U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2005–5051

Porosity-Depth Trends and Regional Uplift 

Calculated from Sonic Logs, National 

Petroleum Reserve in Alaska
Porosity-Depth Trends and Regional Uplift 

Calculated from Sonic Logs, National 

Petroleum Reserve in Alaska

By Philip H. Nelson and Kenneth J. Bird

Scientific Investigations Report 2005–5051

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

For sale by U.S. Geological Survey Information Services

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Denver, CO 80225

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Produced in the Western Region, Menlo Park, California

Manuscript approved for publication, March 7, 2005

Text edited by George A. Havach

Layout and design by Stephen L. Scott 
Contents

Abstract ------------------------------------------------------------------------------------------------------ 1

Introduction -------------------------------------------------------------------------------------------------- 1

Estimation of Porosity from Sonic Velocity --------------------------------------------------------------- 2

Acoustic-Formation-Factor Equation ---------------------------------------------------------------3

Estimation of Shale Fraction ------------------------------------------------------------------------- 4

Comparison with Other Porosity Transforms ------------------------------------------------------------ 4

Time-Average Equation ------------------------------------------------------------------------------- 4

Sonic Velocity As a Function of Porosity, Effective Stress, and Clay Fraction ----------------- 6

Sonic Velocity As a Function of Porosity and Lithology ------------------------------------------ 7

Erickson-Jarrard Function --------------------------------------------------------------------------- 8

Predictive Accuracy ---------------------------------------------------------------------------------- 8

Shale Porosity Versus Depth ------------------------------------------------------------------------------ 8

Porosity As a Function of Vitrinite Reflectance --------------------------------------------------------- 13

Uplift---------------------------------------------------------------------------------------------------------- 15

Summary and Conclusions -------------------------------------------------------------------------------- 17

References Cited ------------------------------------------------------------------------------------------- 21

Figures

1. Map of the National Petroleum Reserve in Alaska, showing the locations of wells used 

 in this study ----------------------------------------------------------------------------------------------- 2

2. Plot of average porosity calculated from core data versus average sonic velocity 

 calculated from sonic logs within 41 intervals in 16 wells drilled in the National 

 Petroleum Reserve in Alaska --------------------------------------------------------------------------- 3

3. Plot of porosity versus depth, showing trendlines determined by Issler (1992) for five

 areas in the Beaufort-Mackenzie Basin, northwestern Canada ----------------------------------- 6

4. Plot of porosity versus depth in eight wells drilled into Tertiary and Cretaceous shales

 on the U.S. gulf coast, with porosity-depth trendlines determined by Issler (1992) for 

 five areas in the Beaufort-Mackenzie Basin, northwestern Canada, shown for 

 comparison ------------------------------------------------------------------------------------------------ 6

5. Plot of average porosity calculated from core data versus sonic velocity and traveltime 

 calculated from sonic logs in 13 wells drilled in the National Petroleum Reserve in 

 Alaska, with curves for sandstone and shale shown for comparison ----------------------------- 7

6. Plot of average porosity calculated from core data versus sonic velocity and traveltime

 calculated from sonic logs in 13 wells drilled in the National Petroleum Reserve in Alaska, 

 with curves for sandstone and shale and regression fits to laboratory measurements 

 shown for comparison ----------------------------------------------------------------------------------- 7

7. Plot of average porosity calculated from core data versus sonic velocity and traveltime 

 calculated from sonic logs in 13 wells drilled in the National Petroleum Reserve in Alaska, 

 with curves for sandstone and shale and regression fits to laboratory measurements on 

 arenites, wackes, and shales shown for comparison ----------------------------------------------- 8

III
 8. Plot of average porosity calculated from core data versus sonic velocity and travel-

 time calculated from sonic logs in 13 wells drilled in the National Petroleum Reserve 

 in Alaska, with curves for 0.0, 0.5, and 1.0 shale fractions shown for comparison ------------- 9

 9. Plot of average porosity calculated from core data versus porosity calculated from 

 sonic logs over the same intervals in 13 wells drilled in the National Petroleum 

 Reserve in Alaska, referenced to ranges of gamma-ray values, with y-on-x regression 

 line and 1:1 line shown for comparison -------------------------------------------------------------- 9

10. Plot of average porosity calculated from core data versus porosity calculated from 

 sonic logs over same intervals in 13 wells drilled in the National Petroleum Reserve 

 in Alaska, referenced to depth ranges, with y-on-x regression line and 1:1 line shown 

 for comparison ------------------------------------------------------------------------------------------ 9

11. Multiplot of electrical resistivity from deep induction log, of shale fraction calculated 

 from gamma-ray log, and of porosity calculated from sonic log versus depth in the 

 Phoenix well, National Petroleum Reserve in Alaska --------------------------------------------- 10

12. Multiplots of electrical resistivity from deep induction logs, of shale fraction calculated 

 from gamma-ray logs, and of porosity calculated from sonic logs versus depth in eight 

 wells representative of areas A through G in the National Petroleum Reserve in Alaska ---- 11

13. Plot of average porosity in shales versus depth within the Torok Formation in wells 

 drilled in coastal areas and offshore of the National Petroleum Reserve in Alaska, 

 with porosity-depth trendlines determined by Issler (1992) for five areas in the Beaufort-

 Mackenzie Basin, northwestern Canada, shown for comparison ------------------------------- 18

14. Plot of average porosity in shales versus depth within the Torok Formation in wells 

 drilled in the foothills and central and western areas of the National Petroleum Reserve 

 in Alaska, with porosity-depth trendlines determined by Issler (1992) for five areas in 

 the Beaufort-Mackenzie Basin, northwestern Canada, shown for comparison --------------- 19

15. Plot of porosity loss in shales from top to bottom of the Torok Formation versus 

 thickness of the Torok Formation in wells drilled in areas A through G in the National 

 Petroleum Reserve in Alaska ------------------------------------------------------------------------- 19

16. Plot of average porosity in shales versus vitrinite reflectance in wells drilled in 

 coastal areas of the National Petroleum Reserve in Alaska ------------------------------------- 19

17. Plot of average porosity in shales versus vitrinite reflectance in wells drilled in 

 the foothills and central and western parts of the National Petroleum Reserve 

 in Alaska ------------------------------------------------------------------------------------------------ 21

18. Map of the National Petroleum Reserve in Alaska, showing uplift estimated from 

 porosity trends calculated from sonic logs in wells ----------------------------------------------- 22

19. Plot of uplift along the Barrow Arch estimated by three different methods: vitrinite 

 reflectance, porosity trends calculated from sonic logs, and apatite fission-track 

 analysis ------------------------------------------------------------------------------------------------- 23

Tables

1. Locations of wells drilled in the National Petroleum Reserve in Alaska in which 

 porosity has been calculated from sonic logs -------------------------------------------------------- 4

2. Sonic-log and core data from 46 intervals in 17 wells drilled in the National 

 Petroleum Reserve in Alaska --------------------------------------------------------------------------- 5

3. Values of coefficients in the acoustic-formation-factor equation ---------------------------------- 6

4. Porosities and estimated uplift in the Torok and Lower Torok Formations ----------------------- 20

IV
Abstract

Porosity decreases with depth in sedimentary basins, 

owing to the combined effects of compaction and cementation. The porosity profile in any individual well depends on 

the maximum effective stress, which is generally determined 

by the maximum burial depth. As a result, present-day porosity profiles can be interpreted in terms of maximum burial 

depth and subsequent uplift. Using sonic logs and porosity 

measurements in cored wells, we adapt a method of calculating porosity in siliciclastic rocks from sonic logs and compare 

it with several other algorithms relating sonic velocity and 

porosity. We then calculate porosity from sonic logs in wells 

within and adjacent to the National Petroleum Reserve in 

Alaska (NPRA).

Evaluating the shale-rich Early Cretaceous Torok Formation, we observe that the porosity-depth relation can be 

represented by one or two straight lines in each well. The 

porosity-depth lines are offset among wells in different areas 

within the northern NPRA, reflecting differences in uplift 

along the Barrow Arch. When the line segments are replotted in terms of porosity against vitrinite reflectance instead 

of present-day depth, the trends from areas within the coastal 

plain nearly coalesce, showing that the effect of maximum 

burial depth explains much, but not all, of the differences in 

the porosity profiles. Relative to a single offshore well where 

zero uplift is assumed to have occurred, estimates of uplift 

along the Barrow Arch range from less than 1,000 ft just east 

of the NPRA to 4,600 ft at Point Barrow. In the foothills of the 

southern NPRA, the computational method can provide only 

minimum estimates of uplift, which are less than, but compatible with, estimates of uplift based on the apatite fission-track 

method.

The porosity gradients in wells in the northern NPRA 

(coastal plain and near offshore) are similar to those in wells 

in other areas calculated by other workers: about 3 percent 

per 1,000 ft. In the southern NPRA (foothills), porosity gradients are lower than in the northern NPRA — that is, porosity 

decreases less rapidly with depth in the foothills (approx 1 

percent per 1,000 ft) than in the coastal plain (max 12 percent 

per 1,000 ft). An explanation of the wide variation in porosity 

gradients in the NPRA awaits a better understanding of the 

evolution of pore pressure and effective stress within the context of the burial and uplift history of the Colville Basin.

Introduction

The goals of this study are to estimate present-day 

porosity as a constraint on basin-modeling efforts and to 

constrain estimates of regional uplift and erosion on the 

basis of the variation in porosity gradients.

In this study, we include data from all wells within 

the National Petroleum Reserve in Alaska (NPRA) that 

have sonic logs, a few wells close to the east boundary 

of the NPRA, and four offshore wells, for a total of 40 

wells (fig. 1; table 1). Most wells within the NPRA were 

drilled during the years 1975–81 by the U.S. Government. 

Well density is adequate along the north coastline and the 

southeastern NPRA but poor elsewhere, owing to the small 

number of wells and the absence of sonic logs in the early 

(1944–53) NPRA drilling program.

Core porosity measurements were available from 17 

wells distributed over the NPRA and in one offshore well. 

The depth ranges and formation names are listed in table 

2, along with gamma-ray values and sonic traveltimes 

from well logs, averaged over the same depth ranges as 

the core data. Formations range in age from Mississippian 

to Cretaceous. Porosity measurements were included from 

clastic intervals but not from carbonates. Core porosities in 

unconfined samples from the Nanushuk Formation, Torok 

Formation, and Kemik Sandstone, all of Cretaceous age, 

were adjusted by multiplying the measured value by 0.86, 

a reduction factor that we obtained from core tests on confined, stressed samples. Porosities in formations deeper 

than the Kemik Sandstone were not adjusted.

