19 separation of anomalous aerial radiospectrometric zones using ...

* Address for correspondence: 

King Abdulaziz University 

Faculty of Earth Sciences 

P.O. Box 80206 Jeddah 21589, KSA. 

El-Sayed M. Abdelrahman, Ahmed A. Ammar, Hamdy I. E. Hassanein and Khaled S. Soliman 

SEPARATION OF ANOMALOUS AERIAL 

RADIOSPECTROMETRIC ZONES USING LEAST-SQUARES 

METHOD ON A SAMPLE AREA IN EGYPT 

El-Sayed M. Abdelrahman 

Cairo University, Faculty of Sciences, Geophysics Department, Giza, Egypt. 

Ahmed A. Ammar 

Nuclear Materials Authority, P.O. Box. 530, El-Maadi, Cairo, Egypt. 

Hamdy I. E. Hassanein* and Khaled S. Soliman 

Cairo University, Faculty of Sciences, Geophysics Department, Giza, Egypt. 

: ﺔـــﺻﻼــﺨﻟا 

ﻲﻋﺎﻌﺷﻹا ﺢﺴﻤﻟا ