Well Log Analysis to Assist the Interpretation 

of 3-D Seismic Data at Milne Point, 

North Slope of Alaska

By Myung W. Lee

Prepared in cooperation with the Bureau of Land Management under interagency agreement 

LAI 02 00015 and the Department of Energy under interagency agreement DE-AT26-97 FT 34342

Scientific Investigations Report 2005-5048

U.S. Department of the Interior

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

Gale A. Norton, Secretary

U.S. Geological Survey

Charles G. Groat, Director

U.S. Geological Survey, Reston, Virginia: 2005

Any use of trade, product, or firm names in this publication is for descriptive purposes only 

and does not imply endorsement by the U.S. Government.

Although this report is in the public domain, permission must be secured from the individual 

copyright owners to reproduce any copyrighted materials contained within this report.

This publication is only available online at URL:

http://pubs.usgs.gov/sir/2005/5048/

For information on other USGS products and ordering information:

World Wide Web: http://www.usgs.gov/pubprod/

Telephone: 1-888-ASK-USGS

For more information on the USGS—the Federal source for science about the Earth,

its natural and living resources, natural hazards, and the environment:

World Wide Web: http://www.usgs.gov/

Telephone: 1-888-ASK-USGS
iii

Contents

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

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

Modified Biot-Gassmann Theory ............................................................................................................... 2

Logs ............................................................................................................................................................ 3

Description of Logs.............................................................................................................................. 3

Porosity Relative to Depth.................................................................................................................. 4

Velocity and Resistivity ....................................................................................................................... 4

Log Analysis................................................................................................................................................... 4

Gas-Hydrate/Ice Saturations............................................................................................................. 4

Predicting P-Wave Velocity from Resistivity and Porosity Logs.................................................. 6

Effect of Gas on P-Wave Velocity ..................................................................................................... 8

Editing P-Wave Velocity...................................................................................................................... 8

Predicting S-Wave Velocity ............................................................................................................... 8

Reservoir Properties and Modeling......................................................................................................... 10

Reservoir Properties ......................................................................................................................... 10

Modeling Velocity .............................................................................................................................. 10

Modeling Amplitude .......................................................................................................................... 11

Amplitude Versus Offset (AVO)........................................................................................................ 11

Discussion.................................................................................................................................................... 14

Velocity Relative to Gas Hydrate Amount...................................................................................... 14

Seismic Amplitude Relative to Gas Hydrate Amount................................................................... 14

Discrimination of Pore Fluid............................................................................................................. 16

Conclusions ................................................................................................................................................. 16

Acknowledgments...................................................................................................................................... 17

References................................................................................................................................................... 17

Figures

1–17. Graphs showing: 

1. Relation between measured density porosity and depth (compaction) at 

Milne point wells .................................................................................................................. 4

2. The porosity and depth relationship at the CO MPU 2 well........................................... 5

3. The relationship between P-wave velocity and formation resistivity at the 

CO MPU 1 well ...................................................................................................................... 5

4. Estimated gas-hydrate/ice saturations from the resistivity log and 

density porosity at the CO MPU 2 well.............................................................................. 6

5. Predicted P-wave velocities using the gas-hydrate/ice saturations 

estimated from the resistivity log and porosities plotted against the 

measured P-wave velocities at the CO MPU 2 well ....................................................... 6

6. Porosity and velocity at the AR Fiord 4 well..................................................................... 7
iv

7. Gas-hydrate and gas saturations estimated from the resistivity log at the 

Kuparuk State 7–11–12 well and predicted P-wave velocities under 

the assumption of gas hydrate in the pore space and free gas with the 

measured P-wave velocities at the Kuparuk State 7–11–12 well ................................ 9

8. An example of velocity editing using the predicted P-wave velocity at the 

CO MPU 2 well ...................................................................................................................... 9

9. Gas-hydrate and gas saturations estimated from the resistivity log at the 

CO MPU D–1 well ............................................................................................................... 10

10. P-wave velocity, density porosity, and clay volume content at the 

CO MPU D–1 well within the gas-hydrate stability zone ............................................. 10

11. Parameters for a typical reservoir of gas-hydrate-bearing sediments and 

graph showing measured P-wave velocities at depths between 2,500 and 

3,000 feet at the CO MPU D–1 well and predicted P-wave velocity for the 

clean sand and encasing shaly sandstone.................................................................... 11

12. Modeled P-wave velocity, density, and reflection coefficient for the 

reservoir model shown in figure 11A .............................................................................. 12

13. Modeled reflection amplitude .......................................................................................... 13

14. Modeled velocities for gas-hydrate-bearing sediments and partially 

gas saturated sediments................................................................................................... 14

15. Amplitude versus offset (AVO) relation computed using parameters 

shown in table 2.................................................................................................................. 15

16. Derived fluid factors from the estimated amplitude versus offset 

(AVO) intercepts and AVO gradients for modeled AVO data....................................... 15

17. Various relations between gas-hydrate saturation and P-wave velocity ................ 16

Tables

1. Well name and API numbers for wells used inside the Milne Point area........................ 3

2. Elastic parameters for modeling ........................................................................................... 12
Abstract

In order to assess the resource potential of gas hydrate 

deposits in the North Slope of Alaska, 3-D seismic and 

well data at Milne Point were obtained from BP Exploration (Alaska), Inc. The well-log analysis has three primary 

purposes: (1) Estimate gas hydrate or gas saturations from 

the well logs; (2) predict P-wave velocity where there is no 

measured P-wave velocity in order to generate synthetic 

seismograms; and (3) edit P-wave velocities where degraded 

borehole conditions, such as washouts, affected the P-wave 

measurement significantly. Edited/predicted P-wave velocities were needed to map the gas-hydrate-bearing horizons in 

the complexly faulted upper part of 3-D seismic volume. The 

estimated gas-hydrate/gas saturations from the well logs were 

used to relate to seismic attributes in order to map regional 

distribution of gas hydrate inside the 3-D seismic grid.

The P-wave velocities were predicted using the modified 

Biot-Gassmann theory, herein referred to as BGTL, with gashydrate saturations estimated from the resistivity logs, porosity, and clay volume content. The effect of gas on velocities 

was modeled using the classical Biot-Gassman theory (BGT) 

with parameters estimated from BGTL.

Introduction

Great emphasis is being placed on the exploration for 

and production of cleaner burning natural gas resources. New, 

unconventional sources of natural gas are being evaluated and 

produced, but the largest potential source of natural gas is in 

gas-hydrate-bearing sediments (Kvenvolden, 1993). In order to 

assist the U.S. Geological Survey assessment of the resource 

potential of gas hydrate, a 1996 3-D seismic survey shot for 

BP Exploration (Alaska), Inc., by Northern Geophysical Company, which included part of the Milne Point oil field of the 

North Slope of Alaska, was released to the USGS along with 

pertinent well logs. 

The subsurface geology at the Milne Point area consists 

of an upper Paleozoic and Mesozoic, south-facing, passivecontinental-margin sequence and an upper Mesozoic and 

Cenozoic, north-facing, foreland basin sequence (Collett, 

1993). The foreland basin sequence is composed primarily of 

Cretaceous and Tertiary clastic rocks, where all of the gashydrate-bearing sediments are present and are highly faulted. 

The Barrow Arch, a structural high located southwest of the 

3-D seismic survey area, produces a northeast dip in the strata 

within the 3-D survey area, influencing the migration of free 

gas and the presence of gas-hydrate-bearing sediments.

The average surface temperature in this area ranges from 

–10°C to –12°C; the thermal gradient within the ice-bearing 

permafrost ranges from 1.55°C to 4.21°C/100 meters, and the 

thermal gradient below the base of the ice-bearing permafrost 

varies between 2.69°C to 4.36°C /100 meters. The gas-hydrate 

stability zone (GHSZ) depends on temperature and pressure 

as well as the type of gas. The depth to the top of GHSZ is 

about 210 meters, and the depth to the bottom of GHSZ is 

highly variable, ranging from 360 meters at the South Barrow 

Test Well 8 to 1,288 meters at the Hurl 5-10-113 well (Collett 

and others, 1988). Because of the shallow depths to the top of 

the GHZS, permafrost and gas-hydrate-bearing sediments are 

probably commingled in the upper part of the section.