Sonic velocity is plotted against core porosity in figure 

2, keyed to formation. Younger (Brookian) sedimentary 

rocks plot below older (Ellesmerian) sedimentary rocks, 

and samples from the Kingak Shale fall between the two. 

The method of converting sonic well-log data to porosity 

is based on an analysis of the data plotted in figure 2 and 

listed in table 2.

The algorithm used by Issler (1992) for shales is 

extended herein to all siliciclastic rocks. Because several 

methods of converting sonic logs to porosity are available, 

we compare the algorithm used in this paper with others 

reported in the literature. After establishing a method of 

calculating porosity and comparing it with other methods, we 

next examine the porosity-depth trends in shales of the Torok 

Porosity-Depth Trends and Regional Uplift 

Calculated from Sonic Logs, National 

Petroleum Reserve in Alaska

By Philip H. Nelson and Kenneth J. Bird


Formation, a thick and areally extensive marine mudstone of 

Early Cretaceous age, with the purpose of estimating uplift 

and erosion within and adjacent to the NPRA.

Issler (1992) calculated porosity in shales from sonic logs 

and used the resulting porosity-depth trends to infer uplift and 

overpressure in the Beaufort-Mackenzie Basin of northwestern Canada, an area comparable in size to the NPRA. The 

plot of porosity versus depth in figure 3 summarizes the average porosity-depth trends for rocks of Late Cretaceous and 

Tertiary age in five areas of the Beaufort-Mackenzie Basin. 

Porosities in the inner delta (area 3), an area interpreted to 

have little or no uplift since the time of maximum burial, 

fall along the trend shown by the red curve. Porosities in the 

central and outer shelves (areas 1, 2) are higher at a given 

depth than in the inner delta, a fact attributed to overpressuring caused by rapid deposition. Porosities in the main, 

western, and southern deltas (areas 4, 5) are lower at a given 

depth than in the inner delta. The upward and leftward shift 

of the porosity-depth curves is attributed to uplift and erosion 

(arrow, fig. 3).

Other workers have used straight-line segments to represent porosity-depth trends in shales. Hunt and others (1998) 

presented porosity profiles in shales based on the uptake of an 

organic liquid by dried, evacuated shale cuttings. They demonstrated that, for porosities less than 35 percent, two straight-line 

segments provide a better fit to the data from Tertiary sections 

in the U.S. gulf coast than does a single exponential curve. The 

upper linear trends persist until the porosity decreases to about 

10 percent; below this depth, shale porosity tends to remain 

constant (fig. 4). In two wells, Hunt and others calculated 

porosity gradients of 3.3 percent per 1,000 ft, close to those 

determined by Issler (1992). Porosity gradients in other wells 

plotted in figure 4 are as low as 1.04 percent per 1,000 ft.

Estimation of Porosity from 

Sonic Velocity

Sonic logs are generally presented in terms of “traveltime” (∆t), which is a reciprocal velocity expressed in units of 

microseconds per foot. Other terms for traveltime are slowness 

and transit time. Traveltime is readily convertible to velocity; 

the sonic velocity v is given by 106/∆t ft/s (304.8/∆t km/s).

Figure 1. National Petroleum Reserve in Alaska (NPRA), showing locations of wells in areas A through G used in this study.

Barrow Arch 

N P R A 

A 

B

C

D

E

F 

G

Tungak Creek 

Tunalik 

Peard

Kugrua

South Meade 

Brontosaurus

Walakpa 1 

Walakpa 2 

South Barrow 18 

Tulageak 

West Dease 

Kuyanak

East Simpson 2 

East Simpson 1 

Drew Point 

J. W. Dalton 

Antares

W. T. Foran 

Cape Halkett 

East Teshekpuk Atigaru Point 

North Kalikpik South Harrison Bay 

West Fish Creek 

Colville River 1 

North Inigok 

Inigok

Seabee

Big Bend 

Tulugak 

East Kurupa West Kurupa 

Koluktak

Awuna 

Ikpikpuk

Lisburne

Mukluk

Phoenix

Cabot

South Simpson 

Tulaga 

Well locations 

Well analyzed in this study 

69°

70°

162° 160° 158° 156° 154° 152°

71°

 Porosity-Depth Trends and Regional Uplift Calculated from Sonic Logs, National Petroleum Reserve in Alaska
Sonic logs are commonly used to estimate porosity, which 

is one of the rock parameters controlling sonic velocity. Many 

empirical expressions, sometimes called transforms, have been 

derived to relate sonic velocity and porosity in siliciclastic 

rocks. These empirical expressions satisfy available datasets 

but are not necessarily based on a physical model. In this 

report, we use a transform called the acoustic formation factor 

(AFF) to estimate porosity from sonic logs, and we compare 

this transform with some of the other transforms documented 

in the literature.

Acoustic-Formation-Factor Equation

A relation between traveltime and rock solidity, called the 

AFF equation, was proposed by Raiga-Clemenceau and others 

(1988):

 (1)

where φ is the fractional porosity (the term 1−φ represents the 

solid fraction of the rock), x is an exponent to be determined 

from the data, and ∆tm and vm are the matrix (zero porosity) 

traveltime and sonic velocity, respectively. The corresponding 

expression for porosity is

 

As pointed out by Raiga-Clemenceau and others, equation 1 is 

functionally similar to the relation between electrical resistivity and porosity: it is simple in form, and it relates the velocity 

of a sonic wave to the solid fraction of the medium, rather than 

to the pore space. Raiga-Clemenceau and others tested equation 1 and listed the values of coefficients for porous reservoir 

rocks.

Equation 1 was applied by Issler (1992) in a study of 

compaction in siliciclastic rocks, predominantly shales, in the 

Mackenzie Delta of northern Canada, an area directly east of, 

and comparable in size to, the NPRA. Issler obtained laboratory measurements of porosity in shales and determined a 

value of 2.19 for the exponent x. Issler’s form of equation 1 

was subsequently used by Harrold and others (1999) in a study 

of pore pressure in mudrocks of Southeast Asia. In this report, 

we use a value of 2.19 for x.

Porosity from Core (% )

0 10 20 30 40

Sonic Velocity (km/s) 

2

3

4

5

6

N

N N

N

T 

T 

T 

T 

T 

T 

T 

T 

T 

P 

P 

K

K

K

K

K

K K

K

K

K

R

R R

R

R

R

R

S

S

S

V

V

V V

V

V

V

V V

V

V

V

V

E

E

Brookian sequence 

Nanushuk

Torok 

Pebble shal e

Kemik

Beaufortian sequence Kingak

Ellesmerian sequence 

Sag River 

Shublik

Ivishak

Echooka

Kekiktuk

52

60

70

80

90

100

110 

120

130

140

Travel time (

Ms/foot)

EXPLANATION

Figure 2. Average porosity calculated from core data versus average sonic velocity calculated 

from sonic logs within 41 intervals in 16 wells drilled in the National Petroleum Reserve in Alaska 

(see fig. 1 for locations).



∆tm

∆t = vvm

= ( ) 1− φ x

,

 Estimation of Porosity from Sonic Velocity

φ =1 ∆tm

∆t

 

     

1

x

.
The matrix traveltime, ∆tm, can be either constant or a 

variable. Issler (1992) considered only the intervals of highest 

shale content, using a fixed value of ∆tm=∆tsh=67 μs/ft. In this 

report, ∆tm varies with the shale fraction:

 (2)

where ∆tss and ∆tsh are the traveltimes in zero-porosity sandstone and shale, respectively; and Vsh, the shale fraction, is 

derived from the gamma-ray log, as described in the next subsection. The average porosity calculated from core data is plotted against the average sonic velocity estimated from NPRA 

well logs in figure 5. The values of ∆tss=52 μs/ft and ∆tsh=70 

μs/ft were determined so that the curves for sandstone and 

shale bound the core data.

The usage of a ∆tm value that varies with shale fraction 

(eq. 2) allows the calculation of porosity in all rock types 

within the siliciclastic sequence. Lithology strongly influences porosity. For example, a traveltime of 76 μs/ft (righthand scale, fig. 5), which is equivalent to a sonic velocity of 4 

km/s (left-hand scale), transforms to a porosity of 4 percent in 

a shale end member and to a porosity of 16 percent in a sandstone end member. As the shale fraction ranges from 0 to 1, 

equation 1 sweeps the area bounded by the curves for “sandstone” (AFF sandstone) and “shale” (AFF shale).

As just described, the values of the coefficients in equation 2 were adjusted to fit the core data, whereas the value 

of the exponent x is from Issler (1992). The values of x and 

∆tm used in this report are compared with those from other 

sources in table 3.

Estimation of Shale Fraction

The shale fraction, Vsh , in siliciclastic rocks is estimated 

from the gamma-ray log, using the relation

 

 (3) 

where GR is the logged gamma-ray value, and GRsd and GRsh

are the gamma-ray values in sandstone and shale, respectively. Before applying this transform, the gamma-ray logs 

were inspected and corrected if offsets occurred between 

logging runs. Values of GRsh (generally, 80–120 American 

Petroleum Institute [API] units) and GRsd (25–35) were then 

determined for each well from inspection of the well logs. 

The Vsh value ranges from 0.0 to 1.0. If a calculated Vsh value 

exceeded 1.0 owing to the gamma-ray value exceeding the 

GRsh value, then the Vsh value was set to 1.0. The Vsh parameter 

incorporates both clay and nonclay minerals.

Comparison with Other 

Porosity Transforms

Time-Average Equation

One of the first transforms relating velocity and porosity in siliciclastic rocks was proposed by Wylie and others 

(1956):

 (4)

which states that the traveltime is the linear sum of the 

traveltimes in the solid and porous (fluid filled) fractions. This 

Well No. and name Latitude

N.

Longitude

W.

