Studies by the U.S. Geological Survey in Alaska, 2005

U.S. Geological Survey Professional Paper 1732–D

Estimating the Amount of Eroded Section in a Partially 

Exhumed Basin from Geophysical Well Logs: An Example 

from the North Slope

By W. Matthew Burns, Daniel O. Hayba, Elisabeth L. Rowan, and David W. Houseknecht

Abstract

The reconstruction of burial and thermal histories of 

partially exhumed basins requires an estimation of the amount 

of erosion that has occurred since the time of maximum burial. 

We have developed a method for estimating eroded thickness by using porosity-depth trends derived from borehole 

sonic logs of wells in the Colville Basin of northern Alaska. 

Porosity-depth functions defined from sonic-porosity logs in 

wells drilled in minimally eroded parts of the basin provide 

a baseline for comparison with the porosity-depth trends 

observed in other wells across the basin. Calculated porosities, 

based on porosity-depth functions, were fitted to the observed 

data in each well by varying the amount of section assumed 

to have been eroded from the top of the sedimentary column. 

The result is an estimate of denudation at the wellsite since 

the time of maximum sediment accumulation. Alternative 

methods of estimating exhumation include fission-track analysis and projection of trendlines through vitrinite-reflectance 

profiles. In the Colville Basin, the methodology described 

here provides results generally similar to those from fission-track analysis and vitrinite-reflectance profiles, but with 

greatly improved spatial resolution relative to the published 

fission-track data and with improved reliability relative to the 

vitrinite-reflectance data. In addition, the exhumation estimates derived from sonic-porosity logs are independent of the 

thermal evolution of the basin, allowing these estimates to be 

used as independent variables in thermal-history modeling.

Introduction

Burial- and thermal-history modeling of partially 

exhumed sedimentary basins (that is, basins in which the 

sedimentary fill has been partly removed by erosion) requires 

an estimation of the amount of section deposited and later 

eroded at all modeled sites. The Colville Basin, which spans 

the Alaskan North Slope (fig. 1), has undergone substantial 

exhumation since the time of maximum burial, as indicated 

by stratigraphic evidence, vitrinite-reflectance profiles, and 

fission-track data analysis. None of these datasets, however, 

is sufficient to define the amount of exhumation that occurred 

at the basin scale. Extensive regional exhumation, including 

removal of entire geologic formations across much of the 

basin, makes any reconstruction of the basin’s stratigraphy by 

projection of preserved strata across the eroded areas impossible, whereas estimates of the amount of exhumation from 

fission-track thermochronology or vitrinite-reflectance profiles 

have only a limited value for basin studies, owing to restricted 

availability of fission-track data and inconsistent results from 

vitrinite-reflectance data. Moreover, exhumation estimates 

derived from thermal-history modeling, such as from fissiontrack and vitrinite-reflectance data, create an interdependence 

between the burial- and thermal-history components of basin 

models and may increase the uncertainty of model results.

As an alternative approach to the use of fission-track and 

vitrinite-reflectance data for estimating exhumation in the 

Colville Basin, we have developed a method based on a comparison of regional porosity-depth trends in well data. This 

approach provides increased spatial resolution relative to fission-track data and increased consistency relative to vitrinitereflectance data. Furthermore, it allows us to define the burial 

history as an independent variable within the thermal-history 

model, thereby simplifying the modeling process and reducing 

uncertainty in model results.

Approaches to Assessing Exhumation 

in the Colville Basin

Contractional deformation of Colville Basin fill in the 

Brooks Range foothills (fig. 1) has led to obvious denudation 

where high-relief structures created topographic relief (see 

approximate north limit of high-relief structures, fig. 1). Stratigraphic thicknesses measured in outcrops and from subsurface 

data can be projected across the eroded structures to estimate 
the amount of denudation that has occurred. Broad structural thickening of ductile, shale-rich formations, however, 

extends far northward of the zone of high-relief structures (T. 

Moore, written commun., 2005) and probably resulted in more 

widespread surface uplift and denudation. Furthermore, the 

high vitrinite reflectances measured in outcrops and near-surface samples from undeformed areas of the basin (Johnsson 

and others, 1999) suggest that exhumation also occurred in 

parts of the North Slope that have not undergone significant 

tectonic shortening. Apatite fission-track analyses confirm that 

exhumation has occurred across most of the Colville Basin 

and indicate that as much as ~5,500 ft of basin fill may have 

been removed from some undeformed areas (for example, 

O’Sullivan, 1996), suggesting that exhumation occurred on a 

regional scale. Thus, simple stratigraphic projections across 

individual structures provide a measure of only local differences in exhumation.

Alternative methods to stratigraphic projection for determining the amount of exhumation in a sedimentary basin generally rely on thermal-history modeling, in particular, fissiontrack and vitrinite-reflectance data (for example, Armagnac 

and others, 1989; Bray and others, 1992; Dow, 1977; Green 

and others, 1995). Both fission-track and vitrinite-reflectance 

164° 160° 156° 152° 148°

164° 160° 156° 152° 148°

68°

70°

Federal boundary

Alaska State line

EXPLANATION

0 20 40 60 80 100 MILES

Approximate north limit of high-relief structures

National Petroleum 

Reserve in Alaska

Arctic

National

Wildlife

Refuge

Chukchi Sea

Beaufort Sea

Prudhoe Bay

AXIS OF THE

BARROW ARCH

North limit of deformation

Point

Barrow

Map

area

North limit of Brooks Range

data can be used as maximum temperature indicators, and 

so the downhole trend through maximum temperature estimates derived from either fission-track or vitrinite-reflectance 

data approximates the paleothermal gradient at the time of 

maximum heating/burial. Projection of this gradient to the 

estimated surface temperature at the time of maximum burial 

provides an estimate of the amount of section removed.