Gas hydrate and ice are both electrical insulators, and 

the resistivity response to ice is the same as that of the gas 

hydrate. Both ice and gas hydrate in the pore space increase 

elastic velocities, and the increase of elastic velocities depends 

on the amount of ice or gas hydrate. Therefore, it is difficult 

to differentiate ice from gas hydrate on the basis of the log 

responses. 

In the Milne Point 3-D area, the gas-hydrate-bearing 

sediments are highly compartmented due to complex faulting 

(Inks and others, 2004). Due to this complexity, synthetic seismogram ties to the 3-D seismic data are extremely important. 

Unfortunately, the velocity logs in the upper part of the section 

are either missing or of inadequate quality owing to borehole 

rugosity. To tie the synthetic seismograms to the 3-D seismic 

data, the velocity logs are either predicted using the resistivity or porosity logs, and poor-quality velocity logs are edited 

Well Log Analysis to Assist the Interpretation 

of 3-D Seismic Data at Milne Point, 

North Slope of Alaska

By Myung W. Lee
2 Well Log Analysis to Assist the Interpretation of 3-D Seismic Data at Milne Point, North Slope of Alaska

using the predicted values of velocities. In order to map the 

gas-hydrate distribution and saturation, amplitude and velocity 

responses of typical gas-hydrate-bearing sediments are then 

modeled using the edited logs.

Modified Biot-Gassmann Theory

Lee (2003) derived the following shear modulus based on 

the assumption that n Vs �VpG�(1��) , where Vp is the P-wave 

velocity, Vs is the S-wave velocity, α is the Vs/Vp of the matrix 

material, and φ is porosity. G and n are parameters depending 

on differential pressure, consolidation, and clay content. The 

shear modulus is given by

Conventionally, it is assumed that fluid in the pore space 

does not change the shear modulus of sediments. In other 

words, the shear modulus of dry rock is the same as that of 

water-saturated sediments. Under this assumption, therefore, 

equation 4 can be used for water-saturated sediments also. 

On the other hand, equation 1 implies that the shear modulus 

of water-saturated sediments, derived from the velocity ratio, 

depends on the fluid in the pore through a constant M, defined 

in equation 1. Even though equation 4 is not part of the 

Biot-Gassmann theory, in order to differentiate two different 

approaches of shear modulus, it is conveniently called classical Biot-Gassmann theory (BGT) in the case that equation 4 

is used for the shear modulus, and modified Biot-Gassmann 

theory by Lee (BGTL) in the case that equation 1 is used for 

the shear modulus (Lee, 2002). 

For soft rocks or unconsolidated sediments, the following 

Biot coefficient is used (Lee, 2002):

4 [1 (1 ) ]/ 3

(1 ) (1 ) (1 ) 2 2

2 2 2 2 2

n

ma ma

n

ma

n

ma ma

k G

k G MG

� �

� � � � � � �

� � �

� � � � �

ma fl M k k

� � � � � � 1 ( )

k kma M

2 � (1� � ) � �

�

� 4� / 3 � k Vp �

� Vs �

� � � (1� � ) ma

(1)

where

kma, μma, kfl, φ, β are the bulk modulus of matrix, the shear 

modulus of the matrix, the bulk modulus of the fluid, 

porosity, and the Biot coefficient, respectively.

For bulk modulus of sediments, the Biot-Gassmann 

theory gives 

, and

(2)

Elastic velocities of water-saturated sediments can be computed from the elastic moduli by the following formulas:

and (3)

where 

ρ is density of the formation given by � � �� � ma � �� fl (1 )

ρma and ρfl are the matrix density and pore fluid density, 

respectively.

If it is assumed that the velocity ratio, Vp/Vs, is constant 

irrespective of porosity, which is approximately true for partially gas saturated sediments (Pickett, 1963), the shear modulus of sediments in dry rock can be derived by the following 

formula (Krief and others, 1990):

(4)

0.98469

1

68.7421

( 0.40635) / 0.09425 �

�

� � � � � e

3.8 � �1� (1��)

n m Log p [10 ]/ (0.426 0.235 ) � 10 �

/ 0.06714 2 G 0.9552 0.0448e 0.18S Cv � � � �

(5)

For hard or consolidated formations, the equation by Krief and 

others (1990) is used:

(6)

The exponent n is given by 

and G is given by

(7)

(8)

where 

p is differential pressure in MPa, 

m is a constant related to the degree of consolidation, 

Cv is the decimal clay volume content of the matrix, and 

S is the decimal gas-hydrate saturation in the pore space. 

For a detailed discussion of parameters n and G, consult Lee 

(2003).

The effect of gas hydrate on elastic velocities is modeled 

such that gas hydrate acts as part of the frame or the skeleton. 

The elastic moduli of the composite matrix are computed by 

Hill’s average equation (Hill, 1952). 

The matrix of gas-hydrate-bearing sediments is assumed 

to consist of sand, clay, and gas hydrate. Using the water-filled 

porosity, � f � (1� S)� , defined in Lee and Collett (2001), 

Cv as the volume clay content of the matrix, and S as the gas 

hydrate saturation, the elastic moduli of a composite matrix 

can be written:
where 

f1, f2, and f3 are the volume fractions of sand, clay, and gas 

hydrate in the matrix, respectively. 

In this paper, density porosity or porosity (φ) is the space 

occupied by gas hydrate and (or) water, and the water-filled 

porosity (φf) is the space occupied only by water. 

The effect of free gas on elastic velocities in the framework of BGTL is described in Lee (2004). As mentioned in 

Lee (2002), BGT instead of BGTL should be used for the 

partially gas saturated sediments. However, the Biot coefficient that is appropriate for unconsolidated sediments at a 

given differential pressure is not readily available. Therefore, 

Lee (2004) used the BGTL to derive the appropriate Biot coefficient for partially gas saturated sediment, which is given by

Logs

Descriptions of Logs

The purposes of this study are to estimate gas-hydrate/ice 

and free gas saturations, to predict P-wave velocities for the 

interval where there are no velocity logs, and to edit velocity logs where velocity logs contain large errors due to hole 

condition. The primary logs used in this study are gamma, 

bulk density, electrical resistivity, and P-wave sonic logs. Most 

of density and P-wave velocity logs start at depths deeper 

than the expected permafrost/gas-hydrate stability zone in this 

region. Wells used in this investigation inside the Milne Point 

area are shown in table 1.

Density porosities were derived from the bulk density 

logs with the matrix density of 2.65 g/cm3 (grams per cubic 

centimeter) and water density of 1.0 g/cm3, assuming a twocomponent system (water and matrix). The porosity correction due to the presence of gas-hydrate/ice is accomplished 

simultaneously with the estimation of gas hydrate (Lee and 

Collett, 1999), and the correction for free gas is shown later in 

this report. 

Clay volume content (Cv) is calculated from the shifted 

gamma log by using the following formula pertinent to Tertiary clastics: 

�

�

� �

�

� � � �� � �

� 3

1

3

1

1 ( / ) 2

1

i i

i

i ma

i

ma i ma k f k f k

�

�

� �

�

� � � �� � �

� 3

1

3

1

1 ( / ) 2

1

i i

i

i ma

i

ma i ma � f � f �

i

ma

i

ma i � � f � �

�

3

1

/(1 )

(1 ) /(1 )

(1 )(1 )/(1 )

3

2

1

f

v f

v f

f S

f C

f C

� �

� �

� �

� �

� � �

� � � �

(9a)

(9b)

(9c)

where

ma

bgtl

bgt �

� � �1� (10)

where 

βbgt is the appropriate Biot coefficient for the BGT in calculating velocities for partially gas saturated sediments; 

that is, substituting βbgt into β in equations 2 and 4, 

where μbgtl is the shear modulus of water-saturated sediments at a given differential pressure calculated using 

equation 1.

