Estimation of the Future Rates of 

Oil and Gas Discoveries in the 

Western Gulf of Mexico

GEOLOGICAL SURVEY PROFESSIONAL PAPER 1252
Estimation of the Future Rates of 

Oil and Gas Discoveries in the 

Western Gulf of Mexico

By L. J. DREW, J. H. SCHUENEMEYER, and W. J. BAWIEC

GEOLOGICAL SURVEY PROFESSIONAL PAPER 1252

A discovery-process model adapted to 

forecast future rates of oil and gas 

discoveries under the conditions of 

economic truncation

UNITED STATES GOVERNMENT PRINTING O FFI CE, W ASH I N GT O N: 1 9 8 2
UNITED STATES DEPARTMENT OF THE INTERIOR 

JAMES G. WATT, Secretary

GEOLOGICAL SURVEY 

Dallas L. Peck, Director

Library of Congress Cataloging in Publication Data

Drew, Lawrence J.

Estimation of the future rates of oil and gas discoveries in the western Gulf of Mexico.

(U.S. Geological Survey professional paper ; 1252)

Bibliography: p.

1. Petroleum in submerged lands Mexico, Gulf of Mathematical models. 2. Gas, Natural, in submerged lands Mexico,

Gulf of Mathematical models. 3. Prospecting Mexico, Gulf of Mathematical models. I. Schuenemeyer, J. H.

n. Bawiec, W. J. HI. Title. IV. Series: Geological Survey professional paper ; 1252.

TN872.A5D73 553.2 (8W726 81-6768

AACR2 

______________ _____ ___ _____________________________Rev.

For sale by the Superintendent of Documents, U.S. Government Printing Office

Washington, D.C. 20402
CONTENTS

Introduction 

Compiling the exploratory-well data file 

Analyzing the historical rates of discovery 

Overall discovery rate

Discovery rates for each size class 

Partitioning the data

Page

1 

1 

1 

3 

3

- 7 

9

Page

Estimating the parameters of the discoveryEstimating the parameters for the

Miocene-Pliocene trend 16

Estimating the parameters of the

discovery-process model Continued 

Estimating the incremental future rates of 

oil and gas field discoveries in the 

Miocene-Pliocene trend 

Estimating the parameters for 

the Pleistocene trend 

Estimating the incremental future rates

of oil and gas field discoveries in the

Pleistocene trend -

Conclusions 

References cited -

22

23

24

25

26

ILLUSTRATIONS

Page

FIGURE 1. Map showing location of our study area in the Gulf of Mexic

2. Graph showing rate of discovery of oil and gas in our study area in the Gulf of Mexico in both State and Federal waters

3-4. Graphs showing cumulative volume of oil and gas discovered on Federal Outer Continental Shelf acreage in our study area 

in the Gulf of Mexico on which leases were sold by February 4, 1975:

3. Volume reported as barrels of oil equivalent per cumulative number of leases 5

4. Volume reported as barrels of oil equivalent per cumulative number of wildcat wells 6 

5. Graph showing relationship between the number of wildcat wells drilled per lease and the cumulative number of leases

drilled in our study area in the Gulf of Mexico 7 

6-9. Graphs showing cumulative number of oil and gas fields discovered by December 31, 1976, in our study area in the Gulf

of Mexico in combined State and Federal waters 0-200 m deep in size-classes: 

6. 15-19 

8. 10-13 -

9. 3-9 -

10. Map showing geographic locations of the offshore geologic trend areas in our study area in the Gulf of Mexico 

 8

 9

 10

 11

 12

11-13. Graphs showing cumulative number of oil and gas fields discovered in the Miocene-Pliocene trend of the study area in the 

Gulf of Mexico in combined State and Federal waters 0-200 m deep in size-classes:

13. 9-11 15 

14-15. Graphs showing cumulative number of oil and gas fields discovered in the Pleistocene trend of the study area in the Gulf 

of Mexico in waters 0-200 m deep in size-classes:

16. Graph showing size distribution of oil and gas fields discovered in the Miocene-Pliocene trend of the study area in 

combined State and Federal waters 0-200 m deep 19

m
w CONTENTS

Page

FIGURE 17. Graph showing size-class-by-size-class increase in ultimate frequencies of oil and gas fields in the 0-5,000-foot depth

interval of the Permian basin 20 

18. Schematic diagram of the method used to estimate the part of the field-size distribution below the historical level of

economic truncation 21

TABLES

Page

TABLE 1. Layout of the data file on exploratory wells drilled during 1945-78 offshore Texas and Louisiana in the Gulf of Mexico 2

2. Description of deposit-size classes 7

3. Summary data and estimates of the ultimate number of oil and gas fields by class size and contained resources for the

Miocene-Pliocene trend of the study area 17

4. Forecasted future number of discoveries per increment of 200 wildcat wells drilled in the Miocene-Pliocene trend of the

study area 23

5. Summary data and estimates of the ultimate number of oil and gas fields by class size and contained resources for the

Pleistocene trend of the study area 24

6. Forecasted future number of discoveries per increment of 200 wildcat wells drilled in the Pleistocene trend of

the study area 25
ESTIMATION OF THE FUTURE RATES OF OIL AND GAS DISCOVERIES

IN THE WESTERN GULF OF MEXICO

By L. J. DREW, J. H. ScHUENEMEYER1 , and W. J. BAWIEC

ABSTRACT

A discovery-process model was used to predict, as of January 1, 

1977, the expected number and size distribution of oil and gas fields 

remaining to be discovered in the study area in the Gulf of Mexico 

and also to forecast the rate at which these fields will be discovered 

in the future. These predictions and forecasts were done separately 

for the combined Miocene-Pliocene trend area, which occupies 

123,027 km* of the study area, and the Pleistocene trend area, which 

occupies 33,612 km*. In both these areas, water depths ranged from 0 

to 200m.

As of January 1,1977, more than 2,700 oil and gas fields were still 

expected to be discovered in both trends. These fields range in size 

from 0.76 million to 194.3 million barrels of producible oil equivalent. Most of these fields (94.5 percent) are predicted to contain less 

than 12.14 million BOE (barrels of oil equivalent) each. The rate at 

which these oil and gas fields will be discovered is forecasted to start 

at approximately 1.25 million BOE per wildcat well. This rate is 

forecasted to decline to about half this yield per wildcat well after the 

drilling of 2,600 wildcat wells in the combined Miocene-Pliocene 

trend area and 1,200 wildcat wells in the Pleistocene trend area.

Analysis of data from areas where exploration has been relatively 

unrestricted indicates that the size distribution of oil and gas fields 

has a log-geometric form. As a result of this analysis, a new procedure was devised to estimate the form of the underlying size distribution of oil and gas fields in areas, such as the study area, where 

the discovery-data series has been truncated by economic factors.

INTRODUCTION

The purpose of this study was to devise a model to 

forecast the rate at which oil and gas fields will be 

discovered in the study area in the Gulf of Mexico. The 

study area is off Texas and Louisiana and covers 

156,639 km2 in which water depths are as great as 200 m 

(fig. 1). Making a forecast for this region is more complicated than making a similar forecast for a typical 

onshore basin. These complications arise because exploration for oil and gas in the Gulf of Mexico has been 

both geographically and temporally restrained by economic, technical, legal, and philosophy-of-exploration 

factors. As a consequence of these restraints, the his-

 U.S. Geological Survey and University of Delaware, Newark, Del. 19711.

torical rate for discovery of oil and gas (historical time 

profile of discoveries) in this region is atypical. This 

rate of discovery differs from the normal rate of discovery characteristic of most onshore basins and even 

such offshore basins as the North Sea in that it has remained at a high and approximately constant level for 

nearly the entire 30-year history of exploration in the 

Gulf of Mexico. This rate of discovery is constant 

whether expressed as barrels of oil equivalent (BOE) 

discovered per wildcat well or as 30E discovered per 

lease drilled.

In this paper, we describe the exploratory-well data 

file, the discovery history, our partitioning of the data, 

and how we compensated for the complications in the 

discovery-data series in adapting the Arps-Roberts 

(1958) discovery-process model to predict the ultimate 

number of oil and gas fields existing in the study area 

and the rate at which the remaining fields will be discovered after January 1, 1977. The adaptations of the 

model can be used for other areas where exploration 

has been restricted.

COMPILING THE EXPLORATORY-WELL 

DATA FILE

An exploratory-well data file was compiled covering 

the 1945-78 period of exploratory drilling in the offshore Louisiana and Texas parts of the Gulf of Mexico. 

Many source documents were used in the compilation 

including the International Oil and Gas Scouts Association yearbooks; Petroleum Information, Inc., wellhistory file; the AAPG (American Association of Petroleum Geologists) Bulletin, North American development issues; and studies of offshore oil and gas fields 

published by various professional societies. The file includes specific data on each exploratory well drilled 

during the 1945-78 period; in addition, wildcat wells 

that discovered new fields were identified, and the 

volumes of producible oil and gas contained in the
FUTURE RATES OF OIL AND GAS DISCOVERIES, WESTERN GULF OF MEXICO

TEXAS

GULF OF MEXICO

100 KILOMETERS

FIGURE 1. Location of our study area in the Gulf of Mexico.

fields that they discovered were noted. Estimates of the 

ultimate field productivities on the federally owned 

acreage were supplied by the U.S. Geological Survey, 

and such estimates on the State-owned acreage were 

supplied by the Dallas field office of the U.S. Department of Energy.

The layout of the data file and the data from an example well are given in table 1. The data file contains 

information on a total of 7,077 exploratory wells of 

which 4,639 are wildcats that discovered new fields 

and the other 2,438 wells are either extensions or newpool tests.

Each exploratory well was located within the proper 

geologic trend (Miocene, Pliocene, or Pleistocene) on an 

unpublished geologic-trend map prepared for OCS 

(Outer Continental Shelf) Lease Sale 38 by the U.S. 

Geological Survey, Metairie, La. The source documents 

used to assign a lease number and a lease-sale number 

to the wells drilled in the Federal waters of the Gulf of 

Mexico were provided by the U.S. Geological Survey, 

Reston, Va. The lease numbers for the wells drilled in

TABLE 1. Layout of the data file on exploratory wells drilled during 

1945-78 offshore Texas and Louisiana in the Gulf of Mexico

Columns Data Data for example well

 High IS1

 1QCS

 1,831 

. 206

 L2

-8,587

850

1_11 Subarea - 

12-19 Well number ___ __ 

20-24 Lease number 

25-31 Block number 

32 Block specification 

33-38 Total vertical depth (in feet) 

39-40 Lahee class 

41-42 Completion date (month) 9 

43-44 Completion date (a year between 1945 and 1978) 68

45 Geological region * 1

46-47 Federal lease-sale number 522 

48-57 Producible oil discovered (in millions of barrels

of oil) 0.0 

58-66 Producible gas discovered (in billions of cubic feet) 0.0 

67-72 Area of field (in square kilometers) 0.0 

73-80 Operator Humble

'Designation for "High Island area."

'Designation for "large block."

'Designation for "dry and abandoned wildcat well."

'Designation for "Miocene trend."

'Designation for "Federal lease sale number 22 (which was held on Apr. 21, 1968)."
COMPILING THE EXPLORATORY-WELL DATA FILE

the State waters of the Gulf of Mexico were obtained 

where possible from the International Oil and Gas 

Scouts Association yearbooks.

The encoding sequence used to create the data file 

was as follows:

1. The data were coded according to the format 

shown in table 1 for each exploratory well listed in part 

1 of the International Oil and Gas Scouts Association 

yearbooks for the period 1945 through 1977.

2. A retrieval, to the same format, was made in June 

1979 from the Petroleum Information, Inc., well-history 

control file and provided information on wells not 

described in the International Oil and Gas Scouts Association yearbooks. All the data for wells drilled in 1978 

were obtained from this source.

3. The North American development issues of the 

AAPG Bulletin were then used to add exploratory 

wells recorded in these issues that were not recorded in 

the first two sources.

4. Initially, wildcat discovery wells were designated 

as the last wildcat wells drilled prior to the drilling of 

the first nonwildcat exploratory or development wells 

drilled in each oil or gas field. These designations were 

then revised if the individual field studies published by 

such sources as the Lafayette, New Orleans, Louisiana, 

and other geological societies cited a different wildcat 

well as the actual discovery well.

5. In October 1979, the authors checked the overall 

completeness and correctness of the data file by comparing the file with data in the Metairie, La., office of 

the U.S. Geological Survey. From the results of this 

field check, which were based on a random sample of 

250 OCS leases, we are able to state that the file is 95 

percent complete and correct. We greatly appreciate 

the assistance of Mr. Floyd Bryan for his work in 

checking individual well logs to validate the discoverywell assignments made by the authors.

ANALYZING THE HISTORICAL RATES 

OF DISCOVERY

OVERALL DISCOVERY RATE

Almost all acreage blocks drilled in the Gulf of Mexico 

are on acreage owned by the Federal Government and 

sold in some 30 Federal lease sales beginning in 1954. 

Much of this acreage was later subject to a jurisdictional dispute between the Federal Government and 

the State of Louisiana, which took more than 20 years 

to resolve. When these disputed acreages were finally 

drilled, several large oil and gas fields were found that 

normally would have been discovered earlier had exploration not been restricted.

Exploratory drilling during the 1950's and early 

1960's was limited to shallow waters near the shoreline. As deep-water drilling technology improved and 

as pipeline infrastructure expanded, drilling moved 

into deeper waters in the 1960's.

In about 1970, the petroleum industry anticipated an 

increase in natural-gas prices and began drilling leases 

in areas thought to contain gas. In 1971, however, a 

large oil field, the Eugene Island Block 330, was discovered. Although no more large oil fields were found, 

the subsequent increase in exploratory drilling resulted 

in the discovery of many significant gas fields.

As a result of all these restrictions, the rate-ofdiscovery profiles for the Gulf of Mexico are different 

from the profiles typically observed for many of the 

petroliferous provinces within the United States and 

around the world, where operators have had more or 

less equal access to all the acreage in each province. In 

regions where exploration is relatively unrestricted, 

the initial level of discovery is relatively high because 

large oil and gas fields are found. This short initial 

phase is followed by a transition phase of approximately 

the same duration during which the rate of discovery 

falls rapidly to a low level. During the third phase of 

exploration, the discovery rate persists at a relatively 

low but stable level for a long period of exploratory 

drilling. Mostly small fields are discovered during this 

phase. Various aspects of the unusual discovery history in the study area are illustrated in figures 2-5.

The rate of discovery of oil and gas during the entire 

history of exploratory drilling in our study area in the 

Gulf of Mexico is shown in figure 2. This profile shows 

that early in the exploration history of this region 

(through 1958), the rate of discovery was relatively 

high and remained above 7 million BOE/well. From 

1959 onward, the discovery rate oscillated around 2 

million BOE/well. The high rate of discovery recorded 

during the early years of exploration in the Gulf of 

Mexico is attributed, to a large degree, to the discovery 

of several giant oil and gas fields such as Bay Marchand Block 2 and the combined South Pass Block 

24-27 fields. These fields were included in the data set 

even though they are not entirely offshore. The normal 

convention was followed here by allowing such fields to 

be called offshore fields. For the purpose of this study, 

this distinction is not important because no more fields 

this large are expected to be discovered.

Within the part of the Gulf of Mexico owned and 

leased by the Federal Government, the rate of discovery of oil and gas has been essentially constant during the entire history of exploration in this region. This 

region also contains the vast majority of the favorable 

acreage for oil and gas. In figure 3, cumulative volume
FUTURE RATES OF OIL AND GAS DISCOVERIES, WESTERN GULF OF MEXICO

TIME

25.0

1955 1960 1965 1970 1975

0 1000 2000 3000 4000 5000 6000 7000

CUMULATIVE NUMBER OF EXPLORATORY WELLS

FIGURE 2. Rate of discovery of oil and gas in our study area in the Gulf of Mexico in both State and Federal waters 0-200 m deep.

of oil and gas discoveries in this region is plotted 

against the cumulative number of leases drilled. Each 

data point was created by cumulating the discoveries 

made in each lease-sale area and adding this quantity 

to the quantity of oil and gas discovered as a result of 

all previous lease sales. These data cover the entire 

history of exploration in this region from the first

Federal sale held on October 13,1954, through sale No. 

37 held on February 4, 1975.

Examination of the graph shown in figure 3 reveals 

that the volume of producible oil and gas discovered on 

a lease-by-lease basis has been nearly constant from 

the earliest leases drilled to the recently drilled leases. 

The curvature defined by the data points covering the
ANALYZING THE HISTORICAL RATES OF DISCOVERY

15.0

14.0

13.0

12.0

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)rainage-lease sales

Drainage-lease sale

)rainage-lease sales

O

4.0

3.0-

2.0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 

CUMULATIVE NUMBER OF LEASES DRILLED

FIGURE 3. Cumulative volume of oil and gas discovered on Federal Outer Continental Shelf acreage in our study area in the Gulf of Mexfto 

on which leases were sold by February 4, 1975 volume reported as barrels of oil equivalent (BOB) per cumulative number of leases. 

Discoveries associated with drainage-lease sales are explained in the text. The first data point represents the 2.3 billion BOB discovered 

on acreage that is now under Federal jurisdiction but that originally was leased by the State of Louisiana. All this oil and gas was 

discovered on leases sold before the first Federal sale, which was held October 13,1954. The last data point includes drilling done through 

December 31, 1978, on acreage on which leases were sold by February 4, 1975.

last four to five lease sales appears to indicate that the 

rate of return to exploratory drilling has started to 

diminish in this region. Several more years will be 

needed to determine if the rate is actually diminishing 

or if, instead, the fields discovered in the last few leasesale areas will be found by further drilling to be large 

enough to reestablish the previous constant rate of 

return to exploratory drilling. The "tight" collections 

of data points in the middle sector of figure 3 represent 

the results of drilling a few exploration leases included 

in nine drainage-lease sales held between 1962 and 

1971. The general intent of drainage-lease sales is to

sell leases on structures previously proved to be productive. In most drainage-lease sales, however, a few exploration leases are included. The data from the drainage-lease sales plot as tight clusters because not more 

than three new-field discoveries were made on the acreage leased in any of these sales.

The graph produced by plotting the cumulative 

volume of oil and gas discovered in this region against 

the cumulative number of wildcat wells (fig. 4) shows 

essentially the same pattern as that shown in figure 3. 