Fission-track thermochronology (for example, 

O’Sullivan, 1996, 1999) and vitrinite-reflectance profiles 

(Armagnac and others, 1989) have been used in previous 

studies of exhumation in the Colville Basin; however, the 

published exhumation estimates from both fission-track and 

vitrinite-reflectance data are too sparse for confident regional 

interpolation and application in a basinwide burial-history 

model. Nonetheless, additional vitrinite-reflectance measurements on dispersed vitrinite that are available for numerous 

wells on the North Slope (Johnsson and others, 1999) could 

serve as a source of the basinwide estimates of exhumation 

that are needed for modeling. In many wells across the North 

Slope, however, the measured vitrinite reflectances appear 

to reflect deposition of recycled vitrinite (Houseknecht and 

Hayba, 1998). Therefore, reflectance-depth trends are difficult 

to interpret and, in many places, probably do not represent the 

Figure 1. Alaskan North Slope, showing locations of study area and key geographic and geologic features. North limit of deformation 

from T. Moore (written commun., 2005).

 Studies by the U.S. Geological Survey in Alaska, 2005
Estimating the Amount of Eroded Section in a Partially Exhumed Basin from Geophysical Well Logs 

true paleothermal gradient, reducing their usefulness as guides 

to the amount of exhumation that has occurred.

Additionally, multiple and conflicting vitrinite-reflectance datasets exist for many wells, increasing the uncertainty 

in exhumation estimates calculated from vitrinite-reflectance 

profiles. In a particularly extreme example (fig. 2), two 

vitrinite-reflectance datasets for the same well, but obtained by 

different laboratories, result in erosion estimates that differ by 

thousands of feet. The cause of such disagreements between 

vitrinite-reflectance datasets for North Slope wells is unclear. 

As a result, determination of preferred reflectance-depth trends 

in these wells is ambiguous. Moreover, such marked disagreement between datasets for the same well suggests that vitrinite-reflectance datasets for the North Slope should generally 

be regarded with skepticism.

Finally, the use of either fission-track or vitrinite-reflectance data to define the amount of exhumation in a basin can 

complicate burial/thermal-history modeling and increase the 

uncertainty of model results. Amounts of exhumation and the 

corresponding burial histories derived from paleotemperature 

indicators (that is, fission-track and vitrinite-reflectance data) 

will be dependent variables when applied within a thermal-hisPredicted maximum burial

surface (dataset 1)

Predicted maximum burial

surface (dataset 2)

-6,000

-4,000

-2,000

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

0.1 1 10

VITRINITE REFLECTANCE, IN PERCENT

DEPTH, IN FEET

Figure 2. Vitrinite reflectance versus depth in the Itkillik River Unit 1 well on the Alaskan North Slope (fig. 1). Single best-fit trendlines 

are projected through two apparently conflicting vitrinite-reflectance datasets to predicted maximum-burial surfaces corresponding to 

R0=0.2 percent. Implied depths of burial and exhumation based on the two datasets differ by thousands of feet.
tory model because the amount of inferred exhumation will 

vary with the assumed values of thermal parameters (that is, 

thermal gradient, thermal conductivity, heat flow). Thus, the 

accuracy of burial- and thermal-history models is limited by 

the typically large uncertainties in paleoheat flow and thermal 

conductivity (see Deming and others, 1990). For the purposes 

of burial/thermal-history modeling, we would prefer that the 

amount of exhumation and, therefore, the maximum burial 

depth be determined independently from thermal parameters.

Estimating Amount of Exhumation from 

Porosity Logs

To avoid the problems with fission-track and vitrinite-reflectance methods, we have developed an alternative 

methodology for estimating amount of exhumation, based on 

an analysis of porosity-depth trends in sonic-porosity logs. 

Owing to the largely irreversible effect of sediment compaction (for example, Hedberg, 1936; Magara, 1980), porositydepth trends in well data can be used to estimate the amount 

of missing sedimentary section in areas that have undergone 

significant erosion. Although core-porosity measurements 

are typically made for only a small part of the total sedimentary section penetrated in a well, various commonly acquired 

geophysical logs can be used to estimate porosity for the entire 

borehole. Most notably, sonic-transit-time logs have been used 

to determine downhole porosity specifically as a means of 

defining shale-compaction trends for estimating erosion (for 

example, Magara, 1976; Issler, 1992; Nelson and Bird, 2005).

Numerous empirical transforms relate sonic velocity 

to porosity in sedimentary rocks. Nelson and Bird (2005) 

reviewed several of these transforms and noted that the 

acoustic formation factor defined by Raiga-Clemenceau and 

others (1988) provides a relatively accurate means of calculating porosity (φ) from sonic transit time (t) as a function of 

rock type:

where t

ma is the sonic transit time for the rock matrix at zero 

porosity and x is an exponent specific to the matrix lithology. 

Issler (1992) adopted this approach for defining porosity in 

shales in the Beaufort-Mackenzie Basin of northern Canada, 

and the compaction curves derived from those porosities 

became the basis for estimating the amount of erosion that 

had occurred in different parts of the basin. Issler defined 

a reference compaction (porosity-depth) curve from sonicporosity logs in a part of the basin that has undergone little or 

no erosion and compared that curve with the sonic-porosity 

logs in wells within other parts of the basin. The vertical offset 

between the reference curve and the sonic-porosity logs represents the amount of erosion that has occurred at each wellsite.