1 Antares 1 - - - - - - - - - - - - - - - - - - - - - - 71.03598o 152.72372o

2 Atigaru Point - - - - - - - - - - - - - - - - - 70.55612o 151.71707o

3 Awuna - - - - - - - - - - - - - - - - - - - - - - - - - - 69.15320o 158.02244o

4 Big Bend - - - - - - - - - - - - - - - - - - - - - - - 69.16196o 152.26711o

5 Brontosaurus - - - - - - - - - - - - - - - - - - 70.90902o 157.24560o

6 Cabot - - - - - - - - - - - - - - - - - - - - - - - - - - - 71.32526o 155.21576o

7 Cape Halkett - - - - - - - - - - - - - - - - - - 70.76740o 152.46673o

8 Colville River 1 - - - - - - - - - - - - - - 70.31165o 150.65390o

9 Drew Point - - - - - - - - - - - - - - - - - - - - 70.87976o 153.89997o

10 East Kurupa - - - - - - - - - - - - - - - - - - - 68.84651o 153.31789o

11 East Simpson 1 - - - - - - - - - - - - - - - 70.91778o 154.61799o

12 East Simpson 2 - - - - - - - - - - - - - - - 70.97861o 154.67387o

13 East Teshekpuk - - - - - - - - - - - - - - 70.56992o 152.94362o

14 Ikpikpuk - - - - - - - - - - - - - - - - - - - - - - - 70.45547o 154.33133o

15 Inigok - - - - - - - - - - - - - - - - - - - - - - - - - - - 70.00486o 153.09913o

16 J.W. Dalton - - - - - - - - - - - - - - - - - - - 70.92050o 153.13753o

17 Koluktak - - - - - - - - - - - - - - - - - - - - - - - 69.75250o 154.11110o

18 Kugrua - - - - - - - - - - - - - - - - - - - - - - - - - 70.58702o 158.66203o

19 Kuyanak - - - - - - - - - - - - - - - - - - - - - - - 70.93152o 156.03781o

20 Mukluk - - - - - - - - - - - - - - - - - - - - - - - - - 70.68334o 150.91997o

21 North Inigok - - - - - - - - - - - - - - - - - - 70.25759o 152.76598o

22 North Kalikpik - - - - - - - - - - - - - - - 70.50918o 152.36787o

23 Peard - - - - - - - - - - - - - - - - - - - - - - - - - - - - 70.71565o 159.00071o

24 Phoenix - - - - - - - - - - - - - - - - - - - - - - - - 70.71722o 150.42781o

25 Seabee - - - - - - - - - - - - - - - - - - - - - - - - - - 69.38015o 152.17534o

26 South Barrow 18 - - - - - - - - - - - - 71.23972o 156.31142o

27 South Harrison Bay - - - - - - - - - 70.42297o 151.72795o

28 South Meade - - - - - - - - - - - - - - - - - - 70.61498o 156.88260o

29 South Simpson - - - - - - - - - - - - - - - 70.81242o 155.00005o

30 Tulaga - - - - - - - - - - - - - - - - - - - - - - - - - - 69.70390o 151.07579o

31 Tulageak - - - - - - - - - - - - - - - - - - - - - - - 71.18934o 155.73357o

32 Tulugak - - - - - - - - - - - - - - - - - - - - - - - - 68.98481o 151.32976o

33 Tunalik - - - - - - - - - - - - - - - - - - - - - - - - - 70.20596o 161.06915o

34 Tungak Creek - - - - - - - - - - - - - - - - 69.88390o 162.27319o

35 W.T. Foran - - - - - - - - - - - - - - - - - - - - 70.82685o 152.28586o

36 Walakpa - - - - - - - - - - - - - - - - - - - - - - - - 71.09934o 156.88434o

37 Walakpa - - - - - - - - - - - - - - - - - - - - - - - - 71.05000o 156.95277o

38 West Dease - - - - - - - - - - - - - - - - - - - 71.15907o 155.62918o

39 West Fish Creek - - - - - - - - - - - - - 70.32200o 152.06548o

40 West Kurupa - - - - - - - - - - - - - - - - - - 68.88295o 155.25497o

Table 1. Locations of wells drilled in the National Petroleum 

Reserve in Alaska in which porosity has been calculated from 

sonic logs.

[Data from Alaska Division of Oil and Gas, URL http://www.dog.dnr.state.ak.us/products/

data/Excel_files/www_well_lat_lon.xls]

 Porosity-Depth Trends and Regional Uplift Calculated from Sonic Logs, National Petroleum Reserve in Alaska

∆tm = 1 − Vsh ( ) ∆tss + Vsh ∆ tsh ,

Vsh = GR − GRsd

GRsh − GRsh

,

∆t = ( ) 1 − φ ∆t m + φ∆t f ,
Table 2. Sonic-log and core data from 46 intervals in 17 wells drilled in the National Petroleum Reserve in Alaska.

[Sonic traveltimes and gamma-ray values are averaged over cored intervals ; porosities are averaged from laboratory measurements. Sonic velocity is traveltime converted to units of 

kilometers per second. Difference is between porosity calculated from sonic velocity and porosity measured in core samples]

often-quoted relation is plotted in figure 5, where a value of 

∆tf =189 μs/ft is used for the fluid and ∆tm=(1−Vsh ) ∆tss+Vsh∆tsh, 

as discussed in the previous subsection. At porosities less than 

5 percent, the time-average equation is similar to the AFF 

equation, but they differ markedly for porosities greater than 

15 percent.

Both the AFF and time-average equations are curvilinear on a plot of sonic velocity versus porosity (fig. 5). The 

slopes and intercepts depend on a parameter that is lithology 

dependent, namely, ∆tm. Neither the AFF nor the time-average equation, however, depends explicitly on stress. The AFF 

sandstone and AFF shale curves in figure 5 span most of the 

 Estimation of Porosity from Sonic Velocity 
core data, whereas several data points fall below the shale 

curve of Wylie and others (1956).

Sonic Velocity as a Function of Porosity, 

Effective Stress, and Clay Fraction

Using laboratory studies, numerous workers have determined linear relations between sonic velocity and porosity. 

Eberhart-Phillips and others (1989) analyzed velocity data 

on 64 water-saturated sandstones that were measured over 

a range of effective stress. The resulting relation shows that 

increases in both porosity (φ) and clay fraction (C) both lead 

to a decrease in compressional velocity, vp (in kilometers per 

second):

 (5)

Beaufort-Mackenzie Basin 

Porosity (percent) 

0 10 20 30 40

Depth (feet) 

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

138∞ 134∞ 130∞ 

71∞ 

70∞ 

69∞ 

68∞ 138∞ 134∞ 130∞ 68∞ 

69∞ 

70∞ 

71∞ 

0 km 120

5

1

2

3

4

5, western and southern delta 

4, main delta 

3, inner shelf - inner delta 

2, central shelf 

1, outer shelf 

Top of 

overpressured

interval

Uplift and 

erosion

Figure 3. Porosity versus depth, showing trendlines determined by 

Issler (1992) for five areas (1–5) in the Beaufort-Mackenzie Basin, 

northwestern Canada.

U.S. Gulf Coast 

Porosity (percent) 

Depth (feet) 

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

5

4

3

2

1

0 10 20 30

Figure 4. Porosity versus depth in eight wells (solid curves) drilled 

into Tertiary and Cretaceous shales on the U.S. gulf coast (from Hunt 

and others, 1998), with porosity-depth trendlines determined by Issler 

(1992) for five areas in the Beaufort-Mackenzie Basin, northwestern 

Canada (numbered dashed curves; see fig. 3), shown for comparison. 

Break in each curve represents point at which porosity ceases to 

decrease with depth.

vp = 5.77−6.94φ−1.73 C +0.446[Pe − exp(−16.7Pe )].

Rock or matrix type Reference 

Matrix

traveltime 

( s/ft) 

Exponent

Silica - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Raiga-Clemenceau and others (1988) - - - - - - - - - 55.5 1.60 

Calcite - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Raiga-Clemenceau and others (1988) - - - - - - - - - 47.6 1.76 

Dolomite - - - - - - - - - - - - - - - - - - - - - - - - - - - - Raiga-Clemenceau and others (1988) - - - - - - - - - 43.5 2.00 

Mudstone, regression fit - - - - - - - Issler (1992) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 67.1 2.19 

Mudstone, alternative fit - - - - - - - Issler (1992) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 63.4 2.34 

Mudstone and sandstone - - - - - - - This report - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 52–70 2.19 

Table 3. Values of coefficients in the acoustic-formation-factor equation.

 Porosity-Depth Trends and Regional Uplift Calculated from Sonic Logs, National Petroleum Reserve in Alaska
The effective stress, Pe (in kilobars), is the difference 

between the confining and hydrostatic stresses. The first 

term in equation 5, 5.77 km/s, which is equivalent to a traveltime of 52.8 μs/ft, represents the compressional velocity 

at zero porosity, zero clay fraction, and an effective stress of 

12.5 MPa. At an effective stress of 0.125 kbars (equivalent 

to 12.5 MPa or 1,813 lb/in2—if pore pressure is hydrostatic, 

this effective stress would be reached at a depth of about 

3,250 ft, or slightly less than 1 km), the fourth term is zero, 

and the remaining expression, dependent only on φ and 

C, takes on the values displayed in figure 6. At effective 

stresses greater than 12.5 MPa, the family of black lines 

shifts to the right, so that at a given value of sonic velocity and clay fraction, the porosity is increased by 2, 3, and 

4 percent at depths of about 5,000, 8,000, and 12,000 ft, 

respectively.

As a rule of thumb, clay constitutes 60 weight percent 

of an average shale (Hearst and others, 2000, p. 366). Thus, 

the 0.6-clay-fraction line in figure 6 should be comparable 

to the “AFF shale” curve, and the 0.0-clay-fraction line and 

“AFF sandstone” curve both represent sandstones. At any 

given sonic velocity and clay (or shale) fraction, equation 5 

yields higher estimates of porosity than does the AFF equation.

Sonic Velocity as a Function of Porosity 

and Lithology

Vernik and Nur (1992) and Vernik (1997) divided 

siliciclastic rocks into four classes on the basis of clay content and observed that the velocity-porosity relation is well 

described by linear functions (fig. 7). Their dataset incorporated the same samples used by Eberhart-Phillips and 

others (1989), as well as other samples. To eliminate the 

dependence on stress, they restricted their dataset to samples 

subjected to an effective stress of 40 MPa. The four classes 

of siliciclastic rocks and their clay contents are: clean arenites (<2–3 weight percent), arenites (3–15 weight percent), 

wackes (15–35 weight percent), and shales (>35 weight percent).