The graph in figure 4 does, however, change its slope 

somewhat after the drilling of the 1,000th wildcat well
FUTURE RATES OF OIL AND GAS DISCOVERIES, WESTERN GULF OF MEXICO

15.0

14.0

13.0

12.0

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1.0 

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200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 

CUMULATIVE NUMBER OF WILDCAT WELLS

2800 3000 3200

FIGURE 4. Cumulative volume of oil and gas discovered on Federal Outer Continental Shelf acreage in our study area in the Gulf of Mexico 

on which leases were sold by February 4, 1975 volume reported as barrels of oil equivalent (BOE) per cumulative number of wildcat 

wells. The first data point represents the 2.3 billion BOE discovered on acreage that is now under Federal jurisdiction but that originally 

was leased by the State of Louisiana. All this oil and gas was discovered on leases sold before the first Federal sale, which was held 

October 13, 1954. The last data point includes drilling done through December 31, 1978, on acreage on which leases were sold by 

February 4, 1975.

in this region (in 1966). This difference in slope shows 

that the rate of discovery of oil and gas was somewhat 

higher during the earlier period of exploration than 

during the later period. When the first 1,000 wildcat 

wells were drilled, exploratory drilling was confined, 

in large part, to Miocene and Pliocene rocks on the Federal OCS acreage off Louisiana. The second segment of 

the graph covers the period 1967-78 when the exploratory drilling was focused in the Pleistocene deposits. 

The centers of this exploration play were the adjoining 

subregions of West Cameron (offshore Louisiana) and 

High Island (offshore Texas). This play has produced 

mainly gas, whereas the Miocene and Pliocene rocks 

produced a much larger proportion of crude oil.

The strong similarity between the shapes of the two 

graphs in figures 3 and 4 is a consequence of the consis-
ANALYZING THE HISTORICAL RATES OF DISCOVERY

4.0

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0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 

CUMULATIVE NUMBER OF OUTER CONTINENTAL SHELF LEASES DRILLED

FIGURE 5. Relationship between the number of wildcat wells drilled per lease and the cumulative number of leases drilled in our study area 

in the Gulf of Mexico. The figure reflects drilling done through December 31,1979, on acreage on which leases were sold by June 29,1979 

(sale 48).

tent manner used by offshore operators to evaluate the 

result of wildcat drilling through time. The graph in 

figure 5 shows that no discernible trend exists in the 

number of wildcat wells drilled per lease during the entire history of wildcat drilling on the Federal OCS acreage. The data points in figure 5 that plot at less than 

one wildcat well per lease are for drainage-lease sales 

or for multiple-lease-block structures for which only 

one or two wildcat wells were used to prove up a 

structure.

DISCOVERY RATES FOR EACH SIZE CLASS

Analysis of the graphs of the rate of discovery of individual size classes of fields (figs. 6-9) reveals clearly 

why the overall rate of discovery of oil and gas in the 

Gulf of Mexico has remained essentially constant during the history of exploration in this region. The endpoints of each of these class intervals are given in table 

2. In figure 6, the graphs of the cumulative discovery 

curves for oil and gas fields in classes 17 through 19 

show that most of these largest fields were discovered 

very early in the exploration history of the region. For 

example, half the fields in these three largest field-size 

classes were discovered by 1958 when only 400 wildcat 

wells had been drilled in the region. This pattern of discovery, in which the largest fields are discovered early, 

is widely observed in basins and similar large regions 

when the exploration process has not been restricted,

and, to that extent, the historical pattern of discovery 

in the Gulf of Mexico is similar to the pattern in many 

other regions. However, for all but the largest size 

classes of fields, the pattern of discoveries in the Gulf of 

Mexico is quite different from the patterns for other

TABLE 2. Description of deposit-size classes

Class

2

4 -

5 ________

Q

7 

10

11

12 -

1 q

14 -

1 K

16 

17 -

-I Q

1Q

Size range1

.006 to .012

- - - .012 to .024

- - - - 024 to 047

 .047 to .095 

 .095 to .19

- - 19 to 38

OQ 4-^ net

.76 to 1.52

1.52 to 3.04

3.04 to 6.07

- 6 07 to 12 14

12.14 to 24.3

24.3 to 48.6

48 6 to 97 2

...... Q7 2 tn 1 94 3

1 f\A O 4-~ OQO C

QQQ C 4-n TT7 O

lit O f n 1 HHA A

'Millions of barrels of oil equivalent.
FUTURE RATES OF OIL AND GAS DISCOVERIES, WESTERN GULF OF MEXICO

TIME

60

50

3COVERIES

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1955 1960 1965 1970 1975

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 .15

 16

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 » 19

\ 500 1000 1500 2000 2500 3000 3500 4000 4500

CUMULATIVE NUMBER OF WILDCAT WELLS

FIGURE 6. Cumulative number of oil and gas fields discovered by December 31,1976, in size-classes 15 through 19 in our study area in the

Gulf of Mexico in combined State and Federal waters 0-200 m deep.

regions. For example, a strong reversal in the slopes of 

the cumulative discovery graphs for size-classes 9 

through 15 (figs. 6-9) took place in the early 1970's. 

This reversal in the rate of discovery also took place in 

1971 to a lesser degree for size-class 16 (fig. 6).

The pattern of discoveries across size classes that is 

normally observed from the unrestricted exploration of 

such a large region as the Gulf of Mexico consists of the 

following general elements: (1) the graphs of the cumulative discoveries across field-size classes have the 

same general analytic form and show that the rate of 

return to exploratory drilling diminishes even though, 

at any point in the exploration process, the decrease 

may not be obvious, (2) the degree of the diminishing 

rates of return will be less obvious in each successively 

smaller size class, and, for the smallest field-size class, 

it may not be evident until very late in the exploration 

history of a region, and (3) on the average, at any particular point in the exploration of a region, more discoveries will have been made in a given field-size class 

than in the next largest size class, if the discovery process has not been affected by economic factors and also 

if, on the average, more fields remain to be discovered 

in a given field-size class than in the next class at this 

same point in the exploration history of the region.

The marked upturn in the rate of discovery of fields 

in size-class 16 and smaller fields during the early 

1970's is then an atypical pattern, which can be explained as a consequence of the restraints that were 

placed upon exploration processes in the past in this 

region. We believe that the rate of discovery of fields in 

these size classes would not have increased at all if 

natural-gas prices had been on a par with crude-oil 

prices. The exploration history indicates that the exploration companies knew that the central and western Gulf of Mexico was likely to contain gas and that
ANALYZING THE HISTORICAL RATES OF DISCOVERY

70

60

__50

o 

o

u. 40 

O

cc

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m

30

| 20 

o

10

1955 1960 1965

TIME 

1970 1975

500 1000 1500 2000 2500 3000

CUMULATIVE NUMBER OF WILDCAT WELLS

3500 4000 4500

FIGURE 7. Cumulative number of oil and gas fields discovered by December 31, 1976, in size-class 14 in our study area in the Gulf of

Mexico in combined State and Federal waters 0-200 m deep.

they also avoided this area because a large part of it 

consisted of Pleistocene deposits, which in the 1950's 

and 1960's were thought to contain, at best, poorquality reservoirs. Not until 1971, when the giant 

Eugene Island Block 330 field was discovered in 

Pleistocene deposits, were rocks of this age demonstrated to have high-quality reservoirs containing 

large reserves of oil and gas.

Additional factors such as the status of the pipeline 

infrastructure and water depths also explain why some 

discoveries have been made later than they otherwise 

would have been. But with regard to the marked upturn in discovery rates for fields in size-classes 16 and 

smaller (figs. 6-9), we conclude here that the artificially low price of natural gas during the 1950's and

1960's was the main contributing factor that delayed 

the exploration and development of the gas fields that 

were discovered in the central and western Gulf of 

Mexico after 1970. In summary, then, had the price of 

natural gas been on a par with the price of crude oil, 

the Pleistocene deposits would almost certainly have 

been explored earlier than they were and a more normal decline pattern in the rate of returns to exploratory drilling would have been observed.

PARTITIONING THE DATA

Because the normal pattern of declining rates of 

return to exploratory drilling does not exist in the
10 FUTURE RATES OF OIL AND GAS DISCOVERIES, WESTERN GULF OF MEXICO

1955 1960 1965

TIME 

1970 1975

0 500 1000 1500 2000 2500 3000 3500 4000 4500

CUMULATIVE NUMBER OF WILDCAT WELLS

FIGURE 8. Cumulative number of oil and gas fields discovered by December 31, 1976, in size-classes 10 through 13 in our study area in

the Gulf of Mexico in combined State and Federal waters 0-200 m deep.

discovery-data series through 1976 for the combined 

State and federally owned sections of the Gulf of Mexico (0-200 m water depth), we cannot use a discoveryprocess model to forecast either the ultimate number of 

oil and gas fields that are expected to exist in each size 

class or the rate at which they will be discovered. This 

conclusion does not imply that this type of model cannot be used at all to produce these predictions for the 

Gulf of Mexico. In fact, this forecasting problem can be

solved by blocking the total discovery time series into 

subsets that do show the necessary declining rate of 

return to exploratory drilling and then performing the 

forecasting tasks. Although many blocking schemes 

could conceivably be used, the scheme of blocking according to geologic trends appears to be the most direct 

approach. Examples of other schemes that could be used 

are blocking according to water depth intervals or 

blocking by geographic subregions.
PARTITIONING THE DATA 11

60 

50

LU

OC 

HI

oO40

Q

LL 

O

OC

OQ 30

D 

Z

HI

§20

D

D 

O

10 

0(

1955 1960

/

/'"'

^

1965

.

__/

I

^^«

S

1

/

/

/

TIME 

1970

X

"^

\ \

.^^

/

^^-*/

I I

1975

/

r

>* *j"~y

-

) 500 1000 1500 2000 2500 3000 3500 4000 4500

CUMULATIVE NUMBER OF WILDCAT WELLS

FIGURE 9. Cumulative number of oil and gas fields discovered by December 31, 1976, in size-classes 3 through 9 in our study area in the

Gulf of Mexico in combined State and Federal waters 0-200 m deep.