Working with well data from the Alaskan North Slope 

and the Beaufort Sea, Rowan and others (2003) expanded 

upon Issler’s (1992) use of the acoustic formation factor 

(Raiga-Clemenceau and others, 1988) for defining compaction curves from sonic-porosity logs, incorporating not only 

shale but also all siliciclastic rocks. Rowan and others normalized gamma-ray logs for each well to create shale-fraction 

(vshale) logs, which provide a measure of the lithology for each 

sonic-transit-time measurement. Combining shale-fraction 

logs and the corresponding sonic-transit-time logs from wells 

in the noneroded offshore part of the basin, they determined 

matrix transit times (52 and 67 ms) and x values (2.05 and 

2.19) for shale and sandstone end members, respectively. They 

then calculated sonic-porosity logs, using these parameters 

in conjunction with sonic-transit-time logs for 19 wells in 

offshore and coastal areas where stratigraphic evidence indicates that erosion is minimal, and used these sonic-porosity 

logs as a basis for defining compaction curves for the basin. 

They edited the logs to remove invalid porosities caused by 

permafrost and borehole washouts; also, they excluded zones 

of undercompacted sediment caused by pore-fluid overpressuring to improve the resolution of normal compaction trends 

in the data. Finally, they used only the sections of the logs 

corresponding to the Brookian megasequence (Cretaceous and 

Tertiary age) to define compaction trends in order to avoid 

potential differences in porosity trends across the underlying 

Lower Cretaceous unconformity. The edited logs were compiled by rock type, allowing a definition of compaction curves 

that represent the porosity-depth behavior of sandstone, shale, 

and a nominal siltstone (that is, vshale= 0.5). They selected an 

exponential form of the equation proposed by Athy (1930) for 

the compaction curves:

where φz is the porosity fraction at depth z, φ0 is the initial 

porosity fraction, and b is a variable that reflects the curvature 

of the porosity-depth trend. Alternative approaches to an exponential compaction curve include linear and reciprocal forms 

(for example, Falvey and Middleton, 1981; Hunt and others, 

1998). Whereas Nelson and Bird (2005) used a two-point linear fit to represent shale porosity in a recent study of porositydepth trends on the Alaskan North Slope, Rowan and others 

preferred the exponential form more commonly used in basin 

modeling. From a visual fitting of the data, the parameters that 

they defined are listed in table 1.

Application to the Colville Basin

Rowan and others’ (2003) compaction parameters, 

derived from nonexhumed parts of the Colville Basin (fig. 

1), provide a frame of reference for judging the amount of 

exhumation that has occurred at other wellsites in the basin. 

A porosity-depth curve modeled from Rowan and others’ 

parameters could be fitted to the corresponding sonic-porosity log by adjusting the datum of the modeled curve relative 

to the current ground surface to achieve agreement with the 

 Studies by the U.S. Geological Survey in Alaska, 2005

φ = − 









 1

1

t

t

ma x

,

φ φ z = −bz 0 exp( ),
Estimating the Amount of Eroded Section in a Partially Exhumed Basin from Geophysical Well Logs   

measured porosities. Given that significant sedimentation had 

not occurred after exhumation, the difference between the 

adjusted datum and the current ground surface would indicate 

the total stratal thickness that has been removed since the time 

of maximum burial.

Before the approach to estimating exhumation outlined 

above could be applied throughout the Colville Basin (fig. 1), 

we needed to construct a second set of porosity-depth curves 

derived from Lower Cretaceous and older strata to be used 

in conjunction with the porosity-depth functions of Rowan 

and others (2003). Maximum burial in the Colville Basin 

resulted from west-to-east, axial progradation of the clastic 

Brookian megasequence during the Cretaceous and Tertiary 

(Molenaar, 1985). Rowan and others’ exclusive use of well 

data from parts of the basin that have not undergone significant exhumation since the time of maximum burial led them 

to prefer wells in the east half of the basin (fig. 3), where the 

Brookian megasequence is predominantly Late Cretaceous 

and Tertiary. In contrast, the Brookian megasequence in the 

west half of the basin is dominated by Aptian through Albian 

strata that appear to have followed different porosity-depth 

paths than the younger sedimentary rocks, possibly owing to 

differences in sediment composition. The calculated sonic 

porosity in the Nechelik 1 well is plotted against the porosity 

predicted by using Rowan and others’ parameters in figure 4. 

This well, which is located adjacent to the northeastern part 

of the National Petroleum Reserve in Alaska (NPRA, fig. 1), 

penetrates a thick succession of Aptian through Albian strata 

capped by a thinner section of younger strata. Within the 

Aptian through Albian section, Rowan and others’ porositydepth functions generally overestimate porosity with increasing depth. In contrast, the porosity log for overlying Upper 

Cretaceous through Tertiary rocks agrees closely with calculated values. In this and similar wells that sample both porosity-depth trends, Rowan and others’ compaction curves can 

be used to determine the amount of exhumation by applying 

them to only the upper part of the porosity log, corresponding 

to Upper Cretaceous and younger strata. Most of the western 

160° 155° 150°

160° 155° 150° 145°

68°

69°

70°

71°

National Petroleum Reserve in Alaska

Beaufort Sea

Arctic National

Wildlife Refuge

Well used by Rowan and others (2003)

Well used in this study

EXPLANATION 0 25 50 75 100

Figure 3. Alaskan North Slope, showing distribution of wells used in definition of compaction parameters by Rowan and others (2003) 

and in this study.
0

2,000

4,000

6,000

8,000

10,000

-0.20 -0.10 0.00 0.10 0.20

DEPTH BELOW THE KELLY BUSHING, IN FEET

Albian and older

post-Albian

Bottom of well

POROSITY DIFFERENCE (PORE FRACTION)

Figure 4. Difference (x-value) between calculated sonic porosity and porosity predicted by using 

Rowan and others’ (2003) porosity-depth functions versus depth below the Kelly bushing in a well 

on the Alaskan North Slope (fig. 1). Positive x-values occur where predicted porosity is less than 

calculated, and negative x-values where predicted porosity is greater than calculated. Orange and 

green markers represent pure sandstone (vshale<0.01) and shale (vshale>0.99), respectively; gray 

markers represent all intermediate mixtures, as defined by shale-fraction log.