Core data from NPRA wells lie well below the 0.0-

clay-fraction line in figure 6 and the “clean arenites” line 

in figure 7, indicating that the sample sets of Eberhart-Phillips and others (1989), Vernik and Nur (1992), and Vernik 

(1997) included higher-velocity samples than the NPRA 

samples. Thus, the field defined by the AFF equation used 

in this report (AFF sandstone and AFF shale curves, figs. 6, 

7) is more restricted than the fields defined by those workers. There are two possible reasons for the absence of highGamma-ray value 

Porosity (percent) 

0 10 20 30 40

Sonic Velocity (km/s) 

2

3

4

5

6

20 - 37 

38 - 51 

52 - 67 

68 - 103 

AFF shale 

AFF sandstone 

W shale 

W sandstone 

140

130

120

110 

100

90

80

70

60

52

Travel time (μs/foot) 

EXPLANATION

Figure 5. Average porosity calculated from core data versus sonic 

velocity and traveltime calculated from sonic logs in 13 wells drilled in 

the National Petroleum Reserve in Alaska (see fig. 1 for locations and 

table 2 for well data). Data points show ranges of gamma-ray values 

over same depth interval. AFF sandstone and AFF shale, curves for 

sandstone (shale fraction, 0.0) and shale (shale fraction, 1.0), as calculated with acoustic-formation-factor (AFF) equation; W sandstone 

and W shale, curves calculated with time-average equation of Wylie 

and others (1956).

Gamma-ray value 

Porosity (percent) 

0 10 20 30 40

Sonic Velocity (km/s) 

2

3

4

5

6

20 - 37 

38 - 51 

52 - 67 

68 - 103 

0.0

0.1

0.2

0.3

0.4

0.5

Clay fraction 

0.6

140

52

60

70

80

90

100

110 

120

130

Travel time (μs/foot) 

AFF shale 

AFF sandstone 

EXPLANATION

Figure 6. Average porosity calculated from core data versus sonic 

velocity and traveltime calculated from sonic logs in 13 wells drilled in 

the National Petroleum Reserve in Alaska (see fig. 1 for locations and 

table 2 for well data). Data points show ranges of gamma-ray values 

over same depth interval. AFF sandstone and AFF shale, curves for 

sandstone (shale fraction, 0.0) and shale (shale fraction, 1.0), as 

calculated with acoustic-formation-factor (AFF) equation; numbered 

straight lines, regression fit to laboratory measurements by EberhartPhillips and others (1989) at 12.5-MPa effective stress and various 

clay fractions (0.0–0.6).

 Estimation of Porosity from Sonic Velocity 
velocity samples in the NPRA wells: (1) many of the cored 

intervals are at present-day depths less than 4,000 ft (table 2) 

and thus are at effective stresses considerably less than 40 MPa, 

which is approximately equivalent to a burial depth of 10,500 ft; 

and (2) none of the cored intervals are dominated by low-clay 

arenites, as indicated by the average gamma-ray values listed in 

table 2. Figures 6 and 7 serve as reminders that the AFF equation, as defined in this report, is strongly conditioned by the 

availability of core data from NPRA wells.

Erickson-Jarrard Function

Using 23 experimental datasets and a set of empirical 

constraints, Erickson and Jarrard (1998) developed a transform that allows the calculation of sonic compressional velocity as a function of porosity and shale fraction (fig. 8). The 

functional form of their algorithm is rather ornate, and so the 

shale-dependent curves merge at a “critical point” porosity of 

31 percent. The curves corresponding to the Erickson-Jarrard 

relation are similar to those of the AFF equation adopted for 

use in this report. The two shale-fraction lines (lowermost pair 

of lines, fig. 8) are virtually identical. The 0.5-shale-fraction 

lines are similar over the porosity range 0–15 percent, divergFigure 7. Average porosity calculated from core data versus sonic 

velocity calculated from sonic logs in 13 wells drilled in the National 

Petroleum Reserve in Alaska (see fig. 1 for locations and table 2 for 

well data). Data points show ranges of gamma-ray values over same 

depth interval. AFF sandstone and AFF shale, curves for sandstone 

(shale fraction, 0.0) and shale (shale fraction, 1.0), as calculated with 

acoustic-formation-factor (AFF) equation; dashed curves, regression fit to laboratory measurements on clean arenites, arenites, and 

wackes (Vernik and Nur, 1992) and on shales (Vernik, 1997) at 40-MPa 

effective stress.

Porosity (percent) 

0 10 20 30 40

Sonic Velocity (km/s) 

2

3

4

5

6

20 - 37 

38 - 51 

52 - 67 

68 - 103 

Gamma-ray value 

Arenites

Wackes 

Shales

52

60

70

80

90

100

110 

120

130

140

Travel time (μs/foot) 

AFF sandstone 

AFF shale 

Clean arenites 

EXPLANATION

ing at higher porosities. At zero shale fraction (uppermost pair 

of lines), the slopes of the two lines differ, and so differences of 

−2 and +2 percent exist at 5.25 and 4.0 km/s, respectively.

Although sonic velocity can be calculated as a function 

of porosity and shale fraction from the Erickson-Jarrard relation, the complex form of their algorithm makes it difficult to 

calculate porosity from sonic velocity and shale fraction. The 

AFF equation, however, is easier to use. Though reassuring, the 

good match between the AFF equation and the Erickson-Jarrard relation, which is based on a collection of datasets, may be 

only coincidental.

Predictive Accuracy

The porosity calculated from the sonic log is compared 

with the average porosity measured from core samples in figures 9 (symbols corresponding to gamma-ray response) and 

10 (symbols corresponding to depth of cored interval). The 

difference between the regression line and the one-to-one line 

indicates that, on a statistical basis, the AFF equation slightly 

underpredicts the high porosities and slightly overpredicts the 

low porosities. More significant are the vertical departures of 

individual points from the one-to-one line, which are equivalent 

to the differences listed in the right-hand column of table 2. Of 

the 46 data points, 12 values calculated from the sonic log differ 

from the core values by more than ±3 percent and 5 values 

differ by more than ±4 percent. Referring to figure 10, depth 

dependence of porosity appears to be significant only for the 

shallowest (1,900–3,000-ft depth) samples: six of seven samples 

in the shallowest depth category lie above the one-to-one line, 

indicating that the AFF equation is likely to overpredict the true 

porosity at depths less than 3,000 ft.

Shale Porosity Versus Depth

The Torok Formation was selected for analysis of shale 

porosity versus depth because it is a thick, areally widespread, 

and relatively homogeneous lithologic unit. It represents a 

significant proportion of the Colville foreland-basin fill and is 

mid-Cretaceous (Aptian through Cenomanian) in age (Mull and 

others, 2003). As summarized by Molenaar (1988), it occurs 

throughout the NPRA, where it ranges in thickness from somewhat less than 900 m in the north to more than 6,000 m in the 

south. Uplift and erosion are indicated by surface exposures in 

the foothills of the Brooks Range and the occurrence of Torok 

rocks just beneath surficial Pliocene and (or) Pleistocene deposits on the Barrow peninsula (area C, fig. 1).

The Torok Formation is characterized by clinoform 

seismic geometry. Where completely preserved, the seismic 

reflectors indicate that approximately the upper tenth of the 

Torok represents shelf environments, the middle 40–60 percent slope environments, and the lowermost 30–50 percent 

basinal environments. Turbidite sandstones are most common 

in the lowermost part of slope and in the basinal settings. The 

 Porosity-Depth Trends and Regional Uplift Calculated from Sonic Logs, National Petroleum Reserve in Alaska
Torok Formation is the lateral equivalent of the fluvial-deltaic 

Nanushuk Formation and, in its lowermost and southernmost 

parts, probably equivalent to the Fortress Mountain Formation. 

Wells located south of lat 70° N., except for the Tulaga (area G, 

fig. 1), were drilled on anticlines in which the Torok is structurally thickened by some combination of thrust faulting and 

shale flowage. The anticlines were formed in early Tertiary time 

(60–45 Ma), according to apatite fission-track analysis (Potter 

and Moore, 2003).

A modest sampling (18 samples from 11 wells; BartschWinkler and Huffman, 1988) indicates that Torok sandstones are 

composed, on average, of 54 volume percent quartz, 18 volume 

percent feldspar, and 28 volume percent lithic grains. Lithic 

grains are represented, on average, by 24 volume percent volcanic-rock, 17 volume percent metamorphic-rock, and 59 percent 

sedimentary-rock grains. In addition, Torok sandstones were 

determined to contain from 10 to more than 30 percent clayrich matrix, believed to be composed of mudstone and siltstone 

grains that have been molded between more resistant grains, so 

that they have lost their original shape identifying them as detrital grains.

Porosity was calculated from sonic logs in 40 wells penetrating most or all of the Torok Formation within and immediately adjacent to the NPRA (fig. 1; table 1). First, the shale 

fraction was calculated from the gamma-ray log (shale-fraction 

Gamma-ray value 

Porosity (percent) 

0 10 20 30 40

Sonic Velocity (km/s) 

2

3

4

5

6

20 - 37 

38 - 51 

52 - 67 

68 - 103 

1.0

0.5

0.0 140

130

120

110 

100

90

80

70

60

52

Travel time (μs/foot) 

EXPLANATION

Figure 8. Average porosity calculated from core data versus sonic 

velocity and traveltime calculated from sonic logs in 13 wells drilled in 

the National Petroleum Reserve in Alaska (see fig. 1 for locations and 

table 2 for well data), with curves for shale fractions of 0.0, 0.5, and 

1.0 calculated with acoustic-formation-factor (AFF) equation (solid 

curves) and with normal consolidation model of Erickson and Jarrard 

(1998) (dashed curves) shown for comparison. Data points show 

ranges of gamma-ray values over same depth interval.

Porosity calculated from core data (percent) 

0 20 30 40

Porosity calculated from sonic log (percent) 

0

10

20

30

20 - 37 

38 - 51 

52 - 67 

68 - 103 

Gamma-ray value 

EXPLANATION

Figure 9. Average porosity calculated from core data versus porosity 

calculated from sonic logs over same intervals in 13 wells drilled in 

the National Petroleum Reserve in Alaska (see fig. 1 for locations and 

table 2 for well data), referenced to ranges of gamma-ray values, with 

y-on-x regression line (solid curve) and 1:1 line (dashed curve) shown 

for comparison. Symbols indicate ranges of gamma-ray values.

Figure 10. Average porosity calculated from core data versus porosity calculated from sonic logs over same intervals in 13 wells drilled 

in the National Petroleum Reserve in Alaska (see fig. 1 for locations 

and table 2 for well data), referenced to depth ranges, showing y-on-x

regression line (solid curve) and 1:1 line (dashed curve).