The study area in the Gulf of Mexico was divided into 

two regions: the combined Miocene-Pliocene trend 

region and the Pleistocene trend region (fig. 10). The 

map used for this purpose is an unpublished map of the 

Gulf of Mexico prepared by the U.S. Geological Survey, 

Metairie, La., for Federal OCS Lease Sale 38 held in 

1975. The graphs of the cumulative number of discoveries made as a function of the cumulative number 

of wildcat wells drilled by size class in each trend area 

for the combined Miocene-Pliocene trend region are 

shown in figures 11-13, and similar graphs for the 

Pleistocene trend region are shown in figures 14-15.

Figure 11 shows the graphs of the cumulative number 

of fields discovered in size-classes 15 through 19 as a 

function of the cumulative number of wildcat wells 

drilled within the Miocene-Pliocene trend. These five 

graphs are similar in overall form to the five graphs in

figure 6 because most oil and gas fields discovered in 

these five largest size classes in the entire Gulf of Mexico study area were discovered in the Miocene or Pliocene geologic trends. For example, both of the class-19 

fields discovered in the Gulf of Mexico were discovered 

in the Miocene trend. In addition, 17 of the 20 class-17 

fields were discovered in either the Miocene or Pliocene 

trends, as were 42 of the 53 class-15 fields.

Although, to the human eye, the separation of the 

discovery-data series according to geologic trends appears to have achieved only a small improvement in 

isolating regions that show diminishing rates of return 

to wildcat drilling, this scheme did yield enough of an 

improvement to allow the parameters of the ArpsRoberts (1958) discovery-process model to be estimated 

simultaneously from the discovery-data series for each 

of the five field-size classes shown in figure 11. These
12 FUTURE RATES OF OIL AND GAS DISCOVERIES, WESTERN GULF OF MEXICO

TEXAS

GULF OF MEXICO

100 KILOMETERS

FIGURE 10. Geographic locations of the offshore geologic trend areas in our study area in the Gulf of Mexico (from unpublished map of 

the Gulf of Mexico prepared by the U.S. Geological Survey for Federal OCS Lease Sale 38 held in 1975).

parameters are the ultimate number of oil and gas 

fields expected to exist in each size class and the efficiency of discovery within each size class.

With respect to the rates of discovery of oil and gas 

fields in size-class 14, and each successively smaller 

size class down to and including size-class 9, this blocking routine (the separation of data according to geologic 

trends) yielded a substantial improvement in isolating 

the effect (that is, removing the effect in the subsets) 

the increased price of natural gas had upon the classby-class rates of discovery (figs. 12 and 13). This effect 

was removed to a large enough degree so that within 

the Miocene-Pliocene data set, stable estimates were 

obtained for both the critical parameters of the ArpsRoberts (1958) discovery-process model. The blocking 

of the total discovery-data series in the Gulf of Mexico 

study area according to geologic trends did not, however, completely isolate the effect that the enormous 

increase in price of natural gas during the 1970's had 

upon the rate of discovery of gas fields in the Gulf of 

Mexico. For example, by 1974, at least modest reversals

in the slopes of the cumulative discovery graphs had 

taken place for field-size-classes 9-15 in the MiocenePliocene data subset (figs. 11-13). These reversals are 

the result of the recording of an increase in the rate of 

discovery of gas fields in these size classes mainly 

within the Vermillion, East Cameron, West Cameron, 

and High Island regions of the Gulf of Mexico.

We conclude here that the Pleistocene trend and, to 

some extent, the Pliocene and Miocene trends within 

these regions were known to contain gas and consequently were not explored intensely until expectations 

were created in the late 1960's and early 1970's that 

the price of gas was going to increase rapidly in the 

near future. Although, after the fact, a data-blocking 

scheme could be constructed to isolate these regions 

containing gas for separate treatment, the arbitrariness required to outline such regions would almost certainly be subject to criticism. For this reason, we 

decided to block the data according to geologic trends, 

which are clearly defined and widely recognized 

entities.
PARTITIONING THE DATA 13

1955 1960 1965

TIME

1970 1975

500 1000 1500 2000 2500 

CUMULATIVE NUMBER OF WILDCAT WELLS

3000 3500

FIGURE 11. Cumulative number of oil and gas fields discovered in size-classes 15 through 19 in the Miocene-Pliocene trend of the study 

area in the Gulf of Mexico in combined State and Federal waters 0-200 m deep.

The graphs of the cumulative number of oil and gas 

fields discovered in the Pleistocene geologic trend in 

size-classes 9 through 18 are shown in figures 14 and 

15. With exception of the graphs for size-classes 17 and 

18, the graphs in these two figures reveal that within 

the Pleistocene trend, at least through the end of 1976, 

little evidence exists for diminishing returns to wildcat 

drilling. The nearly complete absence of size-class-bysize-class diminishing rates of return to wildcat drilling within the Pleistocene trend prevented the direct 

estimation of the two critical parameters in the ArpsRoberts (1958) discovery-process model within this 

region. The method used to predict (1) the ultimate 

number of oil and gas fields expected to exist in each 

field-size class and (2) the rate at which these fields will 

be discovered in the future is discussed in detail in the 

following section.

ESTIMATING THE PARAMETERS OF THE 

DISCOVERY-PROCESS MODEL

The method used to estimate the ultimate number of 

oil and gas fields expected to exist within each fieldsize class and the rate at which these fields are expected to be discovered in the future is based upon the 

discovery-process model devised by Arps and Roberts 

(1958). This model incorporates the well-documented 

characteristic of the petroleum discovery process that 

the larger an oil or gas field is, the earlier it will tend 

to be discovered in the exploration history of any 

region. For examples of this phenomenon, see reports 

by Ryan (1973a, b), Drew (1975), Kaufman, Balcer, and 

Kruyt (1975), and Root and Drew (1979).

In the Arps-Roberts model, the probability that the 

next wildcat well will discover a given oil or gas field is
14 FUTURE RATES OF OIL AND GAS DISCOVERIES, WESTERN GULF OF MEXICO

1975

500 1000 1500 2000 2500 

CUMULATIVE NUMBER OF WILDCAT WELLS

3000 3500

FIGURE 12. Cumulative number of oil and gas fields discovered in size-classes 12 through 14 in the Miocene-Pliocene trend of the study 

area in the Gulf of Mexico in combined State and Federal waters 0-200 m deep.

assumed to be proportional to the ratio of the area of 

the field to the area of the basin. The form of this model 

that predicts the cumulative number of discoveries expected to be made within a given field-size class by the 

drilling of w wildcat wells is

FA(w) = Fx(oo){l - exp[- C(A)Aw/B]}, (1)

where FA(w) = the cumulative number of fields expected to be discovered in size-class 

A by the drilling of w wildcat wells; 

-^(oo) = the ultimate number of oil and gas 

fields in size-class A that exist in 

the basin; 

B = area of basin;

w = cumulative number of wildcat wells;

A = average areal extent of the fields in 

the given size class;

C(A) = the efficiency of discovering fields of

size A.

In their study of the Denver basin, Arps and Roberts 

(1958) determined the values of both B and C(A) exogenously. In addition, they reduced the estimation 

problem for the C(A)'s by assuming a constant value 

for this parameter across field-size classes. Given the 

assumed value of the parameter C, and estimating the 

size of the basin B from geological data, they then 

solved equation 1 to obtain estimates of the ultimate 

number of fields expected to exist in each field-size 

class. This method of forecasting gave reasonable 

results for the Denver basin (Drew, Attanasi, and Root,
ESTIMATING THE PARAMETERS OF THE DISCOVERY-PROCESS MODEL 15

1955 1960

TIME

1965 1970 1975

500 1000 1500 2000 2500 

CUMULATIVE NUMBER OF WILDCAT WELLS

3000 3500

FIGURE 13. Cumulative number of oil and gas fields discovered in size-classes 9 through 11 in the Miocene-Pliocene trend of the study 

area in the Gulf of Mexico in combined State and Federal waters 0-200 m deep.

TIME

1965 1970 1975

200 400 600 800 

CUMULATIVE NUMBER OF WILDCAT WELLS

1000

FIGURE 14. Cumulative number of oil and gas fields discovered in size-classes 13 through 18 in the 

Pleistocene trend of the study area in the Gulf of Mexico in water 0-200 m deep.
16 FUTURE RATES OF OIL AND GAS DISCOVERIES, WESTERN GULF OF MEXICO

TIME

1965 1970 1975

200 400 600 800 

CUMULATIVE NUMBER OF WILDCAT WELLS

1000

FIGURE 15. Cumulative number of oil and gas fields discovered in size-classes 9 through 12 in the 

Pleistocene trend of the study area in the Gulf of Mexico in water 0-200 m deep.

1977) and also for the Permian basin (Drew, Root, and 

Bawiec, 1979).

However, application of a discovery-process model 

based on the concept of the area of influence of a drill 

hole (Drew, Schuenemeyer, and Root, 1980) and the 

variation in the forms of the cumulative-discovery 

curves for the Permian basin (Root and Drew, 1979) 

clearly indicate that the efficiency of discovery varies 

across class sizes. This conclusion can also be reached 

from inspection of the cumulative-discovery curves for 

the largest field-size classes in the Miocene-Pliocene 

trend in the Gulf of Mexico (fig. 11).