��������� �����������������������������������������������������������������������

������������������������������������

���������� ��������� �����������

��������� ������������ ��������������

��������� ������������ ��������������

����������� ������������ ��������������

����������� ������������ ��������������

����������� ������������ ��������������

����������� ����������������� ��������������

����������� ����������������� ��������������

���������������������� ���������������� ��������������

0.083(2 1) 3.7 � �nI Cv (11)

where

sh cn

cn

n G G

G G I �� � and

G, Gcn, and Gsh are measured gamma log, gamma log 

response in a zone considered clean, and log response 

in a shale bed (Western Atlas International Inc., 1995), 

respectively. 

In this analysis, Gcn is about 20–25 in API units and Gsh is 

about 120–180 in API units.

Logs 3
4 Well Log Analysis to Assist the Interpretation of 3-D Seismic Data at Milne Point, North Slope of Alaska

Porosity Relative to Depth

In order to estimate gas-hydrate/ice saturations either 

from resistivity or velocity logs, porosity is required. Porosity 

usually decreases with depth depending on grain geometry, 

packing, compaction, and cementation. Figure 1 shows the 

measured porosity/depth relationship at Milne Point wells with 

two empirical curves; large open circles show the empirical 

relationship of depth relative to porosity for sandstone, and 

large diamond symbols show this relationship for shale. The 

dashed line in figure 1 is a least-squares-fit (LSF) curve to the 

measured porosity at the CO MPU D-1 well, which is given by / 6442 0.532 d e� � � , where d is depth in feet; the LSF appears to 

fit the adjacent wells in this area adequately. The majority of 

porosity data shown in figure 1 lies between clean sandstone 

and shale curves. The rest of the well-log data in this study 

area indicates that it is appropriate to use the LSF curve shown 

in figure 1 with a bias to fit the local porosity/velocity trend. 

An example at the CO MPU 2 well is shown in figure 2. 

The upper part of the porosity log, where the density 

porosities are not available, is supplemented by the porosity from the compaction curve with a bias −0.02. The bias of 

–0.02 suggests that the sediments at the CO MPU 2 well are 

slightly more compacted than sediments at the CO MPU D-1 

well. 

Velocity and Resistivity

Both velocity and resistivity strongly depend on porosity. Therefore, in general, the resistivity and velocity trends 

are similar to each other. However, in this study area, this 

relationship is not simple. Figure 3 shows an example of the 

relationship between resistivity and P-wave velocity at CO 

MPU 1 well. Three branches have been interpreted. The first 

branch is defined for depth interval less than about 2,500 ft, 

where the P-wave velocity increases as resistivity increases 

mainly from the accumulation of gas-hydrate/ice in the pore 

space. The second branch is defined for depths between 2,500 

ft and 5,600 ft, where the P-wave velocity decreases as the 

resistivity increases, mainly because the resistivity of connate 

water decreases as depth increases in this interval. The second 

branch is observed at almost all well logs measured below gashydrate-bearing sediments, where the excluded salts during 

the formation of gas hydrate could have migrated downward 

due to gravity. The third branch is for depths greater than 

5,600 ft, where the P-wave velocity increases as the resistivity 

increases, mainly because of the compaction and consolidation. The rate of velocity increase with respect to resistivity 

for Branch 3 is higher than the rate that for Branch 1, which 

implies that the effect of consolidation on velocity is higher 

than the effect of gas-hydrate/ice saturation in the pore. For 

a given velocity, the resistivity for Branch 1 is more than one 

order of magnitude higher than resistivity that for Branch 3, 

reflecting the effect of resistivity of connate water and shale.

The horseshoe shape of the velocity and resistivity relationship is persistent in most of the well logs in this area. The 

circled region in figure 3 indicates possible free gas intervals, 

where low P-wave velocities are associated with high resistivity, a typical relationship for the free-gas interval. Because 

of the unsatisfactory quality of P-wave velocity logs, it is not 

certain whether the low velocities are caused by free gas or by 

cycle skipping.

Log Analysis

Gas-Hydrate/Ice Saturations

The gas-hydrate stability zone (GHSZ) overlaps with the 

permafrost zone, so it is difficult to differentiate the ice saturation from the gas-hydrate saturation solely on the basis of the 

available logs such as resistivity and velocity. The physical 

properties of gas hydrate and ice are similar to each other, so 

Figure 1. Relation between measured density porosity and depth 

(compaction) at Milne Point wells with some empirical formulas for 

shaly sands by Baldwin and Butler (1985) and for clean sandstones by 

Sclater and Christie (1980). A least-squares fitting to the CO MPU D-1 

well is given by / 6442 0.532 d e� � � , where d is the depth in feet and φ is 

porosity in fraction.
their responses to log measurements also are similar. Both gas 

hydrate and ice are electrical insulators, so there is no electrical resistivity difference between permafrost and gas-hydratebearing sediments. The P-wave velocity of ice (about 3.8 to 

4.0 km/s), however, is higher than that of gas hydrate (about 

3.2 km/s), so there is a difference in the velocity between permafrost and gas-hydrate-bearing sediments for a given saturation. If a thick gas-hydrate formation exists and both P- and 

S-wave velocities are measured, the velocity ratio can be used 

to differentiate ice from gas hydrate. However, S-wave velocities are not available for the GHSZ. Therefore, in this analysis, 

it is assumed that the pore-filling material in the GHSZ and 

permafrost interval is gas hydrate. Under this assumption, the 

saturations estimated from the resistivity are the same as saturations estimated under the assumption of ice. However, the 

saturations estimated from P-wave velocities using gas hydrate 

as a pore-filling material should be higher than those estimated 

under the assumption of ice.

The upper part of P-wave velocity logs appears to be 

more degraded than resistivity logs by poor borehole conditions. Also there exists uncertainty of ice and gas hydrate as 

the pore-filling material in GHSZ, so only resistivity logs are 

used in order to estimate gas-hydrate/ice saturations. 

The formation resistivity of sediments (Ro) is given by 

Figure 2. The porosity and depth relationship at the CO MPU 2 well. 

The compaction curve with a bias of –0.02 is used for the upper part 

of the well to a depth of 2,635 feet. 

Figure 3. The relationship between P-wave velocity and formation 

resistivity at the CO MPU 1 well. Three groups depending on depths 

are shown with approximate linear relationships for each group. 

n

w

k

w

o S

aR R

� �

1/1.9386

1 �

�

�

�

�

�

�

� � �

o

k

w

R

aR S

�

where 

a and n are constants, 

Rw is the resistivity of connate water, 

k is a cementation factor, and 

Sw is the water saturation. 

From equation 12, the saturation of gas-hydrate/ice (S) can be 

estimated from the resistivity by using

(12)

(13)

The cementation factor k and apparent resistivity (Ra), 

Ra = aRw, in equation 13 can be estimated if resistivity and 

porosity for water-saturated sediments are available. However, most of the sediments in the upper part of the section 

inside GHSZ are concentrated either by ice or by gas hydrate, 

Log Analysis 5
6 Well Log Analysis to Assist the Interpretation of 3-D Seismic Data at Milne Point, North Slope of Alaska

so k and Rw are not readily evaluated. In this analysis, k = 2.15 

and aRw = 1 ohm-meter are used. 

The gas-hydrate saturations estimated from the resistivity log using Ra = 1.0 ohm-meter and k = 2.15 at the CO 

MPU 2 well are shown in figure 4. These parameters are not 

well constrained. However, if the estimated gas-hydrate/ice 

saturations are high, the estimation errors associated with 

uncertainties of k and Ra are small. For example, the saturation 

error associated with k with ∆k/k= 0.2 is less than –5 percent 

at saturations above 60 percent for 50-percent porosity sediments. For a given fractional error, the error associated with Ra

is less than that associated with k (Lee and Collett, 2001) for 

all porosity and saturation ranges. For a typical reservoir in the 

Milne 3-D area with φ = 0.35 and S = 0.8, the fractional error 

of the saturation associated with ∆k/k = .2 is about –2 percent.

permafrost), velocities predicted from the acoustic equation 

with gas-hydrate saturations estimated from the resistivity are 

more accurate than those predicted from the LSF method. The 

method used in this study is as follows:

1. Estimate gas-hydrate saturations from the resistivity 

and porosity logs.