Porosity calculated from core data (percent) 

0 20 30 40

Porosity calculated from sonic log (percent) 

0

10

20

30

1,900 - 3,000 

3,000 - 4,000 

5,000 - 7,000 

7,000 - 8,000 

8,000 - 11,000 

Depth range (ft) 

EXPLANATION

 Shale Porosity Versus Depth
The bulk of the Torok Formation is composed of finegrained sandstone, siltstone, and mudstone. Few sandstone 

intervals are thick enough to be discernible on the gamma-ray 

log, and those that are recognizable have gamma-ray values not 

much lower than those of the siltstones and mudstones. Torok 

sandstones are reported to contain low-grade metasedimentaryrock fragments (David Houseknecht, oral commun., 2004) and 

are known to have high feldspar and lithic-grain contents, which 

cause elevated gamma-ray values that would result in a low 

calculated porosity (eqs. 1, 2). In addition, Torok sandstones in 

outcrop are observed to be well cemented (Chris Schenk, oral 

commun., 2002). From these observations, the low porosities 

calculated in sandier units of the Torok Formation could be 

due to a combination of elevated gamma-ray values and a high 

degree of cementation.

Figure 11. Electrical resistivity from deep induction log, shale fraction calculated from gamma-ray log, and porosity calculated from sonic log 

versus depth in the Phoenix well in area E, National Petroleum Reserve in Alaska (see fig. 1 for location and table 2 for well data). Solid irregular 

curve labeled “sandstone” tracks porosity in sandiest intervals, and dashed irregular curve labeled “shale” tracks porosity in shaliest intervals. 

Relation between porosity in sandstone and shale reverses at about 500 ft above top of the Torok Formation. Brookian units above the Torok 

Formation: MT, Mikkelsen Tongue of the Canning Formation; PC/SB, Prince Creek/Shrader Bluff Formation, undifferentiated; Sag, Sagavanirktok 

Formation; Sb, Seabee Formation; ST, Staines Tongue of the Sagavanirktok Formation; Tu, Tuluvak Formation.

curves, figs. 11, 12). Then the porosity was calculated from the 

sonic log, using equations 1 and 2. Both filtered (smoothed) 

and unfiltered forms are shown in figure 12. Porosity decreases 

with depth throughout the Brookian sequence (1,000–7,400-ft 

depth, fig. 11). From 1,000- to 5,500-ft depth, the porosity in 

sandier (low shale fraction) intervals is greater than in shalier 

(high shale fraction) intervals, as also determined by Rowan 

and others (2002, 2003) in wells offshore the North Slope of 

Alaska. Commencing some 500 ft above the top of the Torok 

Formation, however, the relation reverses, and the porosity in 

sandier units is less than in shalier units. This reversed relation is observed in the Torok Formation in all the wells that we 

have studied, as shown by the examples in figure 12. (The trend 

in the overpressured Tunalik well in fig. 12A does not show a 

reversed relation.)

Phoenix 

DEPTH (feet) 

1,000 

1,500 

2,000 

2,500 

3,000 

3,500 

4,000 

4,500 

5,000 

5,500 

6,000 

6,500 

7,000 

Resistivity

0.2 20 

(ohm-m)

 Shale (fraction) 0 1.0 

0 

Porosity (fraction)

0.25 0.5 

Shale 

Sandstone 

Sag 

MT

ST

Tu

PC/SB 

Sb 

Torok 

Formation 

Unit 

10 Porosity-Depth Trends and Regional Uplift Calculated from Sonic Logs, National Petroleum Reserve in Alaska
To compare the porosity-depth trends in shales from different wells, it is desirable to select a line representing the shale 

edge of the porosity-depth curve. We chose to represent shale 

porosity with a two-point linear fit within the Torok Formation 

for each well, as illustrated in figure 12, whereas Rowan and 

others (2002, 2003) used exponential relations to represent the 

porosity-depth relations for both sandstones and shales throughout the Brookian section. Exponential relations are generally 

used when seeking a single equation to represent the porositydepth relation for various geologic formations within an entire 

basin. To represent the porosity-depth relation for the Torok 

Formation within individual wells, however, a linear fit was 

determined to be sufficient.

The two depth points were chosen with several considerations in mind: representation of shaly rather than sandy 

sequences, adequate depth separation to minimize errors in 

calculating the slope, avoidance of enlarged or rough wellbore 

where the sonic traveltime may be erroneous, and avoidance of 

zones that may be overpressured. Zones of high organic-carbon 

content were also avoided, although such zones are rare within 

Figure 12. Electrical resistivity from deep induction logs, shale fraction calculated from gamma-ray logs, and porosity (blue, unfiltered; yellow, 

filtered) calculated from sonic logs (using acoustic-formation-factor equation; see text) versus depth in eight wells representative of areas A 

through G, National Petroleum Reserve in Alaska (see fig. 1 for locations and table 2 for well data), with caliper and mud weight shown for reference. Porosity-depth curve is drawn for shaliest parts of the Torok Formation. A, Tunalik well (area A). Mud weight indicates overpressure. Drillbit 

spiraled in interval from 6,250- to 7,250-ft depth, which is out of gauge. B, Peard well (area B). Mud weight indicates normal pressure. Exceptionally high gamma-ray value at 5,810-ft depth gives an erroneously high porosity. C, Kuyanak well (area C). Mud weight indicates normal pressure. 

D, J.W. Dalton well (area D). Mud weight indicates normal pressure. E, South Harrison Bay well (area E). Mud weight and hydraulic-pressure gradient (calculated from drillstem tests) indicate near-normal pressure. F, Phoenix well (area E). Mud weight indicates normal pressure. G, Inigok 

well (area F). Mud weight indicates normal pressure. H, Tulugak well (area G). Mud weight indicates some overpressure. Well penetrated 8,000 ft 

of the Lower Torok Formation (not shown), requiring mud weights as high as 15.7 lb/gal. Drillstem test through perforated intervals between 7,898- 

and 8,571-ft depth produced light gas flow to surface at a hydraulic-pressure gradient of 0.48 lb/in2 per foot.

Tunalik 1 

DEPTH (feet) 

6,500 

7,000 

7,500 

8,000 

8,500 

9,000 

9,500 

10,000 

10,500 

1 100 

Resisitivity (ohm-m) 

0 0.1 0.2 

Porosity (fraction)

6 36 

Shale (fraction) 1 

Caliper

0 

8 

0.3 

Mud weight 18 

Torok 

Formation 

Casing 

point 

Porosity, 

filtered and unfiltered 

Porosity trendline 

Mud weight 

Shale 

Caliper 

Unit 

12A 

 Shale Porosity Versus Depth 11
the Torok Formation. The porosities at each of the two depth 

points were averaged over depth intervals ranging from 10 to 

100 ft, depending on the characteristics of the calculated porosity-depth curve. The porosity gradient (percent porosity change 

per 1,000 ft of depth) of the two-point line segment was calculated from the differences between the average porosities and 

the depths at the two points (table 4). The line was extrapolated 

to the top and bottom of the Torok Formation, as indicated in 

figure 11; the porosities and depths for each well are listed in 

table 4.

Porosity trendlines for all wells are plotted in figures 13 

and 14, coded according to area. All the trendlines from wells 

in the coastal area and offshore (fig. 13) fall within the average 

trendlines compiled by Issler (1992) for areas 3 through 5 in the 

Mackenzie Delta (fig. 3). Trendlines for the easternmost wells 

plot deeper than those for all the others, indicating that the strata 

in these wells have been uplifted less than in wells to the west 

(compare fig. 3). Except for the high porosity gradients in area 

C, the gradients of the trendlines in figure 13 are similar to the 

gradients of Issler’s average trendlines.

In contrast, the porosity trendlines for all wells in the 

foothills, central, and western areas (fig. 14) do not match the 

average trendlines established by Issler (1992). Some of these 

trendlines are composed of two line segments, in which the 

lower line segment represents the porosity trend in the lower 

Torok/Fortress Mountain depositional sequence. The very steep 

trendlines displaying low porosity gradients in figure 14 indicate 

a different compaction history than that manifested in the wells 

in figure 13. Issler observed low porosity gradients in offshore 

environments of the Beaufort-Mackenzie Basin where overpressure exists today, as shown by the curves for areas 1 and 2 in 

figures 3 and 14.

Because overpressure reduces the effective stress, the 

porosity at a given depth remains greater than if the hydrostatic 

pressure were normal. Magara (1978) stated that the signature 

of overpressured conditions remains in the sonic logs; that is, 

the sonic velocity remains low even after the rocks have been 

uplifted and the hydraulic pressure has returned to normal. 

Much of the increase in sonic velocity with compaction and 

cementation is permanent, resulting in a hysteresis effect 

Figure 12.—Continued.

Peard 1 

DEPTH (feet) 

2,500

3,000

3,500

4,000

4,500

5,000

5,500

6,000

Resistivity (ohm-m) 

1 100 0 0.1 0.2

Porosity (fraction) 

6 36

Shale (fraction) 1

Caliper

0

8

0.3

Mud weight 18

Torok 

Formation

Casing

point

Shale

Caliper

Mud weight 

Porosity, 

filtered and unfiltered 

Porosity trendline 

Unit

12B

12 Porosity-Depth Trends and Regional Uplift Calculated from Sonic Logs, National Petroleum Reserve in Alaska
during uplift. In any case, we attribute the mismatch between 

the porosity trendlines and Issler’s (1992) trendlines in figure 

14 to a combination of overpressure, which somehow produced the low porosity gradients, and uplift, which causes the 

(largely unaltered) steep trendlines to overlie the normal porosity gradients. For example, rapid deposition and subsidence in 

the Colville Trough may have led to overpressured conditions 

during the burial of Torok sedimentary deposits. Then uplift 

and erosion cause the porosity trendlines in figure 14 to plot at 

a shallow depth. The exact sequence of deposition, overpressuring, and uplift remains to be determined. Clearly, however, 

the porosities and porosity gradients differ among wells, and so 

the degree and spatial extent of overpressure must have varied 

throughout the basin.