The efficiency of discovery does not depend nearly as 

much on class size for the Pleistocene trend area. Only 

for the three largest field-size classes (classes 16-18) 

had rates of return to wildcat drilling begun to 

decrease by the end of 1976 (fig. 14). The declining 

rates of discovery in these three field-size classes have 

been offset, however, by either approximately constant 

or increasing rates of discovery in field-size classes 

9-15 (figs. 14 and 15). We conclude here that, even 

through the end of 1976, the Pleistocene geologic trend 

had to be considered an immature region; that is, many 

more discoveries were going to be made after 1976 in 

this region. More simply put, the Pleistocene trend was 

still a favorable place to explore for gas fields starting 

January 1, 1977. Because many more fields remain to 

be discovered in the Pleistocene trend, size-class-bysize-class discovery efficiencies could not be estimated 

directly from the discovery-data series. The discovery 

efficiencies for this trend area were then assumed to be 

the same as the corresponding efficiencies estimated 

from the Miocene-Pliocene trend area where direct estimation from the discovery-data series was possible.

ESTIMATING THE PARAMETERS FOR THE 

MIOCENE-PLIOCENE TREND

Before estimates could be made of the ultimate 

number of oil and gas fields expected to exist in each 

field-size class [the Fx(o>)'s in equation 1] and the corresponding discovery efficiencies [the C(A)'s in equation 1], several preliminary data analyses had to be 

done. These tasks included the planimetering of the 

areal extents of the combined Miocene-Pliocene and 

Pleistocene trend areas. The Miocene-Pliocene trend in 

the study area was determined to cover 123,027 km*, 

and the Pleistocene trend to cover 33,612 km*. These 

values were used as the respective basin-size estimates 

(the variable B in equation 1). Additional tasks included the restructuring of the cumulative-discovery 

curves shown in figures 11-13 onto a uniform scale of 

wildcat wells. This restructuring was done to produce 

an even distribution of discovery data points across the 

wildcat drilling history of each region because the estimation algorithm goes more smoothly when the data 

are presented as a function of even increments of the 

independent variable. The average areal extent of the 

oil and gas fields that have been discovered in each 

field-size class was also computed. These averages 

were used as estimates of the variable A in equation 1. 

Data for this purpose were obtained from the Transco 

Company maps (Transcontinental Gas Pipe Line 

Corporation and Transco Exploration Company, 1980; 

Stanley and Evans, 1979) of the oil and gas fields and 

natural gas pipelines in the Gulf of Mexico as of 

September 1979 and March 1980.

These estimates of A and B and the nonlinear leastsquares algorithm (NLIN2) by Marquardt (1963) were 

used to obtain simultaneous estimates of the C(A)'s
ESTIMATING THE PARAMETERS OF THE DISCOVERY-PROCESS MODEL 17

and the Fx(«)'s in equation 1. The NLIN2 algorithm 

chooses successive estimates of C(A) and FA(oo) for each 

field-size class so as to minimize the sum of squares between the observed and predicted value of FA(w). Good 

initial values for C(A) and FA(v>) were obtained by solving equation 1 for known values of w and FA(w). The 

choices of successive values of the parameters are determined by evaluating the partial derivatives of FA(w) 

with respect to C(A) and FA(<x>\ Estimates of the CfA/s 

for size-classes 13-17 (table 3) and class 12 were found 

to be greater than 1. An efficiency of 1 is used to 

describe random drilling.

Too few fields have been found in classes 18 and 19 to 

permit meaningful statistical estimation. This lack of 

data is unimportant because no additional discoveries 

are expected to be made in these two largest field-size 

classes. The estimates for the CfA/s in size-classes 9 

through 11 were determined to be approximately equal 

tol.

Fewer discoveries were made in the smaller size 

classes (classes 9-12) than otherwise would have been 

expected because of economic factors such as the artificially low price of natural gas during the 1950's and 

1960's and into the early 1970's. Other truncation factors are water depth and infrastructure status.

The main effect of the pre-1979 economic truncation 

in the Gulf of Mexico was the nonreporting of the actual discovery of many small gas fields containing less

than 25 BCF (billion cubic feet) because, at the time of 

their discovery, such fields were rarely profitable to 

develop. However, today, gas fields in the 10-20-BCF 

size range are commercial at a wide variety of locations 

and water depths. Gas fields containing less than 10 

BCF are also economically viable under some situations today and will become increasingly important if 

the real price of natural gas continues to increase as is 

currently (1981) being projected. As a result of this 

situation, a forecast of the future rates of discovery of 

these small fields has to be made even though little information exists on their past rates of discovery that 

can be used to estimate the parameters in a discoveryprocess model.

We argue here that the size class in which an 

economic truncation first appears can be determined 

by inspecting the relative positions of each of the 

cumulative-discovery curves. For example, the 

post-1965 part of the cumulative-discovery curve for 

each successively smaller field-size class in the 

Miocene-Pliocene trend, down to size-class 14, lies 

above the discovery curve for each successively larger 

size class (figs. 11-12). We thereby identify size-class 

13 as the smallest size class not to be seriously affected 

by economic truncation.

Another way in which this truncation phenomenon 

can be visualized is to construct a histogram of the 

number of recorded discoveries and to observe where

TABLE 3. Summary data and estimates of the ultimate number of oil and gas fields by class size and contained resources for the

Miocene-Pliocene trend of the study area

[Dash leaders indicate that the nonlinear least-squares procedure could not be used; BOE, barrels of oil equivalent]

Size 

class1

9

10

11

12

13

14

15

16

17

18

19

Number of fields 

found by 3,100 

wildcat wells

24

27

27

35

50

42

43

25

17

5

2

,,,

889.4

539.1

326.7

198.0

120.3

65.9

50.7

25.8

17.0

5.0

2.0

Unsmoothed

_

2.55

4.78

4.94

3.31

5.35

(4)

(4)

Smoothed

_

_

2.65

3.40

4.15

4.89

5.65

(4)

(4)

Expected total 

ultimate 

resource 

(BOE x 101)

1005.0

1223.8

1509.4

1716.7

2223.1

2282.1

3551.0

3302.7

4583.7

2873.2

2273.7

Expected 

remaining 

resource* 

(BOE x 101)

977.9

1162.5

1384.6

1413.2

1299.1

827.7

539.3

102.4

.0

.0

.0

Percent 

of total 

resource 

remaining

12.7

15.1

18.0

18.3

16.9

10.7

7.0

1.3

.0

.0

.0

Total- 297 2,239.9 26,544.4 7,706.7 100.0

'See table 2 for definition of field-size classes.

The ultimate numbers of fields estimated to exist in size-classes 13-19 were estimated directly from the discovery-data series. The ultimate numbers of fields in size-classes 9-12 were 

estimated by applying the average f,.Jf, = 1.65 ratio determined from size-classes 13 through 17. 

'Amounts are for the period starting 1/1/77. 

'Insufficient data to estimate £(A).
18 FUTURE RATES OF OIL AND GAS DISCOVERIES, WESTERN GULF OF MEXICO

the mode of the distribution exists. In the MiocenePliocene trend, the mode of the distribution is in sizeclass 13, which contains fields in the size range of 12.14 

million to 24.3 million BOE (or 72.84 billion to 145.8 

BCF of gas equivalent). We argue here that the recording of discoveries in the field-size classes below this 

level has been truncated. Some truncation may also 

have affected field-size-class 13. Therefore, we believe 

that fields containing more than 24.3 million BOE of 

producible reserves have been economically viable 

from the beginning of exploration in the MiocenePliocene trend area. We, of course, allow for the exception that a few fields above this size may not have been 

developed after their discovery because of peculiarities 

in the evaluation and decisionmaking process.

The assertion that the field-size class below which 

economic truncation has taken place can be determined by inspection of the discovery-rate curve or a 

histogram of reported discoveries is supported by the 

following semiquantitative and qualitative data. First, 

in the 1950's, 1960's, and even into the early 1970's, 

gas fields containing 100-150 BCF in the MiocenePliocene trend generally were considered marginal to 

develop. This truncation level can be checked by 

calculating the cost of developing such a field by using 

the prices and costs of completion and operation that 

prevailed at that time.

Additional support for the assertion that the part of 

the recorded field-size distribution at and below its 

mode has been truncated by economic factors is gained 

by examining data from areas where the costs of exploration and production differ. An excellent example 

of such a situation is illustrated in the Permian basin, 

where the location of the mode of the recorded field-size 

distribution is strongly related to the depth of the discoveries (Drew, Schuenemeyer, and Bawiec, 1981). In 

this basin, the mode of the field-size distribution for the 

discoveries recorded through the end of 1974 in the 

0-5,000-foot depth interval is in size-class 6. In the 

5,000-10,000-foot interval, the mode is in field-sizeclass 7. In the 10,000-15,000-foot depth interval, the 

mode is in field-size-class 11. This migration of the 

mode of the recorded field-size distribution across 

depth intervals is almost certainly related to the economic cost conditions that prevailed in the basin before 

1975.

Further information to support this assertion exists 

in the fact that many noncommercial discoveries, often 

referred to as "shows of oil and gas," had been recorded 

before 1975 in the Permian basin and in most other 

basins in the United States. Since then, as a result of 

the large price increases in recent years, many of these 

have been reentered and recompleted as commercial

wells. These recompletions are then in fact "filling 

out" the recorded size distributions of discoveries, 

thereby causing the location of the mode of the fieldsize distributions to shift toward the smaller field sizes. 