2. Using the gas-hydrate saturations, porosity, and clay 

volume content, calculate the P-wave velocities from 

the BGTL (Lee, 2002, 2003).

3. If a porosity log is not available for entire interval, use 

a regional compaction curve with a bias to fit the compaction curve to the trend of measured porosity. 

4. If gas content is estimated from the resistivity log, 

include this in the P-wave velocity prediction as shown 

in the later section “Effect of Gas on P-Wave Velocity.”

Figure 5 shows P-wave velocity calculated from the 

BGTL with m = 1.45, the Biot coefficient given in equation 

5, the gas-hydrate saturations shown in figure 4, the density 

porosity shown in figure 2, and clay volume content calculated from the gamma log. In deriving the exponent, n, normal 

hydraulic pressure (no overpressure) is assumed to derive 

depth-dependent differential pressure. Because most of the 

pore-filling material is ice in the upper part of the CO MPU 

2 well, actual velocities would be a little higher than those 

shown in figure 5.

Figure 4. Estimated gas-hydrate/ice saturations from the resistivity 

log and density porosity at the CO MPU 2 well. Equation 12 used to 

estimate saturation with aRw = 1 ohm-meter and k = 2.15. φ, porosity 

in fraction; Rw, resistivity of connate water; Ro, formation resistivity; a

and k, Archie constants.

Predicting P-Wave Velocity from 

Resistivity and Porosity Logs

Usually P-wave velocity log in the upper part of section is either of poor quality or is missing altogether, so it is 

necessary to predict P-wave velocity for the upper part of the 

well in order to generate a synthetic seismogram. In general, 

the P-wave velocities are predicted from the resistivity log 

by using a least-squares method (Rudman and others, 1975). 

However, as shown in figure 3, the relationship between 

velocity and resistivity is complicated in this area. In order to 

predict velocities, at least three LSF curves are required for 

CO MPU 1 well, one for each branch. Lee (1999) demonstrated that for gas-hydrate-bearing sediments (likewise for 

Figure 5. Predicted P-wave velocities using the gas-hydrate/ice 

saturations (fig. 4) estimated from the resistivity log and porosities 

are plotted against the measured P-wave velocities at the CO MPU 2 

well. BGTL parameter m = 1.45, depth-dependent differential pressure under normal hydraulic pressure, porosity bias of –0.02, and 2.15 Ro � 1.0 /� are used to predict the P-wave velocity.

If porosity derived from the compaction curve is the 

only variable used in the prediction, porosity monotonically 

decreases as depth increases to about 2,600 ft. However, as 

indicated in figure 4, the gas-hydrate/ice saturation varies with 
depth. Therefore, the P-wave velocities are highly variable due 

to gas-hydrate/ice saturations and variable clay contents to the 

depth of 2,600 ft. For depths deeper than 2,600 ft, only porosity and clay volume content are used in predicting the P-wave 

velocity. 

As depth increases, sediments are compacted and consolidated. As a consequence, the nature of sediments changes as 

depth increases. In order to accommodate the changes of consolidation and compaction with depth, the following geometric 

mean of the Biot coefficient is proposed, which is appropriate 

for sediments that are neither consolidated nor unconsolidated.

porosity calculated from the resistivity contain much higher 

frequency. Because there is no P-wave velocity measured at 

AR Fiord 4 well, the accuracy of predicted P-wave velocity 

is unknown. It is a worthwhile exercise, however, to predict 

P-wave velocity from a variety of sources to generate synthetic 

seismograms for the interpretation of 3-D seismic data in this 

area.

� � � � � � � 1

1 2

k

o

w

res R

aR 1/ � � ( )

(14)

where

β1 is the Biot coefficient for unconsolidated sediments 

(equation 5), 

β2 is the Biot coefficient for consolidated sediments (equation 6), and 

δ is a weight. 

When δ = 1, the mean Biot coefficient is just the Biot coefficient for unconsolidated sediments. When δ = 0, the mean 

Biot coefficient is that of consolidated sediments. 

Sometimes porosity calculated from the resistivity log 

can be used to predict P-wave velocity. For water-bearing sediments, porosity can be estimated from equation 12 by

(15)

where 

φres is porosity calculated from the resistivity.

Equation 14 assumes that the resistivity of connate water does 

not change; that is, Ra is constant and there is no gas hydrate, 

gas, or ice in the pore (S = 0). Therefore, equation 14 can be 

used for the deeper part of the section with caution, as shown 

in Branch 3 in figure 3. 

Figure 6 shows the estimated porosity from the resistivity (fig. 6A) and predicted P-wave velocities using the BGTL 

(fig. 6B) with the P-wave velocity at the nearby AR Fiord 5 

well. At the AR Fiord 4 well, only gamma and resistivity logs 

are available. The P-wave velocities were predicted using 

the BGTL with a variable Biot coefficient and m with δ = 1 

when depths are less than 1,000 ft and δ = 0.3 when depths are 

greater than 4,000 ft. The weight δ varies linearly with depth 

between 1,000 and 4,000 ft. At the same time, it is assumed 

that the constant m varies linearly with δ in such a way that m

= 2 when δ = 1, and m = 4 when δ = 0. The light line represents the predicted P-wave velocity using the porosities from 

the compaction curve and clay volume content, and the dark 

solid line represents the P-wave velocity using the porosities derived from the resistivity log and clay volume content. 

The general trend of predicted P-wave velocity agrees well 

with that of the AR Fiord 5 well, and the velocities using the 

A

B

Figure 6. Porosity and velocity at the AR Fiord 4 well. A, Porosities 

estimated from the resistivity log are compared to porosities from the 

compaction curve. B, Predicted P-wave velocities at the AR Fiord 

4 well using the compaction curve and porosity estimated from the 

resistivity logs are plotted against measured velocities at the nearby 

well, AR Fiord 5. 

Log Analysis 7
8 Well Log Analysis to Assist the Interpretation of 3-D Seismic Data at Milne Point, North Slope of Alaska

Effect of Gas on P-Wave Velocity

Usually the density porosity calculated from the bulk 

density is affected by gas/gas hydrate because a two-component system—matrix and water—is assumed. When a resistivity log is used to calculate the saturation, the saturation is independent of gas or gas hydrate in the pore space because gas 

and gas hydrate both are electrical insulators. In the following 

discussion, it is assumed that the saturations are calculated 

from the density and resistivity logs. If some of the intervals 

contain free gas instead of gas hydrate, accurate velocities can 

be calculated in the following way:

1. Calculate new porosity with the assumption of free 

gas, instead of gas hydrate, in the pore using the threecomponent system of matrix, water, and gas; 

2. Calculate gas content using the new porosity from step 

1; then

3. Calculate P-wave velocity using the BGT with parameters calculated from the BGTL (Lee, 2004).

Let us define: 

φa to be density porosity assuming two-component system 

(matrix and water),

Sa to be saturation calculated from the resistivity log using 

φa (equation 13),

φ to be true porosity accounting for the presence of gas, and

S to be true gas saturation.

Then,

Figure 7 shows an example of calculated P-wave velocities and gas/gas-hydrate saturations for the MO Kuparuk State 

7-11-12 well. Figure 7A shows the gas-hydrate saturations 

(Sa in equation 20) estimated from porosity and resistivity log 

using k = 2.15 and Ra= 1.0 ohm-meter as a solid line (compaction curve with no bias to the depth of 2,500 ft and measured 

porosity for the rest of the log). The gas saturation S calculated 

from equation 20 is shown as a dotted line and is a little less 

than gas-hydrate saturations. Figure 7B shows measured and 

predicted P-wave velocities. Zone A is probably a gas hydrate 

interval because the predicted P-wave velocity matches with 

the measured velocity for gas hydrates. However, zones B and 

C may be free gas zones because the predicted velocity using 

free gas matches a little better with the measured velocity.

