report 2009–5141