This same phenomenon is also taking place currently 

in the Gulf of Mexico, where many lease blocks that 

were previously leased, drilled, and dropped as noncommercial are now being re-leased, redrilled, and put 

into commercial production.

Accepting the assertion that, in the Miocene-Pliocene 

trend area, the part of the recorded field-size distribution below the mode (size-class 12 and smaller, fig. 16) 

has been truncated establishes a requirement for a 

technique to remove the effect of this type of truncation. If the effect of this truncation were not removed 

from the data, the future rates of discovery forecasted 

by the Arps-Roberts (1958) discovery-process model 

would be biased downward; that is, the rates would be 

underestimated.

The approach taken here to estimate how many oil 

and gas fields would have been recorded as discoveries 

in size-class 12 and smaller size classes had the price of 

natural gas and crude oil been on par with current 

prices is based upon observations about the form of the 

field-size distributions in other areas such as the Permian and Denver basins. Figure 17 is a graph of the increases in the size-class-by-size-class frequencies of the 

fields expected ultimately to be discovered in the 

0-5,000-foot depth interval in the Permian basin. Each 

point on this graph is the ratio of the ultimate number 

of oil and gas fields expected to exist in a given class, 

ft-iy to the ultimate number of oil and gas fields expected to exist in the next largest size class, ft. This 

graph is then read as follows: take, for example, the 

ratio between size-classes 11 and 12 where 

fi-i/fi = 1.65, that is, where 1.65 times as many fields 

are expected to exist in size-class 11 as in size-class 12. 

This ratio is based on /J-i«n = 85.2 and /J=12 = 51.5 for 

oil and gas fields ultimately expected to exist in these 

two size classes in the 0-5,000-foot depth interval in 

the Permian basin.

The graph in figure 17 shows that no trend is apparent in the ft-Jft ratio across the entire range of size 

classes above size-class 6, below which economic truncation is believed to take place. This lack of a trend in 

the fi-i/fi ratio for size classes above the size class in 

which economic truncation takes place characterizes 

both the 5,000-10,000-foot and 10,000-15,000-foot 

depth intervals in this same basin and also characterizes the Denver* basin as a whole. Therefore, we assume 

that, in general, the frequency of fields in the ultimate 

underlying field-size distribution based upon a Iog2 

size-class scaling progresses across size classes as a
ESTIMATING THE PARAMETERS OF THE DISCOVERY-PROCESS MODEL 19

60

50

CO 

Q

30foc

LU

£20

10

ZONE OF ECONOMIC TRUNCATION

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

SIZE CLASSES

FIGURE 16. Size distribution of oil and gas fields discovered in the Miocene-Pliocene trend of the study area in combined State and

Federal waters 0-200 m deep as of December 31, 1976.

geometric series. We, therefore, believe that the underlying field-size distribution is approximately loggeometric in form.

The above observations and conclusions were used to 

form a basis for a technique to remove the effect of 

economic truncation upon the observed distribution of 

oil and gas field discoveries made by any given point 

in time. In figure 18, this technique is schematically 

diagramed for a hypothetical region.

In figure 18, the /J_/s represent the estimated frequencies (number of fields) in each size class below the 

historical economic truncation level. In this example, 

the smallest size class in which no economic truncation 

has taken place is assumed to be the 12-24-millionBOE size class. In all, 26 oil and gas fields are estimated to exist in this size class. This estimate normally would be derived from the historical discovery-data 

series by use of a discovery-process model.

The number of fields in the 6-12-million-BOE size 

class (defined to be fc-i) is estimated to be 43.7 by 

multiplying the average increase in frequency factor of 

r = 1.68 by ^ = 26 fields. This multiplication factor is 

the computed average increase in the ultimate number 

of oil and gas fields estimated to exist in each size class 

above the 12-million-BOE field-size-class truncation 

level. The ultimate number of fields expected to exist 

in each smaller size class under consideration is estimated in a similar manner.

For example, the ultimate number of fields estimated 

to exist in the 3-6-million-BOE field-size class is determined to be fi-2 = 43.7 x 1.68 = 73.4 fields. Given a 

complete set of estimates of the expected ultimate
20 FUTURE RATES OF OIL AND GAS DISCOVERIES, WESTERN GULF OF MEXICO

3.0

2.0

1.0

0.0

10 11 12 13 

SIZE CLASS,M

14 15 16 17 18 19

FIGURE 17. Size-class-by-size-class increase in ultimate frequencies of oil and gas fields in the 0-5,000-foot depth interval of the Permian

basin. The average rate of increase is fi-Jfi = 1.67.

number of fields in each size class to be considered, we 

can use a discovery-process model to estimate the rates 

at which the remaining fields will be discovered.

This same procedure has been used to estimate the 

field-size distribution of fields in the Miocene-Pliocene 

trend of the study area that have been subject to economic truncation. A geometric progression was observed in the ultimate number of fields in each class 

from class 17 to class 13. The average increase in this 

progression is equal to r = 1.65. This average was used 

to estimate the ultimate number of oil and gas fields 

expected to exist in size-classes 12 down through and

including size-class 9 in the Miocene-Pliocene trend 

area. The results of this estimation process are shown 

in the first four rows of column 3 of table 3. The estimation of the ultimate field-size distribution was terminated at field-size-class 9 because fields containing 

less than 760,000 BOE are unlikely to be commercial 

unless they are under very shallow water or close to an 

existing production facility. The data from size-classes 

18 and 19 were not considered because too few discoveries were made in these classes to allow meaningful estimation and because no more fields in these 

classes are expected to be discovered.
ESTIMATING THE PARAMETERS OF THE DISCOVERY-PROCESS MODEL 21

210

200

130

120

110

100

ill

cc LIJ

DO

= 123.3 x 1.68=207.2 FIELDS

£-3=73.4 x 1.68 = 123.3 FIELDS

/U=43.7 x 1.68=73.4 FIELDS

1.68=43.7 FIELDS

NO ECONOMIC 

TRUNCATION

AVERAGE

/:=26 INCREASE IN 

FREQUENCY=1.68

0.38 0.75 1.5 3 6 12 24 48 96 192 384 768

MILLIONS OF BARRELS OF OIL EQUIVALENT

FIGURE 18. Schematic diagram of the method used to estimate the part of the field-size distribution below the historical

level of economic truncation.
22 FUTURE RATES OF OIL AND GAS DISCOVERIES, WESTERN GULF OF MEXICO

In order to reduce the effects of statistical variation 

upon estimates of the ultimate numbers of fields in 

classes 12 to 9, a smoothed estimate is used for class 13. 

This estimate is based upon a reestimation, for smoothing purposes only, of fn.

Let T = L fif

.=13

then ?17 = 7Tr-l)/(r 5 - 1).

because T represents the partial sum of a geometric 

series and /J3 = r 4/17 .

Another method of estimating the average ratio f 

(David H. Root, 1980, oral commun.) is to estimate the 

probability of success p of the truncated Iog2 geometric 

series by the method of maximum likelihood. For this 

procedure, we find the value of p that maximizes

awhere d and e are the lower and upper nontruncated 

class sizes in Iog2 . In our example, they are 13 and 17, 

respectively. The other parameters are

a = i f{ and b = L f^i-l).

i = d i = d

The average ratio r= l/(l-p). Both methods yield 

similar results.

Examination of table 3 shows that after January 1, 

1977, no fields are expected to be discovered in sizeclasses 17-19 in the combined Miocene-Pliocene trend 

area; in other words, we do not expect to find fields containing more than 194.3 million producible BOE (or 

1.17 trillion cubic feet of gas equivalent). The largest 

volume of undiscovered oil and gas within a single size 

class (18.3 percent of the total) is predicted to exist in 

field-size-class 12 (that is, within fields that range in 

size from 6.07 million to 12.14 million BOE or equivalently, from 36.4 to 72.8 BCF of producible gas). In 

this size class, 1.4 billion BOE is predicted to remain to 

be discovered in 163 fields.

In addition, table 3 shows that 64.1 percent of the oil 

and gas remaining to be discovered in the combined 

Miocene-Pliocene trend of the study area is predicted to 

exist in the four smallest field-size classes considered; 

that is, size-classes 9-12. Fields in these size classes 

are within the size range where the field-size distribution was historically truncated by economic factors. 

Although the following conclusions are subject to 

qualifications, we believe that we can say with a high 

degree of confidence that the rapid increase in the price 

of natural gas in the middle to late 1970's and, to a

degree, the associated increase in the price of crude oil 

have caused more than half the oil and gas resources 

remaining to be discovered in the combined MiocenePliocene trend of the study area in fields containing 

more than 0.76 million barrels of producible oil equivalent to be converted from the uneconomic category to 

the economic category.

ESTIMATING THE INCREMENTAL FUTURE RATES OF

OIL AND GAS FIELD DISCOVERIES IN THE

MIOCENE-PLIOCENE TREND

Given estimates of the ultimate number of oil and 

gas fields expected to exist in each field-size class and 

their associated discovery efficiencies (table 3), along 

with additional information on average area! extents 

and measurement of the basin size, we calculated the 

future rates of discovery of these fields in the MiocenePliocene trend area by using the Arps-Roberts (1958) 

discovery-process model. This forecast is shown in 

table 4. The numbers of discoveries expected to be made 

in each field-size class by the first increment of 200 

wildcat wells drilled starting January 1, 1977, are 

given in the first row of table 4. These oil and gas fields 

(26.1 fields in all) are predicted to contain 251.1 million 

barrels of producible oil equivalent.