Editing P-Wave Velocity

Predicting P-wave velocity from porosity and clay volume content can be used to edit the velocity log. The proposed 

scheme is as follows:

1. If the fractional errors of the predicted velocities are 

greater than a predetermined value, the predicted 

velocities are used. 

2. If the fractional errors of the predicted velocities are 

less than a predetermined value, the original (measured) velocities are used.

In this text, the fractional error, Ep, is defined as 

ma w

ma b

a � �

� � � �� �

S (1 S) ma g w

ma b

� � �

� � � � �� � �

(1 ) (1 ) /1.9386 /1.9386

a

k

a

k � � S � � � S

ma g

ma b a Sa w g

� �

� � � � � � �� � � � � ( ) (1 )( )

(16)

(17)

where

ρma, ρw, ρg, and ρb are density of matrix, water, gas, and 

sediments, respectively. 

The estimated gas saturations are higher if higher porosities 

are used. Because the density of gas is less than that of water, 

φa is higher than φ. Therefore, the amount of free gas using 

true porosity should be less than the one estimated using φa.

In order to estimate true saturation and porosity from the 

Sa and φa, the relationship shown in equation 13 can be used. 

From equation 13,

(18)

If it is assumed that k ≈ 1.9386 with Sa ≥ 0, then the following 

equations can be derived:

(19)

�

� (1 ) 1 a Sa S � � � (20)

predicted

p

measured

p

predicted

p

p V

V V

E � � (21)

Figure 8 shows an example of edited P-wave velocities 

using the predetermined error of zero (fig. 8A), which is identical to prediction of P-wave velocity, and predetermined error 

of 0.15 (fig. 8B). In both cases, the small P-wave velocities in 

the original logs are replaced with the predicted velocities. As 

predetermined Ep increases, the edited P-wave velocities retain 

more measured P-wave velocities as shown in figure 8B.

Predicting S-Wave Velocity

In mapping the free gas zone below the GHSZ, the Swave velocities can be very useful and can be used to model 

the amplitude relative to offset effect. The prediction of 

S-wave velocity can be accomplished either by the BGTL for 

gas-hydrate-bearing sediments (Lee, 2003) or by the BGT for 

partially gas saturated sediments (Lee, 2004).
Figure 9 shows the result of predicting S-wave velocities 

along with P-wave velocities for the CO MPU D-1 well. Gashydrate or gas saturations are shown in figure 9A. The solid 

lines in figure 9B are the predicted P- and S-wave velocities, 

assuming that the pore-filling material is gas hydrate, and the 

dotted lines are predicted velocities, assuming gas in the pore 

space. Velocities are computed under the assumption of patch 

distribution with a calibration constant e = 6 (Brie and others, 

1995). As shown in figure 9B, the effect of gas hydrate on the 

S-wave velocity is as much as the effect on the P-wave velocity, whereas the effect of free gas on the S-wave velocity is 

much smaller than the effect on the P-wave velocity.

A

B

Figure 7. A, Gas hydrate and gas saturations estimated from the 

resistivity log at the Kuparuk State 7-11-12 well. B, Predicted P-wave 

velocities under the assumption of gas hydrate in the pore space 

(dashed line) and under the assumption of free gas (solid line) with 

the measured P-wave velocities at the Kuparuk State 7-11-12 well.

A

B

Figure 8. An example of velocity editing using the predicted P-wave 

velocity at the CO MPU 2 well. BGTL parameter m = 1.45, depthdependent differential pressure under normal hydraulic pressure, 

porosity bias of –0.02, and 2.15 Ro � 1.0 /� are used to predict the Pwave velocity. A, The solid line shows the predicted (Ep = 0.0) P-wave 

velocity. B, The solid line shows the edited P-wave velocity using the 

predicted P-wave velocity as a guide with Ep = 0.15. 

Log Analysis 9
10 Well Log Analysis to Assist the Interpretation of 3-D Seismic Data at Milne Point, North Slope of Alaska

Reservoir Properties and Modeling

Reservoir Properties

It is demonstrated that gas hydrate accumulates more 

in clean, porous sediments (Jin and others, 2002). Figure 10 

shows the P-wave velocity, density porosity, and clay volume 

content for sediments within GHSZ at the CO MPU D-1 

well. Except for anomalously high porosity spikes, the log 

responses are of good quality. Figure 10 indicates that cleaner 

sediments are associated with low P-wave velocity and high 

density porosity. On the other hand, shaly sands are associated with higher P-wave velocity and lower density porosity. 

By averaging the log values with porosities between 0.29 and 

0.31 and between 0.39 and 0.41, typical reservoir properties 

for gas-hydrate-bearing sediments are derived and shown in 

figure 11A. In the modeling, it is assumed that gas hydrate 

concentrates more in the cleaner sand with the porosity of 0.4 

and that the encasing shaly sands with porosity of 0.3 contain 

no gas hydrate or very low gas-hydrate saturations. Well logs 

in gas-hydrate-bearing sediments at the Northwest Eileen State 

2 well support this model assumption. 

A

B

Figure 9. A, Gas-hydrate and gas saturations estimated from the 

resistivity log at the CO MPU D-1 well. B, Predicted P- and S-wave 

velocities under the assumption of gas hydrate in the pore space 

(solid line) and under the assumption of free gas (dotted line). 

Figure 10. P-wave velocity, density porosity, and clay volume content at the CO MPU D-1 well within gas-hydrate stability zone. 

Modeling Velocity

In order to predict the velocity of gas-hydrate-bearing 

sediments for a given gas- hydrate saturation, the properties 

of sediments that do not contain gas hydrate are required, and 

the pertinent parameters for the BGTL should be derived from 

the elastic properties of sediments without gas hydrate. Figure 

11B shows the measured P-wave velocity, shown in figure 

10, with respect to porosity and shows two modeled P-wave 

velocities calculated from the BGTL with m = 1 and p = 8 

megapascals (MPa). As shown in figure 11B, the predicted 

velocities follow the measured velocities fairly accurately. For 

example, the large circles in figure 11, which represent measured velocities for the shaly sand and clean sand shown in 

figure 11A, do agree with the predicted velocities with greater 

than 96-percent accuracy. The predicted velocity for the clean 

sandstone is 1.845 km/s, whereas the measured velocity is 1.8 

km/s, so there is about 3-percent overestimation. For shaly 

sand, the predicted P-wave velocity is 2.122 km/s, whereas 

the measured velocity is 2.2 km/s, which is about 4-percent 

underestimation. 
Figure 12 shows the modeled P-wave velocity, density, 

and reflection coefficient using the reservoir model shown in 

figure 11A with respect to gas-hydrate saturation (S) in the 

clean sand. It is assumed that the shaly sand contains no gas 

hydrate (S = 0 in the shaly sand). The P-wave velocity varies from 1.85 km/s at S = 0 to 3.82 km/s at S = 1.0. Because 

the density of gas hydrate is less than that of water, the bulk 

density of gas-hydrate-bearing sediments decreases slightly 

as the gas-hydrate saturation increases. The reflection coefficient is –0.11 at S = 0 in the clean sand and is 0.24 at S = 1 

in the clean sand. Note that amplitude is zero near S = 0.4; that 

is, total blanking, and the polarity of reflection changes from 

negative to positive as gas-hydrate saturation increases.