The porosities listed in table 4, plotted in figures 13 and 14 

as a function of depth, are plotted in figure 15 as porosity loss 

(the difference between porosity extrapolated to the top of the 

Torok Formation and the porosity at the base) versus the thickness of the Torok Formation. The Torok Formation is thickest 

and the porosity loss least in wells in the foothills (area G), and 

so the porosity gradients are lowest there, ranging from 0 to 2.3 

percent per 1,000 ft. Data points for wells on the Barrow Arch 

east of Point Barrow (areas D, E) have porosity gradients ranging from 2.4 to 5.0 percent per 1,000 ft. In the Point Barrow 

area (area C), porosity gradients range from 3.7 to 12.1 percent 

per 1,000 ft, and thicknesses are less than 3,500 ft. Thus, a continuum exists between low porosity gradients in the foothills, 

intermediate porosity gradients along the eastern part of the 

Barrow Arch, and high porosity gradients in the Point Barrow 

area.

Porosity As a Function of 

Vitrinite Reflectance

For each well, a relation between vitrinite reflectance, 

R0, and depth z was determined by using linear regression:

 

ln R (6) 0  ln a  bz,

Figure 12.—Continued.

Kuyanak 1

DEPTH (feet) 

1,500 

2,000 

2,500 

3,000 

3,500 

4,000 

4,500 

Resistivity (ohm-m)

1 100 0 0.1 0.2

Porosity (fraction)

6 36 

Shale (fraction) 1 

Caliper

0 

8 

0.3 

Mud Weight 18

Torok 

Formation 

Casing 

point 

Shale 

Caliper 

Mud weight 

Porosity, 

filtered and unfiltered 

Porosity trendline 

Unit 

12C 

 Porosity As a Function of Vitrinite Reflectance 13
Figure 12.—Continued.

J.W. Dalton 1 

DEPTH (feet) 

4,500

5,000

5,500

6,000

6,500

7,000

7,500

Resistivity (ohm-m) 

1 100 0 0.1 0.2

Porosity (fraction) 

6 36

Shale (fraction) 1

Caliper

0

8

0.3

Mud weight 18

Torok 

Formation

Shale

Caliper

Mud weight 

Porosity, 

filtered and unfiltered 

Porosity trendline 

Unit

12D

where a and b are coefficients determined for each well. The 

coefficient a represents the vitrinite reflectance extrapolated to 

the surface. In some wells, all the R0 data from the well were 

used to establish a and b values for that well, and in other wells 

only data from the Torok Formation were used. R0 data were 

available from most NPRA wells (for example, Johnsson and 

others, 1999); in a few wells, a and b values were determined 

from nearby wells. Using equation 6, R0 values were then determined at the top and bottom of the Torok Formation, so that the 

line segments for each well could be plotted in figures 16 and 17.

If porosity loss depended solely on thermal maturity and 

the R0 data were free of systematic errors, then the line segments in figures 16 and 17 would collapse to a single bundle. 

The line segments do coalesce to some extent—plotting porosity as function of vitrinite reflectance (fig. 16) causes a tighter 

grouping of wells than plotting porosity as a function of depth 

(fig. 13)—but the coalescence of line segments within figure 

16 or 17 is incomplete. Moreover, the line segments for wells 

in the foothills (fig. 17) lie below those in the coastal areas (fig. 

16). As discussed in the preceding section, the rapid rate of 

sedimentation and overpressuring may be responsible for the 

preservation of porosity at greater depths in the foothills than in 

the coastal areas.

Three wells in the central area—Inigok, Koluktak, and 

Ikpikpuk (area F, fig. 1)—plot with low porosity gradients, 

similar to wells in the foothills area (figs. 13, 14), but, when 

plotted logarithmically against vitrinite reflectance in figure 

17, overlie the porosity trendlines for wells in the coastal 

areas. In other words, the R0 data indicate thermal maturities 

in wells in the central area comparable to those in wells in 

the north, but the porosities and porosity gradients are more 

comparable to those in wells in the south. The overpressuring and effective stress in the central area apparently was 

similar to that in the foothills, but the depth of burial (and 

the uplift) was less.

The Tulaga well (area G, fig. 1) appears to be an isolated 

case. As calculated from the sonic log, the porosity in Torok 

shales is nearly constant at approximately 10.6 percent over 

the depth range 5,805–10,655 ft. However, vitrinite reflectances are low in comparison with similar porosities in deep 

14 Porosity-Depth Trends and Regional Uplift Calculated from Sonic Logs, National Petroleum Reserve in Alaska
Figure 12.—Continued.

South Harrison Bay 1 

DEPTH (feet) 

4,500 

5,000 

5,500 

6,000 

6,500 

7,000 

Resistivity (ohm-m) 

1 100 0 0.1 0.2 

Porosity (fraction)

6 36 

Shale (fraction) 1 

Caliper

0 

8 

0.3 

Mud weight 18 

Torok 

Formation 

Shale 

Caliper 

Mud weight 

Porosity, 

filtered and unfiltered 

Porosity trendline 

Unit 

12E 

wells in the foothills. Thus, the porosity trendline for the 

Tulaga well plots anomalously above the trendlines for all 

other wells in the foothills in figure 17. The porosities and 

their near-constancy with depth indicate that the Torok Formation was deeply buried, whereas the low vitrinite reflectances imply shallow burial (fig. 16). The consistency of the 

porosities with those in neighboring wells raises concern 

regarding the validity of the R0 data from this well.

Uplift

As pointed out by Issler (1992), the offset of the porositydepth curves in figure 13 can be used to estimate the relative 

amount of uplift between any two wells. This offset can be 

calculated in three ways: (1) by extrapolating to the surface, 

(2) by extrapolating to zero porosity, or (3) by shifting the 

curves vertically and observing the displacement required to 

achieve an overlay. Because the third way is the least sensitive to errors in slope, we use it here. We calculated the uplift 

for all wells in the coastal area relative to the Phoenix well, 

the easternmost well in the study area (area E, fig. 1), which 

has a porosity-depth trend close to that of Issler’s area 3, 

interpreted to mean that the uplift there has been negligible. 

In a separate evaluation of 12 offshore wells, the Phoenix 

well was observed to be one of 4 wells with no discernible 

uplift (Rowan and others, 2002). For wells in areas B through 

E (fig. 13), the uplift was calculated from the difference 

between the depth at which the porosity is 20 percent in a 

given well and the depth at which the porosity is 20 percent in 

the Phoenix well (6,551 ft). The resulting values are mapped 

in figure 18 and listed in table 4.

In the foothills, western, and central areas, the porositydepth curves in figure 14 were shifted downward until they 

lay below Issler’s line of no uplift. The resulting depth displacement is a minimum because the curves could be shifted 

deeper. The minimum uplifts determined for areas A, F, and G 

are mapped in figure 18 and listed in table 4.

Uplift (relative to the Phoenix well) ranges from 0 to 

1,600 ft within the extreme northeastern NPRA and immedi-

 Uplift 15
Figure 12.—Continued.

ately offshore (area E, fig. 18), from 2,000 to 3,200 ft within 

the Simpson Shelf (area D), from 4,100 to 4,900 ft in the Point 

Barrow area (area C), and from 3,700 to 5,100 ft in the area 

southwest of Point Barrow (area B). The maximum uplift 

of 5,100 ft occurs in the Brontosaurus well. Uplift increases 

steadily from east (area E) to west (area C and east end of area 

B) and then decreases at the west end of area B, as shown in 

figures 18 and 19.

Four estimates of uplift from apatite fission-track analysis 

are directly comparable with our estimates of uplift from sonic 

logs. O’Sullivan (1999) calculated 3,900 ft of uplift and erosion in the Walakpa 1 well (area C, fig. 1), in comparison with 

our estimate of 4,800 ft. However, in the three other wells with 

both types of uplift estimate—Tunalik (area A), Inigok (area 

F), and Seabee (area G)—we calculated only minimum uplifts 

from porosity, which are less than, and thus compatible with, 

O’Sullivan’s uplifts estimated from apatite fission-track data 

(fig. 18). Estimates of uplift in paired wells give a sense of relative error: East Simpson 1, 2,700 ft, and East Simpson 2, 3,000 

ft (area D); Walakpa 1, 4,800 ft, and Walakpa 2, 4,800 ft (area 

C); and Tulageak, 4,600 ft, and West Dease, 4,000 ft (area C).

Three estimates of uplift by three different methods 

for wells along the Barrow Arch are compared in figure 19. 

The uplifts estimated from porosity are the same as those 

mapped in figure 18. The uplifts plotted on the west end of 

the red line are averages from the Peard and Kugrua wells 

(area B, fig. 1). The uplifts estimated from vitrinite reflectance are the elevations at which least-squares fits to the R0

data extrapolate to a vitrinite reflectance of 0.25. The uplift 

of 3,900 ft estimated from apatite fission-track data for the 

Walakpa 1 well (area C; O’Sullivan, 1999) is the lowest 

of the three estimates for that well. The uplifts estimated 

from vitrinite reflectance are comparable to the porosities 

estimated in eight wells but are greater by about 2,000 ft 

than the porosities estimated in three wells. Despite these 

discrepancies, the uplifts estimated both from porosity and 

from vitrinite reflectance increase from east to west across 

the study area (fig. 1).

Phoenix 

DEPTH (feet) 

6,500 

7,000 

Resistivity (ohm-m) 

1 100 0 0.1 0.2 

Porosity (fraction) 

6 36 

Shale (fraction) 1 

Caliper

0 

8 

0.3 

Mud weight 18 

Torok 

Formation 

Shale 

Caliper 

Mud weight 

Porosity, 

filtered and unfiltered 

Porosity trendline 

Unit 

12F 

16 Porosity-Depth Trends and Regional Uplift Calculated from Sonic Logs, National Petroleum Reserve in Alaska
Summary and Conclusions

By modifying the AFF equation to incorporate the shale 

fraction from the gamma-ray log, the porosity can be calculated from the sonic log for all siliciclastic rocks. Core data 

from NPRA wells indicate only a slight bias in the resulting estimates of porosity. On a plot of sonic velocity versus 

porosity, the AFF equation used in this report has a narrower 

window than some other transforms (Eberhart-Phillips and 

others, 1989; Vernik, 1997) but is comparable to the one 

developed for a wide range of datasets by Erickson and Jarrard 

(1998).

To examine compaction trends within the NPRA, we 

extracted a porosity-depth trend from the shaliest components 

of the Torok Formation. The decrease in porosity with depth in 

shales is approximately linear—at least, we could see no reason 

to apply a nonlinear trend to the porosity-depth data in the 

Torok Formation.

Porosity-depth trends in wells are grouped into seven areas, 

the characteristics of which are attributed to varying amounts of 

uplift and to the effect of overpressuring during burial in some 

parts of the NPRA. The porosity trendlines from various wells 

cluster better when plotted against vitrinite reflectance than 

against present-day depth, indicating that the use of R0 data to 

compensate for maximum burial depth explains much, but not all, 

of the variation among compaction trends in the northern NPRA.