 Studies by the U.S. Geological Survey in Alaska, 2005
Estimating the Amount of Eroded Section in a Partially Exhumed Basin from Geophysical Well Logs 

part of the Colville Basin, however, has undergone extensive 

to complete erosion of the Upper Cretaceous through Tertiary 

stratigraphic section, and so porosity-depth curves must be 

calibrated to pre-Upper Cretaceous strata to estimate the amount 

of exhumation in that area.

We defined porosity-depth curves for the Lower Cretaceous and older strata by selecting wells that penetrated the 

Brookian megasequence where it comprises significant thicknesses of both Upper Cretaceous through Tertiary and Aptian 

through Albian strata. We combined the well stratigraphy of 

Bird (1988a) and Nelson and others (1998) with updates by 

Houseknecht (2003, 2004). The selected wells lie primarily in 

the northeastern NPRA. Amounts of exhumation were estimated for 15 wells (fig. 3; see table 3 for names and exhumation 

estimates) by visually fitting Rowan and others’ (2003) compaction curves to the shallow sections of porosity logs corresponding to Upper Cretaceous through Tertiary rocks. The lower sections of the porosity logs were then depth shifted, according to 

the estimated amount of exhumation, and compiled into a single 

dataset. According to the methodology of Rowan and others, the 

grouped porosity logs were sorted lithologically, as defined by 

the corresponding shale-fraction logs; zones of anomalous sonic 

porosity were identified; and the corresponding log values were 

removed to enhance resolution of the normal porosity-depth 

trends. Exponential porosity-depth curves were then defined for 

each of the sand (vshale<0.01), shale (vshale>0.99), and siltstone (0.49<vshale<0.51) end members in pre-Late Cretaceous 

rocks (table 2). The combined data were plotted for each endmember rock type along with the corresponding porosity-depth 

curves of Rowan and others and from this study (fig. 5). For all 

three rock types, the porosity-depth curves defined in this study 

fit the data significantly better than do Rowan and others’ curves 

in pre-Late Cretaceous strata.

These new curves provide the means for extending the 

exhumation analysis into parts of the Colville Basin where 

Upper Cretaceous and Tertiary strata have been removed. For 

each of 145 wellsites across the North Slope and adjacent 

offshore area, we calculated and edited sonic-porosity logs for 

obviously invalid or anomalous values caused by permafrost, 

undercompaction, borehole washouts, and rock-type misidentification (fig. 6). A second set of porosities was predicted for 

each well, using the shale-fraction logs to define rock type 

and the porosity-depth data listed in tables 1 and 2 to calculate 

porosity as a function of rock type and depth. The calculated 

and predicted porosities were compared numerically and visually to achieve an approximate best fit. By adjusting the datum 

of the porosity-depth curves to account for the stratigraphic 

thickness removed by erosion, we obtained a minimum rootmean-squared error for the predicted porosity values (fig. 7). 

The corresponding vertical-datum shift represents an initial 

estimate of the amount of erosion that has occurred at the well 

site since the time of maximum burial. Visual assessment of the 

data fit allowed adjustment from the statistical best fit as needed 

in recognition of irregularities remaining in the edited sonicporosity logs (fig. 8). The resulting exhumation estimates are 

listed in table 3.

Validation of Results

The absolute validity of the exhumation estimates for 

the Colville Basin (fig. 1) presented here cannot be verified in 

most places, owing to lack of a true reference value for comparison, although more qualitative analyses of validity are possible. A computer-contoured exhumation map of the Colville 

Basin (fig. 9) was created by interpolation of the exhumation 

estimates listed in table 3, using an inverse-distance-weighted 

algorithm. Moderate and consistent variation between adjacent 

wellsites produces smooth, regular gradients across the study 

area (fig. 1), with little evidence of disagreement between 

adjacent wellsites. Although an explanation of the causes of 

these exhumation patterns is beyond the scope of this chapter, 

the trends shown in figure 9 are consistent with basin morphology and stratigraphy. For example, the maximum denudation is calculated in the deformed southern part of the basin 

(see north limit of deformation, fig. 1), where exhumation is 

expected to be the greatest. Conversely, minimum exhumation is calculated in the northwestern and northeastern parts of 

the basin, both of which represent Tertiary depocenters where 

stratigraphic and fission-track data indicate that deposition was 

ongoing during exhumation of the basin to the south (Grantz 

and May, 1988; Bird and Molenaar, 1992; Sherwood and others, 1998; O’Sullivan, 1999). In addition, exhumation is shown 

to increase westward along the coastline of NPRA toward 

Point Barrow (fig. 1), coinciding with shallowing of the Barrow arch, a well-defined structural feature that existed during 

deposition of the Brookian megasequence (fig. 1; Bird and 

Molenaar, 1992). Seismic and well data clearly demonstrate 

erosional truncation of Brookian strata in the Point Barrow 

Rock type φ0

b

(ft −1)

Sandstone 0.5 0.0000884

Shale 0.4 0.0001280

Siltstone 0.44 0.0001158

Table 1. Compaction parameters for Late 

Cretaceous and younger rocks in the Colville Basin, 

northern Alaska

[See figure 1 for location. φ0, pore fraction. From Rowan and 

others (2003)]