Modeling Amplitude

Seismic amplitude responses to the reservoir model 

shown in figure 11A depend on the gas-hydrate saturation, 

thickness of the reservoir, and frequency content of the seismic wavelet. Figure 13A shows amplitude responses under 

the assumption that the encasing shaly sand contains no gas 

hydrate and gas hydrate is present only in the clean sand, at 

two dominant frequencies (25 and 40 hertz [Hz] of Ricker 

wavelet) and two reservoir thicknesses (10 and 30 ft). Because 

of the interference, the amplitude variation of the 10-ft reservoir is less than that of the 30-ft reservoir. Figure 13B shows 

the amplitude response using a 40-Hz Ricker wavelet with two 

different saturations for the encasing shaly sand. If the shaly 

sand contains gas hydrate, the amplitude response shifts downward, toward more negative amplitude, compared to the model 

using no gas hydrate in the shaly sands. 

Amplitude Versus Offset (AVO)

The Vp/Vs ratios or the Poisson’s ratios of water-saturated, 

gas-hydrate-saturated, and gas-saturated sediments are markedly different, so the amplitude dependence on the offset could 

provide additional information for the assessment of gas or 

gas hydrate in this area. Figure 14 shows the modeled P- and 

S-wave velocities for the clean sandstone reservoir with gashydrate and gas saturations. The density and bulk modulus of 

free gas were computed from the formula given by Batzle and 

Wang (1992) assuming that the pore pressure is 8 MPa and the 

A B

Figure 11. A, Parameters for a typical reservoir of gas-hydrate-bearing sediments. B, Graph showing measured P-wave velocities 

at depths between 2,500 and 3,000 feet at the CO MPU D-1 well and predicted P-wave velocity for the clean sand (reservoir interval) 

and encasing shaly sandstone. Two large circles represent the average velocity and porosity for clean and shaly sands shown in figure 11A. BGTL, modified Biot-Gassmann theory by Lee; φ, porosity in fraction; Cv, clay volume content in fraction; Vp, P-wave velocity; p, differential pressure; km/s, kilometers per second; g/cm3

, grams per cubic centimeter; m, BGTL parameter; MPa, megapascal. 

Reservoir Properties and Modeling 11
12 Well Log Analysis to Assist the Interpretation of 3-D Seismic Data at Milne Point, North Slope of Alaska

temperature of reservoir is 5°C. The velocities of partially gas 

saturated sediments were computed using the patchy distribution with the calibration constant e = 6 (Brie and others, 1995). 

The calculated elastic velocities and densities are shown in 

table 2.

Figure 12. Modeled P-wave velocity, density, and reflection coefficient for the reservoir model shown in figure 11A. The gas-hydrate 

saturation in the encasing shaly sandstone is zero. ρ, density; φ, 

porosity in fraction; Cv, clay volume content in fraction; Vp, P-wave 

velocity; g/cm3, grams per cubic centimeter; km/s, kilometers per 

second.

��������� ���������������������������������

�����������������������������������������������������������������������������������������������������������������������������������������������������������������

������������������������������������������

������ � ��������� ��������� ������������ ���� �����

������������ ��� ����� ����� ����� � � �����

������������ ��� ����� ����� ����� � � �����

������������ ��� ����� ����� ����� �� � �����

������������ ��� ����� ����� ����� �� � �����

������������ ��� ����� ����� ����� �� � �����

������������ ��� ����� ����� ����� � �� �����

������������ ��� ����� ����� ����� � �� �����

������������ ��� ����� ����� ����� � �� �����

Offset dependence of reflection amplitude or amplitude 

versus offset (AVO) is modeled by assuming that the upper 

layer is the shaly sandstone, shown in figure 11A, without gas 

or gas hydrate, and the lower sediments contain either gas 

hydrate or free gas. Figure 15 shows the reflection coefficient 

relative to the angle of incidence using the parameters shown 

in table 2. For sediments with gas hydrate (fig. 15A), the magnitude of reflection slightly decreases as the angle of incidence 

increases until it reaches the critical angle. In this model, there 

is no critical angle until the gas-hydrate saturation reaches 

about 25 percent. 

Figure 15B shows the reflection amplitude relative to the 

angle of incidence for partially gas saturated sediments. The 

magnitude of reflection amplitude increases as the angle of 

incidence increases beyond about 30 degrees. If the angle of 

incidence is less than about 30 degrees, the offset dependence 

of reflection amplitude appears to be similar to each other, 

even though the magnitude of amplitude is much higher for 

gas-saturated sediments.

The dotted curve in figure 15B shows the reflection coefficient from an interface whose upper layer is a gas-hydratebearing sediment with Sh = 80 percent and whose lower layer 

is a partially gas saturated sediment with Sg = 80 percent. 

This mimics an interface expected at the phase boundary. As 

indicated in figure 15B, the amplitude decreases as the angle 

of incidence increases up to about 60 degrees. If the upper 

gas-hydrate-bearing sediment has a low saturation such as 20 

percent, the amplitude would increase, not decrease, as the 

angle of incidence increases. It is important to note that if the 

sediments have high gas-hydrate saturations or high velocities 

due to cementation of gas hydrate, a negative AVO effect is 

expected (Ecker and others, 1998; Lee and others, 1996).

The above AVO analysis was accomplished using the 

exact equation for plane-wave reflection coefficients or Zoeppritz equations (Aki and Richards, 1980). However, in real 

data analysis, an approximate equation is more appropriate. 

Aki and Richards (1980) derived the following approximate 

relationship between angle of incidence and P-P reflection 

coefficient (Rpp) as
where

deviations from the p Vs �V � r� mudrock trend of Castagna 

and others (1985):

A B

Figure 13. Modeled reflection amplitude. A, Comparison of amplitude with respect to the gas-hydrate saturation and to dominant 

frequency under the assumption of no gas hydrate in the encasing shaly sandstone. B, Comparison of amplitude with respect to the 

gas-hydrate saturation of the encasing shaly sandstone.

( ) sin ( ) sin ( )tan ( ) 2 2 2 Rpp � � A � B � � C � � (22)

�

�

�

�

�

�

�

� �

�

� � �

�

p

p

V

V

A

2

1

�

�

�

�

�

�

�

� �

�

�

�

�

�

�

�

�

�

� � � � �

�

s

s

p

s

p

p

V

V

V

V

V

V

B 2 2

2

1 2

p

p

V

V

C

2

� � and

Vp, Vs, and ρ are the average values across the boundary for 

the P-wave, S-wave and density, respectively. 

By least-squares fitting (LSF) of equation 22 to AVO data, 

coefficients A, B, and C can be estimated. Coefficient A is the 

normal incidence reflection coefficient, and B is often called 

the AVO gradient, which represents the change of Poisson’s 

ratio across the boundary (Hilterman, 1989).

AVO analysis can be used to identify the pore fluid in 

sediments. An application of A and B in the analysis of seismic 

attributes is estimating fluid factor. Smith and Gidlow (1987) 

introduced fluid factor (∆F), which was designed to emphasize 

s

s

p

s

p

p

V

V

V

V r V

V

F �

�

�

�

�

�

�

�

� � �

� � (23)

For example, if r = 1.16 and Vp/Vs = 2, then

�F �1.251A � 0.58B (24)

which is zero if the Castagna trend holds.

Figure 16A shows an example of estimated fluid factors 

using equation 24. AVO modeling was done using the Zoeppritz equations where encasing shales have porosities of 0.2, 

0.25, and 0.3 with Cv = 0.3 and reservoirs have porosities of 

0.3, 0.35, and 0.4 with Cv = 0.1. Gas and gas hydrate with 

saturations of 0.4, 0.6, and 0.8 were modeled. By LSF to the 

exact AVO trends with equation 22, A, B, and C are estimated 

and fluid factors are calculated from equation 24. Figure 16A

indicates that even though fluid factors of water-saturated sediReservoir Properties and Modeling 13
14 Well Log Analysis to Assist the Interpretation of 3-D Seismic Data at Milne Point, North Slope of Alaska

ments overlap those of gas-hydrate-bearing sediments, fluid 

factors of partially gas saturated sediments are well separated 

from those of water- or gas-hydrate-bearing sediments.