The record of uplift and erosion is clearly manifested 

in the porosity-depth trends in wells in the northern NPRA, 

where no record of overpressuring is evident. Using Issler’s 

(1992) trendline of no uplift, we have determined uplifts 

ranging from 0 in the east to 5,100 ft in the west. South of the 

Barrow Arch, the rocks have been sufficiently compacted that 

the estimates of uplift are minimums rather than totals. The 

largest minimum uplift was determined in the East Kurupa 

well (area G, fig. 1), where at least 5,700 ft of uplift has 

occurred.

Figure 12.—Continued.

Inigok 1

DEPTH (feet) 4,000

4,500

5,000

5,500

6,000

6,500

7,000

7,500

8,000

8,500

9,000

Resistivity (ohm-m)

1 100 0 0.1 0.2

Porosity (fraction)

6 36

Shale (fraction) 1

Caliper

0

8

0.3

Mud weight 18

Torok

Formation

Casing

point

Shale

Caliper

Mud weight

Porosity,

filtered and unfiltered

Porosity trendline

Unit

12G

 Summary and Conclusions 17
Figure 12.—Continued.

Tulugak 1 

DEPTH (feet) 

3,000 

3,500 

4,000 

4,500 

5,000 

5,500 

6,000 

6,500 

7,000 

7,500 

8,000 

Resistivity (ohm-m) 

1 100 0 0.1 0.2 

Porosity (fraction)

6 36 

Shale (fraction) 1 

Caliper

0 

8 

0.3 

Mud weight 18 

Torok 

Formation 

Casing 

point 

Shale 

Mud weight 

Porosity, 

filtered and unfiltered 

Porosity trendline 

Unit 

12H 

Coastal Plain 

Porosity (percent) 

0 10 20 30 40 

Depth (feet) 

0 

2,000 

4,000 

6,000 

8,000 

10,000 

N P R A 

B 

C D 

E 

Figure 13. Average porosity in shales versus depth within the Torok 

Formation in wells drilled in coastal areas and offshore of the National 

Petroleum Reserve in Alaska (NPRA) (areas B–E, fig. 1), with porositydepth trendlines (dashed curves) determined by Issler (1992) for areas 3 

through 5 in the Beaufort-Mackenzie Basin, northwestern Canada (fig. 3), 

shown for comparison. Short line terminated by circles is porosity-depth 

curve for the Phoenix well.

18 Porosity-Depth Trends and Regional Uplift Calculated from Sonic Logs, National Petroleum Reserve in Alaska
Foothills, Central,

and Western 

areas

Porosity (percent) 

0 10 20 30 40

Depth (feet) 

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

N P R A 

A 

F

G

Figure 14. Average porosity in shales versus depth within the Torok 

Formation in wells drilled in foothills and central and western areas of 

the National Petroleum Reserve in Alaska (areas G, F, and A, respectively, fig. 1), with porosity-depth trendlines (dashed curves) determined by Issler (1992) for areas 1 through 5 in the Beaufort-Mackenzie 

Basin, northwestern Canada (fig. 3), shown for comparison.

Thickness (feet) 

0 2,000 4,000 6,000 8,000 10,000

Porosity loss (percent) 

0

4

8

12

16

20

2

12 8 6 5 4 3

Area (fig. 1) 

A 

B

C

D

E

F

G

EXPLANATION

1

Figure 15. Porosity loss in shales from top to bottom of the Torok Formation versus thickness of the Torok Formation in wells drilled in areas A 

through G, National Petroleum Reserve in Alaska (see fig. 1 for locations 

and table 2 for well data). Each data point represents porosity loss and 

formation thickness in an individual well; lower segments of two-part 

linear fit in five wells (Awuna, Antares, East Kurupa, Seabee, and 

Tulugak) are omitted. Numbered dashed curves, porosity-loss gradients, 

ranging from 1 to 12 percent per 1,000 ft; in comparison, porosity gradient 

determined by Issler (1992) for area 3 of the Beaufort-Mackenzie Basin, 

northwestern Canada (fig. 3), is 3.1 percent per 1,000 ft.

Figure 16. Average porosity in shales versus vitrinite reflectance in 

wells drilled in coastal areas of the National Petroleum Reserve in 

Alaska (NPRA) (areas B–E, fig. 1). Short line terminated by circles is 

porosity-vitrinite reflectance curve for the Phoenix well.

Coastal Plain 

Porosity (percent) 

0 10 20 30 40 

Vitrinite Reflectance (percent)

2.0 

1.5 

1.0 

0.9 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

N P R A 

B 

C D E 

 Summary and Conclusions 19
Table 4. Porosities and estimated uplift in the Torok and lower Torok Formations.

[Five wells are fitted with two straight lines (upper and lower), spanning the Torok and lower Torok Formations. Top 

depth is top of the Torok Formation; bottom depth is bottom of the Torok Formation or bottom of the lower Torok Formation, if present]

Porosity Top Bottom Porosity Porosity Porosity Estimated Thickness gradient Well depth depth at top at bottom loss uplift (ft) (pct per (ft) (ft) (pct) (pct) (pct) (ft) 1,000 ft) 

Tunalik - - - - - - - - - - - - - - - - - - - - - 6,250 10,635 12.2 8.5 4,385 3.7 0.85 2,600 

Tungak Creek - - - - - - - - - - - - 5,415 8,212 15.5 15.5 2,797 .0 .00 2,500 

Brontosaurus - - - - - - - - - - - - - 1,950 3,918 19.0 15.3 1,968 3.7 1.89 5,100 

Kugrua - - - - - - - - - - - - - - - - - - - - - 2,330 6,890 21.0 11.0 4,560 10.1 2.21 3,700 

Peard - - - - - - - - - - - - - - - - - - - - - - - - 2,470 6,195 19.8 10.4 3,725 9.4 2.53 4,200 

South Meade - - - - - - - - - - - - - 2,490 6,475 18.2 7.9 3,985 10.2 2.57 4,800 

Kuyanak - - - - - - - - - - - - - - - - - - - 1,250 4,640 24.6 12.1 3,390 12.5 3.68 4,100 

South Barrow 18 - - - - - - - - 98 1,375 38.3 22.9 1,277 15.4 12.08 4,900 

Tulageak - - - - - - - - - - - - - - - - - - - 100 2,505 29.0 17.5 2,405 11.5 4.79 4,600 

Walakpa 1 - - - - - - - - - - - - - - - - - 101 1,700 32.4 20.7 1,599 11.7 7.33 4,800 

Walakpa 2 - - - - - - - - - - - - - - - - - 98 2,205 32.1 16.3 2,107 15.8 7.50 4,800 

West Dease - - - - - - - - - - - - - - - 80 2,910 30.1 18.4 2,830 11.7 4.12 4,000 

Cabot - - - - - - - - - - - - - - - - - - - - - - - 3,256 7,352 21.5 11.5 4,096 10.0 2.44 2,700 

Drew Point - - - - - - - - - - - - - - - - 3,200 6,700 25.1 12.1 3,500 13.0 3.72 2,000 

East Simpson 1 - - - - - - - - - - 2,690 6,365 23.5 12.1 3,675 11.4 3.11 2,700 

East Simpson 2 - - - - - - - - - - 2,700 6,325 23.3 9.7 3,625 13.5 3.73 3,000 

East Teshekpuk - - - - - - - - - - 3,100 6,850 23.4 10.4 3,750 13.0 3.46 2,500 

J.W. Dalton - - - - - - - - - - - - - - - 4,140 7,480 19.5 4.5 3,340 15.0 4.50 2,500 

North Inigok - - - - - - - - - - - - - - 3,265 7,385 22.1 12.2 4,120 9.9 2.40 2,400 

South Simpson - - - - - - - - - - - 1,910 6,315 25.2 8.9 4,405 16.4 3.71 3,200 

West Fish Creek - - - - - - - - - 3,915 7,280 21.4 9.8 3,365 11.6 3.45 2,200 

Antares 1, lower - - - - - - - - - 6,155 7,142 14.1 13.6 987 0.5 0.51 – – 

Antares 1, upper - - - - - - - - - 4,230 6,155 23.8 14.1 1,925 9.7 5.01 1,600 

Atigaru Point - - - - - - - - - - - - - 4,400 7,280 22.1 12.8 2,880 9.4 3.25 1,500 

Cape Halkett - - - - - - - - - - - - - - 4,235 7,280 23.6 12.3 3,045 11.4 3.73 1,300 

Colville River 1 - - - - - - - - - - 4,044 6,219 23.8 18.1 2,175 5.7 2.60 1,100 

Mukluk - - - - - - - - - - - - - - - - - - - - - 5,308 7,204 21.0 14.3 1,896 6.8 3.57 900 

North Kalikpik - - - - - - - - - - - 3,470 6,895 26.8 17.1 3,425 9.7 2.82 700 

Phoenix - - - - - - - - - - - - - - - - - - - - 6,200 7,335 21.1 17.5 1,135 3.6 3.19 0 

South Harrison Bay - - - - - 4,220 7,290 23.7 13.1 3,070 10.6 3.47 1,300 

W.T. Foran - - - - - - - - - - - - - - - - 4,380 7,340 24.0 13.5 2,960 10.6 3.57 1,000 

Ikpikpuk - - - - - - - - - - - - - - - - - - - 2,950 7,230 17.2 9.1 4,280 8.1 1.89 4,200 

Inigok - - - - - - - - - - - - - - - - - - - - - - 3,935 9,040 16.8 8.2 5,105 8.6 1.68 3,200 

Koluktak - - - - - - - - - - - - - - - - - - - 4,210 5,882 15.8 14.2 1,672 1.7 0.99 3,300 

Area G. Foothills 

A w u n a , l o w e r ----------- 8 ,7 0 0 1 1 2 0 0 0 .9 0 .9 2 ,5 0 0 0 .0 0 .0 0 –– 

A w u n a , u p p e r ----------- 5 0 8 ,7 0 0 2 1. 1 0 .9 8 ,6 5 0 2 0. 2 2 .3 3 > 5 ,6 0 0 

B ig B e n d ------------------ 3 ,6 4 2 1 0, 3 8 0 1 8. 2 8 .4 6 ,7 3 8 9 .8 1 .4 6 > 3 ,2 0 0 