Rock type φ0

b

(ft −1)

Sandstone 0.45 0.0001280

Shale 0.62 0.0002286

Siltstone 0.48 0.0001524

Table 2. Compaction parameters for Albian andolder 

rocks in the Colville Basin, northern Alaska 

[See figure 1 for location. φ0, pore fraction]
Figure 5. Composite sonic porosity versus depth for sand (vshale<0.01), siltstone (0.49<vshale<0.51), and shale (vshale>0.99) lithologic end member

strata, with corresponding porosity-depth curves from Rowan and others (2003) and this study. Data from 15 wells shown in figure 3 and listed in tabl

EXPLANATION

this studyRowan and others (2003)

0

2,0004,0006,0008,000

10,00012,00014,00016,00018,000

0.00 0.10 0.20 0.30 0.40 0.50 0.60

DEPTH, IN FEET

SONIC POROSITY (PORE FRACTION)

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.00 0.10 0.20 0.30 

A B C
Estimating the Amount of Eroded Section in a Partially Exhumed Basin from Geophysical Well Logs 

0.00 0.10 0.20 0.30 0.40

SONIC POROSITY (PORE FRACTION)

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

0.00 0.10 0.20 0.30 0.40

MEASURED DEPTH DOWNHOLE FROM KELLY BUSHING, IN FEET

Porosity

Sandstone

Shale

Undercompaction

in shale-rich zones(?)

Permafrost zone

Miscalculated values in

carbonate-rich section

Possible borehole-washout 

effects

EXPLANATION

A B

Figure 6. Example of calculated sonic-porosity data with aberrant and potentially erroneous values highlighted (A) and after editing 

(B). Note that relatively minor variations from expected trends were not removed to avoid biasing results of best-fit analysis.

area, where the Barrow arch reaches its shallowest levels (for 

example, Bird and Andrews, 1979; Bird, 1988b).

For a more quantitative perspective on the validity of logderived exhumation estimates, we examined borehole stratigraphy from closely spaced wellsite pairs for evidence of the 

relative amount of exhumation. Although regional variations 

in the stratigraphic thickness of the Brookian megasequence 

make a basinwide assessment of relative exhumation difficult 

and uncertain, local variations in thickness are typically small 

enough to allow a comparison of the stratigraphic depths in 

adjacent wells as a measure of relative amount of exhumation. 

For example, in the eastern part of the study area (fig. 1), the 

measured depth to the base of the Brookian megasequence 

decreases southward from 12,364 ft subsea at the West Kavik 

1 well to 3,450 ft subsea at the Kemik 1 well (Nelson and 

others, 1998). Assuming a constant thickness for Brookian 

strata between the two wells, the implied southward increase 

in the amount of exhumation is ~9,000 ft. In comparison, 

the exhumation estimates for these wells differ by 10,500 ft 

(table 3). Given that the Brookian megasequence generally 

thickens southward into the Colville foredeep, the assumption 

of constant thickness probably results in underestimation of 

the difference in amount of exhumation at the two wellsites. 

Thus, the greater relative amount of exhumation calculated 

from sonic-porosity logs is a reasonable alternative. Insofar as 

the wells are spaced sufficiently closely—that is, within ~20 

mi—to allow such comparisons, each of the exhumation estimates presented in this study has been crosschecked against 

stratigraphic data to ensure that the results are consistent with 

the geology. A few wells within the deformed part of the basin 

were excluded from the final analysis, owing to incompatibility of the exhumation estimates with stratigraphic constraints, 

possibly resulting from the preservation of relatively high 

porosities within thick overpressured zones. We note that the 

strata penetrated in wells south of the north limit of deformation (fig. 1) may have undergone structural thickening. 

Therefore, both the depositional stratigraphy and the original 

porosity-depth trends during deposition may be difficult to 

discern, and so the exhumation estimates in the areas of these 

wells are less certain than for wells in undeformed areas.
0

2,0004,0006,0008,000

10,00012,00014,000

0.00 0.10 0.20 0.30 0.40

SONIC POROSITY

(PORE FRACTION)

MEASURED DEPTH DOWNHOLE FROM KELLY BUSHING, IN FEET ~6,000-6,500 ft of erosion implied Porosity log Sandstone Shale

Sandstone curveShale curveSilt curve

EXPLANATION

A

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0 1,000 2,000 3,000 4,000 5,000 

DEPTH OF EROSION,

IN FEET

STANDARD ERROR (POROSITY FRACTION)

Minimum error, 0.02711

at a depth of 6,025 ft

B

Figure 7. Visual comparison of sonic-porosity log and end-member porosity-depth curves (

A) allows initial estimation of amount of erosion from ver

curves. Root-mean-square-error-minimization routine (

B) determines precise amount of erosion required to best fit sonic-porosity data to porosities c

depth functions.
0

2,0004,0006,0008,000

10,00012,00014,000

0.00 0.10 0.20 0.30 0.40

MEASURED DEPTH DOWNHOLE FROM KELLY BUSHING, IN FEET

Standard Error, 0.02711

A

B

Porosity logSandstoneShaleSandstone curveShale curveSilt curve

EXPLANATION

0.00 0.10 0.20 

SONIC

POROSITY (PORE FRACTION)

Standard 

Figure 8. Examples of sonic-porosity log with end-member porosity-depth curves vertically shifted to account for erosion, using best-fit value of 6,0amount of 6,500 ft (

B), chosen to diminish effects of relatively high and potentially erroneous porosities occurring between ~7,500- and 8,000-ft depth. 

erosion results in a small increase from 0.02711 to 0.02779 in calculated standard error of pore fraction (~2.5 percent) but arguably improves agreemevalues and porosity-depth curves.
12  Studies by the U.S. Geological Survey in Alaska, 2005

Well Latitude

(°N.)