Discussion

Velocity Relative to Gas Hydrate Amount 

The modeled velocity shown in figure 12 can be used 

to estimate the gas-hydrate saturations from the seismic 

data if accurate interval velocities can be estimated from the 

seismic data. One approach is that migrated seismic data are 

inverted to the interval velocities such as the seislog approach 

(Lindseth, 1979). Jin and others (2003) applied this method to 

estimate gas hydrate amount at the South Shetland on the continental margin, Antarctica Peninsula. Also, interval velocities 

can be estimated using tomography analysis. Tinivella and 

Lodoro (2000) applied this method to estimate gas-hydrate 

saturation at the Blake Ridge in the North Atlantic Ocean. 

Prestack full waveform inversion of large-offset reflection 

data provides information about P- and S-wave velocities and 

bulk density; thus, it is a powerful tool not only to estimate the 

amount of gas hydrate but also to distinguish gas hydrate from 

free gas. Dutta and others (2003) demonstrated this approach 

for a 3-D seismic data interpretation in the Gulf of Mexico. In 

all of these approaches, the key element is deriving an accurate 

relationship between the interval velocity and gas-hydrate 

saturations. 

Figure 17 shows various relationships between velocity 

and gas-hydrate saturations for the Mallik 5L-38 well (dashed 

lines), from the velocity model shown in figure 12 (circles), 

and from the predicted velocity at the CO MPU C-1 and CO 

MPU D-1 wells (dots) with the LSF curve (solid line). The 

relationship at the Mallik 5L-38 is shifted to the right compared to the modeled relationship (for a given gas-hydrate 

saturation, the P-wave velocities are higher than the modeled 

velocity), which is caused by the lower porosity and increased 

consolidation at the Mallik 5L-38. The average porosity at the 

Mallik 5L-38 well is 30 percent, whereas the modeled porosity 

is 40 percent and the average measured porosities (dots) are 

about 45 percent. The depth to the gas-hydrate-bearing zone 

at the Mallik 5L-38 is deeper than those analyzed at the CO 

MPU C-1 and CO MPU D-1wells. The LSF is very close to 

the modeled velocity relationship. At high saturations, the LSF 

is shifted toward the left compared to the modeled relationship 

because most of the high saturations are from the high-porosity permafrost measurements. Therefore, the modeled velocity and saturation relationship shown in figure 12, which is 

written as 

Figure 14. Modeled velocities for gas-hydrate-bearing sediments 

(solid lines) and partially gas saturated sediments (dotted lines). 

Density and bulk modulus of gas are calculated from Batzle and Wang 

(1992) with pore pressure of 8 megapascals (MPa) and the temperature of 5°C. φ, porosity in fraction; Cv, clay volume content in fraction; 

p, differential pressure; T, temperature; m, BTGL (modified BiotGassmann theory by Lee) parameter; e, calibration constant. 

�

�

�

�

�

�

�

� � � 0.95

0.87

0.87 ln

Vp S (25)

can be used to estimate the amount of gas hydrate from the 

interval velocities derived from 3-D seismic data.

Seismic Amplitude Relative to 

Gas Hydrate Amount

Seismic amplitudes are complexly related to the gashydrate saturations and thickness of reservoir because of constructive and destructive interferences. For a given thickness 

and frequency, the relationship between gas-hydrate saturation 

and seismic amplitude is simple. In the case that there is no 

gas hydrate in the encasing shaly sands, the amplitude relative 

to saturation for a 30-ft-thick reservoir using a 40-Hz Ricker 

wavelet (the dominant frequency in the upper section of 3-D 

volume) can be approximated by

13.36

1

15.19

( 1.53)/ 0.86 �

�

� � A� e

S (26)
A B

Figure 15. Amplitude versus offset (AVO) relation computed using parameters shown in table 2. A, AVO from the interface between upper 

water-saturated sediments and lower gas-hydrate-bearing sediments. B, AVO from the interface between upper water-saturated sediments 

and lower partially gas saturated sediments. The circles represent AVO in the case that the upper layer is gas-hydrate-bearing sediment with 

Sh = 80 percent. Sh, gas-hydrate saturation; Sg, gas saturation; %, percent.

A B

Figure 16. Derived fluid factors from the estimated amplitude versus offset (AVO) intercepts and AVO gradients for modeled AVO data. A, 

Using Castagna mudrock relationship for the velocities of water-saturated sediments. B, Using the properties of modeled velocities of unconsolidated sediments expected at this study area. Vp, P-wave velocity; Vs, S-wave velocity; k, a constant.

Discussion 15
16 Well Log Analysis to Assist the Interpretation of 3-D Seismic Data at Milne Point, North Slope of Alaska

and for a 10-ft-thick reservoir,

prospects in this area. As indicated in the AVO analysis, a 

fluid factor could be used to identify pore fluid by using the 

unstacked seismic data in the offset domain. The fluids factors 

shown in figure 16A are derived using the Castagna mudrock 

relationship, which may not be valid for the sediments in the 

study area. The magnitude of fluid factors of water-saturated 

sediments increases as the magnitude of intercepts (or Rpp) 

increases. On the other hand, fluid factors for gas-hydratebearing sediments are scattered around a zero value. This is 

caused by using the Castagna relationship for water-saturated 

sediments. 

Figure 16B shows fluid factors using the properties of 

unconsolidated sediments modeled in this investigation. The 

relationship of modeled P- and S-wave velocities is given by 

Vp = 1.3137Vs + 1.176. Using this relation and Vp/Vs = 2.7, the 

fluid factor can be found from the following equation:

Figure 17. Various relations between gas-hydrate saturation and 

P-wave velocity. The dashed lines are the relations derived from the 

well logs at the Mallik 5L-38, Mackenzie Delta, Canada; circles denote 

the relations derived from the reservoir model shown in figure 11A; 

dots represent relations derived from the predicted P-wave velocities 

using the gas-hydrate saturation estimated from the resistivity log at 

the CO MPU C-1 and CO MPU D-1 wells; the solid line represents a 

least-squares fit (LSF) to the measured relation. Vp, P-wave velocity in 

kilometers per second; S, gas-hydrate saturation in fraction.

29.35

1

29.81

( 0.58)/ 0.16 �

�

� � A� e

S (27)

where 

A is amplitude of seismic trace including the polarity. 

As the thickness of reservoir increases beyond about 50 ft, 

the amplitude decreases as gas-hydrate saturation increases. 

Because the relationship between amplitude and gas-hydrate 

saturation is complex, it is essential to calculate different reservoir models to extract amplitude information.

Discrimination of Pore Fluid

Differentiating gas hydrate from free gas in the pore 

spaces by using seismic data is important in evaluating 

�F � 0.988A � 0.886B (28)

Figure 16B shows the fluid factors derived using equation 28. The fluid factors of water-saturated sediments scatter 

around zero value, and the magnitude of fluid factors of gashydrate bearing sediments is a little larger than those of watersaturated sediments. Both figures 16A and 16B suggest that 

fluid factors, at least in theory, can be used to discriminate gas 

from gas hydrate in the pore space by using unstacked seismic 

data in the offset domain. 

Conclusions

The P-wave velocities of gas-hydrate-bearing sediments 

are predicted using the gas-hydrate saturations estimated from 

the resistivity log along with porosity and clay volume content 

using the modified Biot-Gassmann theory by Lee, or BGTL. 

The effects of free gas in the elastic velocities are modeled 

using the Biot-Gassmann theory with the Biot coefficient 

derived from the BGTL.

Predicting P- and S-wave velocities is essential to supplement the missing part of sonic logs in order to tie synthetic 

seismograms to the 3-D seismic data at the Milne Point area 

and to model offset-dependent amplitude (AVO). Predicted Pwave velocities can also be used to edit the poor quality sonic 

logs. Because both gas hydrate and free gas are electrical insulators, the resistivity log cannot distinguish gas hydrate from 

gas in the pore space. As a consequence, the predicted P-wave 

velocity contains uncertainty about the pore-filling material 

near the gas-hydrate phase boundary. The predicted AVO 

trend based on the model result can be used to differentiate 

gas hydrate from gas by analyzing the pre-stack 3-D volume. 