E as t K ur u p a , l o w e r ---- 6 ,4 5 0 1 0, 2 9 4 1 0. 4 1 0. 2 3 ,8 4 4 . 2 . 0 6 –– 

E as t K ur u p a , u p p e r ---- 2 ,2 0 0 6 ,4 5 0 1 3. 9 1 0. 4 4 ,2 5 0 3 .5 . 8 2 > 5 ,7 0 0 

S ea b e e , l o w e r ------------ 9 ,5 2 0 1 3, 0 0 0 1 4. 4 1 2. 5 3 ,4 8 0 1 .9 . 5 4 –– S ea b e e , u p p e r ------------ 1 ,2 9 5 9 ,5 2 0 2 1. 3 1 4. 4 8 ,2 2 5 6 .9 . 8 4 > 4 ,6 0 0 

T ul a g a --------------------- 5 ,8 0 5 1 0, 6 5 5 1 0. 9 1 0. 4 4 ,8 5 0 . 5 . 1 0 > 3 ,5 0 0 

T ul u g a k , l o w e r ---------- 7 ,9 0 0 1 5, 9 6 0 1 2. 5 1 0. 0 8 ,0 6 0 2 .5 . 3 1 –– 

T ul u g a k , u p p e r ---------- 2 ,6 6 5 7 ,9 0 0 1 8. 1 1 2. 5 5 ,2 3 5 5 .6 1 .0 7 > 4 ,2 0 0 

W e s t K u r u p a ------------- 1 ,9 6 0 1 1, 0 6 0 1 8. 2 6 .1 9 ,1 0 0 1 2. 2 1 .3 4 > 4 ,8 0 0 

Area F. Central 

Area E. Northeastern 

Area D. Simpson Shelf

Area C. Point Barrow 

Area B. Southwest of Point Barrow 

Area A. Western 

20 Porosity-Depth Trends and Regional Uplift Calculated from Sonic Logs, National Petroleum Reserve in Alaska
Foothills, Central, 

and Western areas highlighted 

Porosity (percent) 

0 10 20 30 40 

Vitrinite Reflectance (percent)

4.0 

3.0 

2.0 

1.5 

1.0 

0.9 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

T 

N P R A 

A 

B 

C D E 

F 

G 

Figure 17. Average porosity in shales versus vitrinite reflectance in wells drilled in 

foothills and central and western areas of the National Petroleum Reserve in Alaska 

(NPRA) (areas G, F, and A, respectively, fig. 1), with porosity trendlines (gray curves) 

for coastal areas from figure 14 shown for comparison. Line T is for the Tulaga well in 

northeast corner of area G.

 Summary and Conclusions

Porosity gradients range from 1 percent per 1,000 ft in 

the foothills, where the Torok section is thickest and burial 

has been deepest, to 12 percent per 1,000 ft in the Point 

Barrow area, where the section is thinnest (fig. 15). This 

range in porosity gradient is greater than that reported in other 

studies, such as by Issler (1992). The determination of its 

cause awaits further investigation of burial history across the 

basin to resolve the effects of sedimentation rate and overpressuring.

References Cited

Bartsch-Winkler, S.B., and Huffman, A.C., 1988, Sandstone 

petrography of the Nanushuk Group and Torok Formation, in Gryc, George, ed., Geology and exploration of 

the National Petroleum Reserve in Alaska, 1974 to 1982: 

U.S. Geological Survey Professional Paper 1399, p. 

801–831.

Eberhart-Phillips, D.M., Han, D.H., and Zoback, M.D., 

1989, Empirical relationships among seismic velocity, 

effective pressure, porosity, and clay content in sandstone: Geophysics, v. 54, no. 1, p. 82–89.

Erickson, S.N., and Jarrard, R.D., 1998, Velocity-porosity 

relationships for water-saturated siliciclastic sediments, 

Journal of Geophysical Research, v. 103, no. B12, p. 

30385–30406.

Harrold, T.W.D., Swarbrick, R.E., and Goulty, N.R., 1999, 

Pore pressure estimation from mudrock porosities in 

21
N P R A 

1,600 

1,500 

1,300 

1,100 

950 

700 

0 

1,300 

1,000 

2,700 

2,000 2,700 

3,000 

4,800 

4,000 

5,100 

3,700 

4,200 

4,800 

2,200 

4,900 

4,800 

4,100 

4,600 

2,500 

2,500 

2,400 

>2,600 

>2,500 

 Well without sonic log 

3,400 Feet of uplift from sonic log 

EXPLANATION 

4,300 Feet of uplift (O'Sullivan, 1999) 

>4,200 

>3,300 

>3,200 

>4,600 

>3,200 

>4,200 

>5,700 >4,800 

>5,600 

4,300 

3,900 

5,600 

6,900 

9,500 

>3,500 

3,200 

A 

B 

C 

D E 

F 

G 69° 

70° 

162° 160° 158° 156° 154° 152° 

71° 

Figure 18. National Petroleum Reserve in Alaska (NPRA), showing uplift (in feet) estimated from porosity trends calculated from 

sonic logs in wells (see fig. 1 for locations and table 2 for well data).

Tertiary basins, southeast Asia: American Association 

of Petroleum Geologists Bulletin, v. 83, no. 7, p. 1057–

1067.

Hearst, J.R, Nelson, P.H., and Paillet, F.L., 2000, Well logging for physical properties; a handbook for geophysicists, geologists, and engineers (2d ed.): Chichester, 

U.K., J. Wiley, 483 p.

Hunt, J.M., Whelan, J.K., Eglinton, L.B., and Cathles, 

L.M., III, 1998, Relation of shale porosities, gas generation, and compaction to deep overpressures in the U.S. 

Gulf Coast, in Law, B.E., Ulmishek, G.F., and Slavin, 

V.I., eds., Abnormal pressures in hydrocarbon environments: American Association of Petroleum Geologists 

Memoir 70, p. 87–104.

Issler, D.R., 1992, A new approach to shale compaction and 

stratigraphic restoration, Beaufort-Mackenzie Basin and 

Mackenzie Corridor, northern Canada: American Association of Petroleum Geologists Bulletin, v. 76, no. 8, p. 

1170–1189.

Johnsson, M. J., Evans, K.R., and Marshall, H.A. 1999, 

Thermal maturity of sedimentary rocks in Alaska; digital 

resources: U.S. Geological Survey Digital Data Series 

DDS–54, CD–ROM [URL http://wrgis.wr.usgs.gov/dds/

dds-54/Data/].

Magara, Kinji, 1978, Compaction and fluid migration; practical petroleum geology (Developments in Petroleum Science, no. 9), Amsterdam, Elsevier, 319 p.

Molenaar, C.M., 1988, Depositional history and seismic 

stratigraphy of Lower Cretaceous rocks in the National 

Petroleum Reserve in Alaska and adjacent areas, in Gryc, 

George, ed., Geology and exploration of the National 

Petroleum Reserve in Alaska, 1974 to 1982: U.S. Geological Survey Professional Paper 1399, p. 593–621.

Mull, C.G., Houseknecht, D.W., and Bird, K.J., 2003, 

Revised Cretaceous and Tertiary stratigraphic nomenclature in the Colville basin, northern Alaska: U.S. Geological Survey Professional Paper 1673 [URL http://pubs.

usgs.gov/pp/p1673/text.html].

O’Sullivan, P.B., 1999, Thermochronology, denudation and 

variations in paleosurface temperature; a case study from 

the North Slope foreland basin, Alaska: Basin Research, 

v. 11, no. 3, p. 191–204.

22 Porosity-Depth Trends and Regional Uplift Calculated from Sonic Logs, National Petroleum Reserve in Alaska
 Summary and Conclusions

Potter, C.J., and Moore, T.E., 2003, Brookian structural 

plays in the National Petroleum Reserve-Alaska: U.S. 

Geological Survey Open-File Report 03–266 [URL 

http://pubs.usgs.gov/of/2003/of03-266/].

Raiga-Clemenceau, Jean, Martin, J.P., and Nicoletis, Serge, 

1988, The concept of acoustic formation factor for more 

accurate porosity determination from sonic transit time 

data: Log Analyst, v. 29, no. 1, p. 54–60.

Rowan, E.L., Hayba, D.O., Nelson, P.H., Burns, W.M., 

and Houseknecht, D.W., 2003, Sandstone and shale 

compaction curves derived from sonic and gamma ray 

logs in offshore wells, North Slope, Alaska—parameters 

for basin modeling: U.S. Geological Survey Open-File 

Report 03–329, 3 sheets.

Rowan, E.L., Nelson, P.H., and Hayba, D.O., 2002, 

Compaction properties of sandstones and shales in the 

National Petroleum Reserve, Alaska (NPRA)—significance for burial and thermal history models [abs.]: American Association of Petroleum Geologists Bulletin, v. 86, 

no. 6, p. 1158.

Vernik, Lev, 1997, Predicting porosity from acoustic velocities in siliciclastics; a new look: Geophysics, v. 62, no. 1, 

p. 118–128.

Vernik, Lev, and Nur, Amos, 1992, Petrophysical classification of siliciclastics for lithology and porosity prediction 

from seismic velocities: American Association of Petroleum Geologists Bulletin, v. 76, no. 9, p. 1295–1309.

Wylie, M.R.J., Gregory, A.F., and Gardner, L.W., 1956, 

Elastic wave velocities in heterogeneous and porous 

media: Geophysics, v. 21, p. 41–70.

Distance from Point Barrow (miles) 

-50 0 50 100 150 

Uplift (feet) 

0 

1,000 

2,000 

3,000 

4,000 

5,000 

6,000 

7,000 

8,000 

Vitrinite reflectance 

Porosity 

Apatite 

fission 

track 

Peard 

Kugrua 

South Meade 

Brontosaurus 

Walakpa 1 

Walakpa 2 

South Barrow 18 

Tulageak 

West Dease 

Kuyanak 

East Simpson 2 

East Simpson 1 

Drew Point 

J. W. Dalton 

Antares 

W. T. Foran 

Cape Halkett 

East Teshekpuk Atigaru Point 

North Kalikpik South Harrison Bay 

West Fish Creek 

Colville River North Inigok 

Ikpikpuk 

Mukluk 

Phoenix 

Cabot 

Point Barrow 

Figure 19. Uplift along the Barrow Arch (fig. 1) estimated by three different methods: vitrinite reflectance, porosity trends calculated from sonic logs, and apatite 

fission-track analysis. Circles, wells with sonic logs; crosses, wells without sonic 

logs.

23