Longitude

(°W.)

Estimated

exhumation

(ft)

Akulik #1 69.000253 163.479263 6,669

Alaska State A–1 70.189183 146.011848 0

Alaska State C–1 70.139890 146.241640 0

Alaska State F–1 70.227261 146.360470 0

Alaska State J–1 69.858346 146.568318 550

Alpenglow 1 70.151781 147.468380 450

Alpine 1 70.333210 151.010300 650

Alpine 3 70.366630 151.011500 800

Amethyst State 69.543530 150.310300 4,875

Atigaru Point 1* 70.552791 151.722177 650

Aufeis Unit 1 69.149937 149.571919 7,600

Awuna 1 69.153205 158.022436 9,000

Badami 1 70.150620 147.085030 0

Badami 2 70.190210 147.168590 0

Beaufort Sea Block 54–1 70.492310 147.982150 0

Beli Unit 1 69.710768 146.535486 6,500

Bergschrund 1* 70.352240 150.916300 700

Big Bend 69.161959 152.267107 8,000

Brontosaurus 70.909018 157.245604 3,400

Burglin 33–1 70.173280 148.577590 700

Bush Federal 69.658610 149.033330 5,800

Canning B–1 69.663845 146.275276 9,525

Cape Halkett 1* 70.767403 152.466727 525

Colville Delta 1* 70.476271 150.396681 525

Colville Delta 2 70.472090 150.267800 250

Colville Delta 3 70.437320 150.329410 300

Colville River 70.311649 150.653900 1,000

Colville St 1 70.360600 150.265280 425

Drew Point 1* 70.879762 153.899973 1,250

E. de K. Leffingwell 70.017837 146.517428 300

Eagle Creek 1 68.716878 162.549336 11,000

East Harrison Bay 1 70.492778 150.031667 450

East Kuparuk Unit 1 69.287815 150.156460 7,000

East Kurupa Unit 1 68.846509 153.317890 9,700

East Mikkelsen Bay 1 70.152020 146.903010 0

East Simpson 1 70.917785 154.617988 1,800

East Simpson 2 70.978607 154.673874 1,800

East Teshekpuk* 70.569920 152.943622 1,500

East Umiat 69.344540 151.742690 7,000

Echooka Unit 69.391770 148.265700 9,000

Fin Creek 1 69.500312 147.600695 8,000

Fiord 2 70.381100 150.752800 400

Fiord 3 70.369010 150.742700 500

Foggy Island 1 70.287850 147.904250 0

Grandstand 1 68.966110 151.917221 8,000

Gubik 1 69.422778 151.447222 5,300

Gubik 2 69.432500 151.464444 5,000

Gull Island 2 70.365990 148.364250 0

Gwydyr Bay 70.419870 149.018060 150

Gyr 1 69.657070 147.279390 5,500

Heavenly 1 69.729283 150.179419 3,200

Hemi Springs 3 70.136371 148.716775 650

Table 3. Exhumation estimates at 145 wellsites on the Alaskan North Slope.

[See figure 1 for location. Asterisk, well used to define compaction parameters]
Estimating the Amount of Eroded Section in a Partially Exhumed Basin from Geophysical Well Logs 13

Iko Bay 71.170229 156.167021 2,900

Ikpikpuk 1 70.455468 154.331330 2,325

Inigok 1* 70.004858 153.099126 3,225

Itkillik River Unit 1 70.065934 150.853092 1,525

Itkillik Unit 1 69.455482 150.575587 5,500

J. W. Dalton 1* 70.920497 153.137526 1,200

Kalubik 1 70.492430 150.275000 0

Kalubik Creek 1 70.404980 150.070240 225

Kavik Unit 1 69.631846 146.569395 10,800

Kemik 1 69.440511 147.269940 14,000

Kookpuk 1 70.292760 150.475140 0

Kugrua 1 70.587025 158.662031 3,200

Kuparuk Uplands (Ekvik) 69.787800 150.434100 3,000

Kuukpik 3 70.462130 150.559620 800

Kuyanak 1 70.931522 156.037813 2,700

Lake 79 Federal 1 70.079742 147.767095 650

Little Twist 69.140713 152.818461 9,000

Long Island 1 70.473350 149.016120 0

Lupine Unit 69.101180 148.618566 10,000

Meltwater North 2A 70.049688 150.418557 1,800

Mikkelsen Bay St 1 70.135190 147.197430 0

Nanuk 1 70.293120 150.979100 1,350

Narvaq 1 69.979200 150.116670 1,900

Nechelik 1* 70.392778 150.978889 650

Niakuk 5 70.367620 148.194470 250

Nora Federal 69.552059 148.752318 6,500

North Franklin Bluffs 70.037110 148.684510 850

North Inigok 1 70.257589 152.765982 1,850

North Kalikpik 1* 70.509176 152.367868 1,525

Northwest Eileen St 1 70.365278 149.358611 200

Nuiqsut 1 70.334100 151.168900 1,300

OCS–Y–1320–1 Crackerjack 1 71.418810 165.541530 0

OCS–Y–0267–1 Fireweed* 71.087982 152.603195 350

OCS–Y–0280–1 Antares 1* 71.035980 152.723724 325

OCS–Y–0302–1 Mars* 70.843000 152.071800 625

OCS–Y–0334–1 Mukluk 70.683342 150.919968 375

OCS–Y–0338–1 Phoenix 70.717216 150.427811 175

OCS–Y–0742–1 Cabot 71.324122 155.212231 1,500

OCS–Y–0804–1 Orion 70.956180 152.062950 475

OCS–Y–0996–1 Diamond 71.332880 161.679880 2,800

OCS–Y–1413–1 Burger 1 71.251390 163.194580 2,300

OCS–Y–1482–1 Klondike 1 70.710880 165.249750 650

Peard 1 70.715647 159.000706 3,150

Pipeline St 1 69.826593 148.904421 2,800

Placid St 70.249650 148.818850 500

Point McIntyre St 3 70.390800 148.580990 300

Point Thomson Unit 1 70.174153 146.337390 0

Point Thomson Unit 2 70.163267 146.515410 0

Point Thomson Unit 3 70.172349 146.252800 0

Prudhoe Bay St 1 70.323378 148.542250 175

Ruby State 1 70.054300 150.055600 1,500

Sag River St 1 70.254720 148.342470 300

Well Latitude

(°N.)