The numbers of discoveries forecasted to be made by 

the first 200 wildcat wells range from a maximum of 

7.78 discoveries expected in size-class 9 down to only 

0.16 expected discoveries in size-class 16. The quantity 

of oil equivalent expected to be discovered at the completion of each successive wildcat-drilling increment is 

forecasted to decline slowly. We forecast that 2,400 additional wildcat wells will have to be drilled in the combined Miocene-Pliocene trend (12 increments of 200 

wildcat wells each) before the forecasted rate of discovery per drilling increment declines to half of that 

forecasted for the first drilling increment. Thus, almost 

as many wildcat wells (79.2 percent as many) have to 

be drilled in the future (2,400 wildcats starting Jan. 1, 

1977) as have been drilled in the past (3,300 wildcats 

through the end of 1976) before the expected level of 

discovery per drilling increment declines to approximately half (125.1 million BOE per increment or 

625,500 BOE per wildcat well) of that forecasted for the 

first drilling increment (251.1 million BOE per increment or 1,255,000 BOE per wildcat well). Such rates of 

discovery are judged to be sufficiently attractive to insure that the Miocene-Pliocene trend area in the Gulf 

of Mexico study area will be an attractive exploration 

theater for 10 to 15 years after the start of the forecast 

at January 1, 1977. This judgement is based upon the 

assumption that it will take 10-15 years or until 

1987-92 to drill the 2,400 wildcat wells forecasted to be
ESTIMATING THE PARAMETERS OF THE DISCOVERY-PROCESS MODEL 23

TABLE 4. Forecasted future number of discoveries per increment of 200 wildcat wells drilled in the Miocene-Pliocene trend of the study area

[BOE, barrels of oil equivalent]

Cumulative 

number of 

wildcat wells

3,300

3,500

3,700

3,900

4,100

4,300

4,500

4,700

4,900

5,100

5,300

5,500

5,700

5,900

6,100

6,300

6,500

6,700

6,900

7,100

Number of fields to be discovered in each class1

9

7.78

7.70

7.62

7.54

7.47

7.39

7.31

7.24

7.16

7.09

7.02

6.95

6.87

6.80

6.73

6.67

6.60

6.53

6.46

6.40

10

5.77

5.70

5.62

5.55

5.48

5.40

5.33

5.26

5.19

5.13

5.06

4.99

4.93

4.86

4.80

4.73

4.67

4.61

4.55

4.49

11

4.36

4.28

4.21

4.13

4.06

3.99

3.92

3.85

3.78

3.72

3.65

3.59

3.53

3.46

3.40

3.34

3.28

3.23

3.17

3.11

12

3.26

3.19

3.11

3.03

2.96

2.89

2.82

2.75

2.69

2.62

2.56

2.50

2.44

2.38

2.32

2.27

2.21

2.16

2.11

2.06

13

2.39

2.31

2.23

2.16

2.08

2.01

1.95

1.88

1.81

1.75

1.69

1.64

1.58

1.53

1.47

1.42

1.38

1.33

1.28

1.24

14

1.51

1.42

1.33

1.24

1.16

1.09

1.02

.96

.90

.84

.79

.74

.69

.65

.61

.57

.53

.50

.47

.44

15

0.88

.78

.69

.61

.54

.48

.42

.38

.33

.29

.26

.23

.20

.18

.16

.14

.13

.11

.10

.09

16

0.16

.13

.10

.08

.06

.05

.04

.03

.03

.02

.02

.01

.01

.01

.01

.01

.00

.00

.00

.00

Incremental discoveries 

in all size classes 

(millions of BOE)

251.1

233.0

217.2

203.2

190.7

179.5

169.4

160.2

151.9

144.3

137.4

131.0

125.1

119.7

114.6

109.9

105.6

101.5

97.6

94.0

'See table 2 for definition of field-size classes.

required to lower the rate of discovery in this region to 

approximately 625,500 BOE per wildcat well.

ESTIMATING THE PARAMETERS FOR THE 

PLEISTOCENE TREND

Estimation of the ultimate number of oil and gas 

fields existing in each field-size class directly from the 

discovery-data series was not possible for fields in the 

Pleistocene trend. This type of estimation was not possible because the exploration history in the region has 

covered too short a period to allow the size-class-bysize-class rates of discovery to decline significantly. 

This lack of decline is not an unexpected result for such 

a short data series that essentially covers only the 

1969-76 period.

Given this situation, assumptions had to be made in 

order to produce a size-class-by-size-class forecast of the 

future rates of discovery in this region. The first 

assumption made was that the discovery efficiency for 

each size class in the Pleistocene trend is the same as 

that determined for the same size class in the MiocenePliocene trend area. We are then assuming that the 

cumulative size-class-by-size-class discovery graphs in 

the Pleistocene trend will be identical to the corresponding graphs in the Miocene-Pliocene trend area. 

The second assumption made was that the part of the 

field-size distribution of oil and gas fields smaller than

fields in size-class 13 has the same general form in this 

trend area as the field-size distribution has in the 

Miocene-Pliocene trend area, that is, the average ft-Jfi 

ratio = 1.65 for size-class 12 and the smaller size 

classes.

Given these two assumptions, the ultimate number 

of oil and gas fields expected to exist in each field-size 

class in the Pleistocene trend was estimated by use of 

the Arps-Roberts (1958) model. These estimates are 

given in column 3 of table 5. For the Pleistocene trend 

area, the same two-stage estimation procedures were 

used as were used for the Miocene-Pliocene trend area. 

In the first stage, estimates were made of the number 

of fields ultimately expected to exist in the first size 

classes unaffected by economic truncation; that is, in 

size-classes 13-17, inclusive. An example calculation is 

shown below for size-class 13:

1. Assume C(A) = 2.65 (the Miocene-Pliocene 

estimate).

2. Given the additional data: 

Ai3 = 6.68 km2; 

w = 1,000 wildcat wells as of approximately

the end of 1976; 

Fi3 (w) = 21 fields discovered by the drilling of

1,000 wildcat wells; 

B = 33,612 km2 = Pleistocene trend area of

study area.
24 FUTURE RATES OF OIL AND GAS DISCOVERIES, WESTERN GULF OF MEXICO

TABLE 5. Summary data and estimates of the ultimate number of 

oil and gas fields by class size and contained resources for the 

Pleistocene trend of the study area

(BOE, barrels of oil equivalent]

Number of fields 

Class found by 1,000 

size1 wildcat wells F*(<*>V

9

10

11

12

13

14

15

16

17

18

9

11

20

17

21

26

9

8

3

1

358.7

217.4

131.8

79.9

51.3

39.9

10.4

8.2

3.0

1.0

Smoothed 

CM,

_

2.65

3.40

4.15

4.89

5.65

Expected 

total ultimate 

resource 

(BOE x 10«)

391.0

450.0

581.2

670.4

871.6

1,392.1

692.7

1,038.9

623.4

502.8

Expected 

remaining 

resource* 

(BOE x 10s)

381.2

427.3

493.0

527.7

514.8

485.0

93.3

25.3

.0

.0

Percent 

of total 

resource 

remaining

12.9

14.5

16.7

17.9

17.5

16.5

3.2

.9

.0

.0

Total 125 901.6 - 7,214.1 2,947.6 100.0

'See table 2 for definition of field-size classes.

 See text for explanation of estimation procedure used.

'Amounts are for the period starting 1/1/77.

3. Solve the Arps-Roberts (1958) model for F^(oo) 

FA(w) = £(oo){l-exp[-CfA;Au>/B]}; 

21 = &(oo){l-exp[(-2.65.6.68

 1,000)733,612]}; 

FA(oo) - 51.3 fields expected to exist in size-class

13.

Given estimates of the F^(<x>)'s made in this manner 

for size-classes 13-17, we proceeded to the second stage 

of estimation by estimating in F^(c»)'s for size-classes 

12 down to and including size-class 9. These four estimates were determined by using the same average 

geometric progressive estimate r 1.65 as was used to 

estimate the ultimate number of fields in these same 

size classes in the Miocene-Pliocene trend area. In taking this approach, we are further assuming that the 

same historical level of economic truncation has taken 

place in both trend areas.

The results from this estimation procedure produce a 

forecast that a total of 901.6 oil and gas fields are ultimately expected to exist in the Pleistocene trend (table 

5); each of these fields contains more than 0.76 million 

barrels of producible oil equivalent. Of this total, 125 

fields have been discovered through the end of 1976. 

The expected ultimate production of these 776.6 oil and 

gas fields remaining to be discovered as of January 1, 

1977, is estimated to be 2.95 billion BOE. This estimate implies then that 40.9 percent of the oil and gas 

ultimately producible from the Pleistocene trend remained to be discovered as of January 1,1977, whereas 

only 29 percent of the oil and gas ultimately producible

from the combined Miocene-Pliocene trend remained to 

be discovered at the same date.

In addition, table 5 shows that no fields in classes 

17-18 (that is, fields containing more than 194.3 

million BOE) are expected to be discovered in the 

Pleistocene trend area; as discussed above, we don't expect to find any fields this size in the Miocene-Pliocene 

trend area either. The field-size class predicted to have 

the largest volume of oil and gas remaining to be discovered as of January 1,1977, is class 12, which is estimated to contain 527.7 million BOE (17.9 percent of 

the total remaining). This volume of oil and gas is expected to exist in 62.9 fields. A similar amount of oil 

and gas is predicted to remain to be discovered in 30.3 

fields of size-class 13; these 30.3 fields are expected 

to contain 514.8 million BOE (17.5 percent of total 

remaining).