The modeled amplitudes and velocities can be used to relate 

seismic attributes from the 3-D volume to the gas-hydrate/gas 

saturations and to spatial distribution of gas or gas hydrate.
Acknowledgments

Discussions with T.S. Collett are appreciated very 

much. I thank P.H. Nelson, J.J. Miller, and T.L. Inks for their 

comments and suggestions. This work was partly funded by 

Bureau of Land Management under interagency agreement 

LAI 02 0015 and the U.S. Department of Energy under interagency agreement DE-AT26-97 FT 34342.

References

Aki, Keiiti, and Richards, P.G., 1980, Quantitative seismology 

theory and methods—Volume 1: New York, W.H. Freeman 

and Co., 557 p.

Baldwin, Brewster, and Butler, C.O., 1985, Compaction 

curves: American Association of Petroleum Geologists Bulletin, v. 69, p. 622−626.

Batzle, Michael, and Wang, Zhijing, 1992, Seismic properties 

of pore fluids: Geophysics, v. 57, p. 1396−1408.

Brie, A., Pampuri, F., Marsala, A.F., and Meazza, O., 1995, 

Shear sonic interpretation in gas-bearing sands: Society of 

Petroleum Engineers Paper 30595, p. 701−710.

Castagna, J.P., Batzle, M.L., and Eastwood, R.L., 1985, 

Relationships between compressional-wave and shear-wave 

velocities in clastic silicate rocks: Geophysics, v. 50, p. 

571−581.

Collett, T.S., 1993, Natural gas hydrates of the Prudhoe Bay 

and Kuparuk River area oil field: American Association of 

Petroleum Geologists Bulletin, v. 77, p. 793−812.

Collett, T.S., Bird, K.J., Kvenvolden, K.A., and Magoon, L.B., 

1988, Geologic interrelation relative to gas hydrates within 

the North Slope of Alaska: U.S. Geological Survey OpenFile Report 88-389, 150 p.

Dutta, N.C., Snyder, F., Dai, J., and Xu, H., 2003, Impact of 

Mallik well on the predictive capability of gas hydrates 

using seismic technology in the Northern Gulf of Mexico: 

Mallik International Symposium in Makuhari, Program and 

Abstracts, p. 10−11, December 8−10, 2003, Chiba City, 

Japan.

Ecker, Christine, Lumlet, D., Dvorkin, J., and Nur, A., 1998, 

Sediments within gas hydrates: Internal structure from seismic AVO: Geophysics, v. 63, p. 1659−1669. 

Hill, R., 1952, The elastic behavior of crystalline aggregate: 

London, Proceedings of the Physical Society, A65, p. 

349−354.

Hilterman, F.J., 1989, Is AVO the seismic signature of lithology?: 59th Annual International Meeting of Society of 

Exploration Geophysicists, Expanded Abstracts, p. 559.

Inks, Tanya, Collett, T.S., Taylor, D., Agena, W., and Lee, M., 

2004, Prospecting for gas hydrate accumulations using 2D 

and 3D seismic data, Milne Point, North Slope : AAPG 

Hedberg Conference on Gas Hydrates: Energy Resource 

Potential and Associated Geologic Hazards, September 

12–16, 2004, Vancouver, BC, Canada

Jin, Y.K., Lee, M.W., and Collett, T.S., 2002, Relationship of 

gas hydrate saturation to porosity and reflection amplitude 

in a research well, Mackenzie Delta, Canada: Marine and 

Petroleum Geology, v. 19, no. 4, p. 407–415.

Jin,Y.K., Lee, M.W., Kim, Y., Nam, S.H., and Kim, K.J., 2003, 

Gas hydrate volume estimations on the South Shetland 

continental margin, Antarctic peninsula: Antarctic Science, 

v. 15, p. 271−282.

Krief, M., Garta, J., Stellingwerff, J., and Ventre, J., 1990, A 

petrophysical interpretation using the velocities of P and S 

waves (Full-waveform sonic): The Log Analyst, v. 31, p. 

355−369.

Kvenvolden, K.A., 1993, Gas hydrate as a potential energy 

source—A review of their methane content, in Howell, 

D.G., ed., The future of energy gases: U.S. Geological Survey Professional Paper 1570, p. 555−561.

Lee, M.W., 1999, Methods of generating synthetic acoustic 

logs from resistivity log for gas-hydrate-bearing sediments: U.S. Geological Survey Bulletin 2170, 11 p., http:

//geology.cr.usgs.gov/pub/bulletins/b2170/, accessed on 

January 13, 2005.

Lee, M.W., 2002, Biot-Gassmann theory for velocities of 

gas-hydrate-bearing sediments: Geophysics, v. 67, p. 

1711−1719.

Lee, M.W., 2003, Elastic properties of overpressured and 

unconsolidated sediments: U.S. Geological Survey Bulletin 

2214, 10 p., http://geology.cr.usgs.gov/pub/bulletins/b2214/, 

accessed on January 13, 2005.

Lee, M.W., 2004, Elastic velocities of partially gas-saturated 

unconsolidated sediments: Marine and Petroleum Geology, 

v. 21, no. 6, p. 641−650.

Lee, M.W., and Collett, T.S., 1999, Gas hydrate amount estimated from compressional- and shear-wave velocities at the 

JAPEX/JNOC/GSC Mallik 2L-38 gas hydrate research well, 

in Dallimore, S.R., and others, eds., Scientific results from 

JAPEX/JNOC/GSC Mallik 2L-38 gas hydrate research well, 

Mackenzie Delta, Northwest Territories, Canada: Geological Survey of Canada, Bulletin 544, p. 313−322.

References 17
18 Well Log Analysis to Assist the Interpretation of 3-D Seismic Data at Milne Point, North Slope of Alaska

Lee, M.W., and Collett, T.S., 2001, Gas hydrate estimation 

error associated with uncertainties of measurement and 

parameters: U.S. Geological Survey Bulletin 2182, 8 p., 

http://geology.cr.usgs.gov/pub/bulletins/b2182/ accessed on 

January 13, 2005.

Lee, M.W., Hutchinson, D.R., Collett, T.S., and Dillon, W.P., 

1996, Seismic velocities for hydrate-bearing sediments 

using weighted equation: Journal of Geophysical Research, 

v. 101, no. B9, p. 20347−20358.

Lindseth, R.O., 1979, Synthetic sonic logs—A process for 

stratigraphic interpretation: Geophysics, v. 44, p. 3−26.

Pickett, G.R., 1963, Acoustic character logs and their applications in formation evaluation: Journal of Petroleum Technology, v. 15, p. 650−667.

Rudman, A.J., Whaley, J.F., Blakely, R.F., and Biggs, M.E., 

1975, Transform of resistivity to pseudovelocity logs: 

American Association of Petroleum Geologists Bulletin, v. 

59, p. 1151−1165.

Sclater, J.G., and Christie, P.A.F., 1980, Continental stretching—An example of the post mid Cretaceous subsidence 

of the central North Sea basin: Journal of Geophysical 

Research, v. 56, p. 51−58.

Smith, G.C., and Gidlow, P.M., 1987, Weighted stacking for 

rock property estimation and detection of gas: Geophysical 

Prospecting, v. 35, p. 993−1014.

Tinivella, Umberta, and Lodoro, E., 2000, The Blake Ridge 

bottom-simulating reflector transect: Tomographic velocity field and theoretical model to estimate methane hydrate 

quantities, in Paull, C.K. and others, eds., Proceedings of 

the Ocean Drilling Program, scientific results, v. 164: College Station, Texas A&M University, p. 273−281.

Western Atlas International Inc., 1995, Introduction to wireline log analysis: Western Atlas International Inc., chapter 

4, 312 p.

Published in the Central Region, Denver, Colorado

Manuscript approved for publication March 3, 2005

Edited by Mary A. Kidd and Richard W. Scott, Jr.

Photocomposition, page layout—Richard W. Scott, Jr.

Graphics by the author