Longitude

(°W.)

Estimated

exhumation

(ft)

Table 3. Exhumation estimates at 145 wellsites on the Alaskan North Slope.—Continued

[See figure 1 for location. Asterisk, well used to define compaction parameters]
14  Studies by the U.S. Geological Survey in Alaska, 2005

Schrader Unit 1 69.177038 151.010910 8,000

Seabee 1 69.380146 152.175335 6,500

Sequoia 70.00995 148.99863 1,500

Shale Wall Unit 69.032404 150.863605 8,000

SOCAL Mobil 33–29E 70.367390 149.396690 400

South Barrow 18 71.239717 156.311421 2,700

South Barrow 20 71.232505 156.336137 2,700

South Harrison Bay 1* 70.422974 151.727949 625

South Meade 1 70.614979 156.882605 3,350

South Simpson 1 70.806667 154.981667 1,950

Susie Unit 69.518720 148.924740 7,000

Tarn 1 70.182440 150.397070 2,000

Tarn 3 70.181810 150.323300 2,000

Tarn 4 70.167490 150.262500 2,000

Temptation 1 70.392070 151.153100 500

Thetis Island 1 70.553250 150.162950 400

Till 1 70.401190 150.584750 700

Toolik Federal 1 70.073177 148.392870 800

Toolik Federal 2 70.072018 149.206688 1,100

Toolik Federal 3 70.076431 149.900724 1,500

Tulaga 69.703896 151.075789 4,500

Tulageak 1 71.189340 155.733573 2,600

Tulugak 1 68.984812 151.329761 8,000

Tunalik 1 70.205960 161.069146 3,000

Tungak Creek 1 69.883904 162.273194 5,000

Ugnu 70.381610 149.826060 500

W T Foran 1* 70.826847 152.285864 425

Walakpa 1 71.099344 156.884339 3,325

Walakpa 2 71.050003 156.952774 3,400

West Dease 1 71.159068 155.629177 2,700

West Fish Creek 1 70.322002 152.065477 1,100

West Kavik 69.770247 147.185561 3,500

West Kuparuk 70.335278 149.306667 650

West Kurupa Unit 1 68.882950 155.254968 7,200

West Mikkelsen St 1 70.182240 147.378340 0

West Mikkelsen St 2 70.221825 147.190020 0

West Sak 4 (25667) 70.238593 149.957774 1,200

West Staines 18–9–23 70.137553 146.388160 0

Wolfbutton 25–6–9 69.842300 149.759880 2,500

Wolfbutton 32–7–8 69.920450 150.194400 2,200

Yukon Gold 1 70.041320 146.294820 700

Table 3. Exhumation estimates at 145 wellsites on the Alaskan North Slope.

[See figure 1 for location. Asterisk, well used to define compaction parameters]

Well Latitude

(°N.)

Longitude

(°W.)

Estimated

exhumation

(ft)
Estimating the Amount of Eroded Section in a Partially Exhumed Basin from Geophysical Well Logs 15

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EXPLANATION

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Figure 9. Alaskan North Slope, showing contours (in feet) of estimated amount of exhumation calculated from 

sonic-porosity logs of wells in study area (fig. 1) and nearby offshore areas. ANWR, Alaska National Wildlife 

Refuge; NPRA, National Petroleum Reserve in Alaska.

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EXPLANATION

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166° 164° 162° 160° 158° 156° 154° 152° 150° 148° 146°

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Figure 10. Alaskan North Slope, showing contours (in feet) of estimated amount of exhumation derived from 

downhole vitrinite-reflectance profiles of wells in study area (figs. 1, 3) and nearby offshore areas. ANWR, Arctic 

National Wildlife Refuge; NPRA, National Petroleum Reserve in Alaska.
16  Studies by the U.S. Geological Survey in Alaska, 2005

Where fission-track or vitrinite-reflectance data are 

available to provide alternative exhumation estimates, we 

compared the various results as another measure of the validity of the sonic-porosity approach to estimating amount of 

exhumation. Exhumation estimates derived from fission-track 

analysis, vitrinite-reflectance data, and sonic-porosity logs 

for the six wells in the Colville Basin for which fission-track 

analyses have been published (O’Sullivan, 1998) are listed in 

table 4. The exhumation estimates derived from fission-track 

and sonic-porosity data agree within 1,000 ft for four of the 

six wells and within 1,500 and 2,500 ft, respectively, for the 

other two wells, Tunalik 1 and Inigok 1. However, vitrinitereflectance data give more varying results than either of the 

other methods, despite efforts to remove clearly aberrant 

data points (for example, recycled vitrinite). In particular, the 

vitrinite-reflectance method demonstrates gross discrepancies 

of many thousands of feet relative to alternative methods for 

the Walakpa 1 and Alaska State C–1 wells. Both wells lie near 

the Alaska coastline, the Walakpa 1 well on Point Barrow and 

the Alaska State C–1 well adjacent to the northwest corner of 

the Alaska National Wildlife Refuge (fig. 1). Neither of these 

wells is located on a structural feature likely to produce such 

large amounts of exhumation. Moreover, the Alaska State C–1 

well penetrates several thousand feet of strata deposited coincident with and subsequent to the latest known exhumation 

event in the basin (O’Sullivan, 1999) and so the stratigraphic 

evidence from this well suggests that little or no exhumation 

occurred in that area. Thus, the large amount of exhumation 

indicated by vitrinite-reflectance trends for the Walakpa 1 

and Alaska State C–1 wells is unlikely, and lower exhumation 

estimates consistent with the fission-track and sonic-porosity 

data are preferred.

For this small set of wells with published fission-track 

analyses, the amounts of exhumation estimated from fissiontrack data and sonic-porosity logs appear to be more reliable 

than those estimated from vitrinite-reflectance profiles. The 

absence of fission-track data for other wells in the Colville 

Basin (fig. 1) precludes more extensive comparison of all three 

methods. However, comparison of the exhumation estimates 

from sonic-porosity and vitrinite-reflectance data in other 

wells further exemplifies the advantages of the sonic-porosity approach. Contours of exhumation in the study area (fig. 

1) created by interpolation of values estimated from borehole 

vitrinite-reflectance trends are mapped in figure 10. For each 

well from which vitrinite-reflectance data are available, the 

amount of exhumation was estimated by the trendline-projection method of Dow (1977). A vitrinite reflectance of 

0.2 percent was assumed for the surface value at the time of 

maximum burial, in accordance with typical surface values 

cited by other workers (for example, Hunt, 1979; Armagnac 

and others, 1989). Spurious data points and obvious irregularities in the vitrinite-reflectance data were removed to 

provide the best possible estimates.

In comparison with figure 9, figure 10 demonstrates similar regional trends, such as increasing amounts of exhumation 

toward the southern foothills and decreasing amounts toward the 

Well

Exhumation estimate (ft)

 Fission

 track

Vitrinite

reflectance

 Sonic

 porosity

Alaska State C–1 0 110,261 0

Inigok 1 5,577 1,989 3,225

Kemik 2 17,388 17,605 2

17,800

Seabee 1 6,890 6,456 6,500

Tunalik 1 4,265 5,321 3,000

Walakpa 1 3,937 9,702 3,325

1

No vitrinite-reflectance data available; estimate derived from the Alaska 

State D–1 well, ~4.5 mi away.

2

Estimated by stratigraphic extrapolation from the Kemik 1 well, ~4.5 mi 

away.

Table 4. Comparison of exhumation estimates for the Colville 

Basin, northern Alaska, derived from fission-track analysis 

(O’Sullivan, 1998), vitrinite-reflectance data (Johnsson and others, 

1999), and sonic-porosity logs (this study)

[Amount of exhumation was estimated by projecting log-linear best-fit curve 

for vitrinite reflectance (R0) versus depth, assuming that paleosurface at time 

of maximum burial coincided with R0= 0.2 (Dow, 1977)]

northwestern and northeastern offshore areas. Yet relative to the 

smooth gradients shown in figure 9, figure 10 displays a marked 

irregularity between wells, and in the coastal areas, the predicted 

amounts of exhumation generally are substantially greater than 

those determined from sonic-porosity data (fig. 9; table 3). 

Given that the stratigraphic and fission-track data (for example, 

Bird and Molenaar, 1992; O’Sullivan, 1999) agree with the 

sonic-porosity data, the sonic-porosity approach appears to 

provide more accurate results, as well as being more consistent 

between wells, than the vitrinite-reflectance approach.

Conclusion

Restoration of original depositional thicknesses of basin 

fill in partially exhumed basins is a fundamental problem in 

constructing burial-history models. We have developed an 

approach to estimating the eroded thickness across a basin 

by using widely available borehole geophysical logs. In the 

Colville Basin (fig. 1), our method produces results similar to 

those from fission-track analysis, but the greater availability of 

geophysical logs relative to fission-track data allows a higher 

spatial resolution in the exhumation estimates presented here 

than in published fission-track studies. However, results from 

both the fission-track method and our sonic-porosity approach 

commonly contrast markedly with those from vitrinite-reflectance data. Furthermore, the vitrinite-reflectance data are 

demonstrably unreliable predictors of amounts of exhumation, 

yielding estimates that are inconsistent from one place to the 

next (fig. 10) and, in many places, inaccurate. In the Colville 
Estimating the Amount of Eroded Section in a Partially Exhumed Basin from Geophysical Well Logs 17

Basin, a burial-history model based on vitrinite-reflectancederived exhumation estimates clearly will not reflect a reasonable basin evolution, whereas a model based on sonic-porosity-derived exhumation estimates, as mapped in figure 9, will 

depict a much more plausible one.

The implications of this study for basin modeling elsewhere are unclear with regard to model accuracy. The reliability of vitrinite-reflectance data for estimating amount of 

exhumation may not be a significant concern in many basins, 

and so these data could provide exhumation estimates with 

similar or greater accuracy than those from sonic-porosity 

logs. However, a significant advantage of the sonic-porosity approach is that the data are independent of the thermal 

evolution of the basin. Fission-track and vitrinite-reflectance 

data, in contrast, are paleotemperature indicators that require 

assumed values for thermal gradient or heat flow and thermal conductivity to calculate the stratigraphic thicknesses of 

denuded sections. Therefore, our approach uniquely results in 

thermal-history models in which burial-history parameters are 

independent variables, simplifying the modeling process and 

reducing overall uncertainty.

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