The total volume of oil and gas remaining to be discovered in the four smallest field-size classes (9 

through 12) is predicted to be 1.8 billion BOE, which is 

62 percent of the total oil and gas resources remaining 

to be discovered in the Pleistocene trend in fields 

larger than 0.76 million BOE. This volume of oil and 

gas is expected to exist in 730.8 fields that range in size 

from 0.76 million to 12.14 million BOE. These fields 

would, on the average, contain 2.5 million BOE. 

Although most of these fields would historically have 

been too small to warrant development, we anticipate 

that, in the future, many of these fields when 

discovered will be put into production.

ESTIMATING THE INCREMENTAL FUTURE RATES OF

OIL AND GAS FIELD DISCOVERIES IN THE

PLEISTOCENE TREND

These estimates of the expected ultimate number of 

oil and gas fields existing in each field-size class were 

used as input for the Arps-Roberts (1958) model to forecast the future rates of discovery in the Pleistocene 

trend area. This forecast (table 6) shows that 25.5 fields 

(in size-classes 9 through 16) are forecasted to be 

discovered by the first increment of 200 wildcat wells 

to be drilled starting January 1, 1977. This collection 

of fields is forecasted to contain 256.8 million BOE or 

an expected yield of 1,284,000 BOE per wildcat well.

The rate of return to wildcat drilling will be reduced 

to approximately half of its initial level by the completion of the sixth drilling increment when the cumulative number of wildcats drilled in the Pleistocene trend 

will stand at 2,200 wells. We forecast that the completion of these 1,200 wildcat wells will result in the discovery of 1.06 billion BOE, which is 35.9 percent of the 

recoverable oil and gas resources forecasted to remain 

to be discovered starting January 1,1977, in Pleistocene
ESTIMATING THE PARAMETERS OF THE DISCOVERY-PROCESS MODEL 25

TABLE 6. Forecasted future number of discoveries per increment of 200 wildcat wells drilled in the Pleistocene trend of the study area

[BOB, barrels of oil equivalent]

Cumulative

number of 

wildcat wells

1,200

1,400

1,600

1,800

2,000

2,200

2,400

2,600

2,800

3,000

3,200

3,400

3,600

3,800

4,000

4,200

4,400

4,600

4,800

5,000

Number of fields to be discovered in each class1

9

5.84

5.73

5.63

5.53

4.53

5.34

5.24

5.15

5.06

4.97

4.88

4.79

4.71

4.62

4.54

4.46

4.38

4.30

4.22

4.15

10

5.18

5.04

4.90

4.77

4.64

4.51

4.39

4.27

4.15

4.04

3.92

3.82

3.71

3.61

3.51

3.42

3.32

3.23

3.14

3.06

11

4.50

4.31

4.12

3.95

3.78

3.62

3.47

3.32

3.18

3.05

2.92

2.79

2.67

2.56

2.45

2.35

2.25

2.15

2.06

1.98

12

3.73

3.49

3.26

3.04

2.84

2.66

2.48

2.32

2.17

2.03

1.89

1.77

1.65

1.55

1.44

1.35

1.26

1.18

1.10

1.03

13

3.03

2.73

2.45

2.21

1.99

1.79

1.61

1.45

1.30

1.17

1.06

.95

.86

.77

.69

.62

.56

.51

.45

.41

14

2.64

2.14

1.73

1.40

1.14

.92

.74

.60

.49

.40

.32

.26

.21

.17

.14

.11

.09

.07

.06

.05

15

0.46

.31

.21

.14

.09

.06

.04

.03

.02

.01

.01

.01

.00

.00

.00

.00

.00

.00

.00

.00

16

0.11

.05

.02

.01

.01

.00

.00

.00

.00

.00

.00

.00

.00

.00

.00

.00

.00

.00

.00

.00

Incremental discoveries 

in all size classes 9-16 

(millions of BOB)

256.8

213.1

180.9

156.0

136.4

120.4

107.2

96.2

86.8

78.8

71.9

65.9

60.6

56.0

51.8

48.2

44.9

41.9

39.3

36.8

 See table 2 for definition of field-size classes.

fields larger than 0.76 million BOE. By comparison, 

1,200 wildcat wells drilled in the combined MiocenePliocene trend area starting January 1, 1977, are 

forecasted to yield 1.27 billion BOE (the sum of the 

yields of the first six drilling increments in table 4) in 

fields of the same size. This combined yield is only 16.6 

percent of the total oil and gas resources forecasted to 

remain in this region in fields of this size starting 

January 1, 1977. Comparison of the forecasts for both 

trend areas shows that the incremental yield per wildcat well in the Pleistocene trend will decline much 

more rapidly than the yields per wildcat well in the 

Miocene-Pliocene trend. To a large extent, this difference in decline rates is a direct consequence of the 

small area occupied by the Pleistocene trend 

(33,612 km2) and the much larger area occupied by the 

Miocene-Pliocene trend (123,027 kma). Both these geologic trends, however, have substantial resources remaining to be discovered as of January 1,1977, and the 

pace of exploration will be intense at least through the 

end of the 1980's.

CONCLUSIONS

The expected number of oil and gas fields remaining 

to be discovered by size class in the Gulf of Mexico was 

estimated. The rate at which these fields will be discovered in the future (starting Jan. 1, 1977) was also 

forecasted. These forecasts were made individually for 

two regions in the study area in the Gulf of Mexico: the 

combined Miocene-Pliocene geologic trend, which occupies 123,027 km2, and the Pleistocene trend, which 

occupies 33,612 km2. The water depth ranges from the 

shoreline to 200 m so that both State and Federal 

waters are included in the study area.

Within the Miocene-Pliocene trend area, 1,943 oil 

and gas fields individually containing more than 0.76 

million BOE (or equivalently 4.6 BCF of gas) are expected to remain to be discovered starting January 1, 

1977. Collectively these fields are estimated to contain 

7.71 billion BOE. Of this total number of fields, 94.7 

percent are estimated to contain individually less than 

12.14 million BOE. These 1,840 fields are predicted to 

contain 4.94 million BOE or 64.1 percent of the total 

volume of oil and gas estimated to exist in the MiocenePliocene trend area.

The comparable estimates for the Pleistocene trend 

are as follows: (1) 776.6 oil and gas fields each larger 

than 0.76 million BOE remain to be discovered as of 

January 1, 1977, collectively containing 2.95 billion 

BOE, and (2) of the 776.6 total fields expected to be remaining to be discovered, 730.8 (94.1 percent) are expected to contain individually between 0.76 million 

and 12.14 million BOE.
26 FUTURE RATES OF OIL AND GAS DISCOVERIES, WESTERN GULF OF MEXICO

In the 1950's, 1960's, and into the early 1970's, fields 

in this size range were economically viable only under 

nearshore or similar low-cost conditions. We argue 

here that the large increase in the price of natural gas 

in the late 1970's (and also, to a degree, the associated 

increase in the price of crude oil) has been sufficient to 

allow fields even as small as 1 million to 2 million BOE 

(6-12 BCF of gas) to be commercial today in water 

10-20 m deep. In the near future, newly devised completion techniques promise to make even smaller fields 

commercial. Therefore, we conclude that recent price 

increases as well as anticipated price increases along 

with the implementation of new production techniques 

have moved the economic truncation level to a level 

low enough that most fields predicted to remain to be 

discovered in size-classes 9 through 12 (0.76 million to 

12.14 million BOE) in both the Miocene-Pliocene and 

Pleistocene trends are now commercially producible. 

More specifically, a large part of the 6.7 billion BOE 

predicted to remain to be discovered in both geologic 

trend areas in fields smaller than 12.14 million BOE 

now can be commercially developed after discovery, 

whereas before the mid-1970's, such small fields could 

not have been commercially developed. This 6.7 billion 

BOE in fields ranging in size from 0.76 million to 12.14 

million BOE is, however, only 19.9 percent of the total 

volume of oil and gas that has been discovered and is predicted to remain to be discovered in the Gulf of Mexico.

Forecasts of the future rates of discovery of oil and 

gas fields in both geologic trend areas were made for a 

succession of wildcat drilling increments of 200 wells 

each. We forecasted that an additional 2,600 wildcat 

wells will be drilled in the combined Miocene-Pliocene 

trend before the yield per wildcat well is reduced to approximately half that to be obtained in the first drilling increment (from 1.255 million to 0.625 million 

BOE per wildcat well). In the Pleistocene trend area, 

the forecasted yield per wildcat well in the first increment of 200 wildcats drilled after January 1, 1977, is 

1.284 million BOE per wildcat well. This yield will be 

reduced to approximately half this level (0.602 million 

BOE per wildcat well) by the completion of the sixth 

drilling increment when 1,200 additional wildcat wells 

will have been drilled in this trend area. Given the 

prediction that many fields remain to be discovered in 

the Gulf of Mexico in water as deep as 200 m and that 

substantial discovery yields per wildcat well will be 

available from the drilling of at least 2,000 wildcat 

wells after January 1, 1977, in this region, we concluded that, if the rate of leasing is not greatly changed, the study area in the Gulf of Mexico will be an active exploration theater into the late 1980's and even 

into the early 1990's.

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Association of Petroleum Geologists Bulletin, v. 42, no. 11, 

p.2549-2566.

Drew, L. J., 1975, Linkage effects between deposit discovery and 

postdiscovery exploratory drilling: U.S. Geological Survey Journal of Research, v. 3, no. 2, p. 169-179.

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Geological Survey Professional Paper 1138-A, 11 p.

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Root, D. H., and Drew, L. J., 1979, The pattern of petroleum discovery 

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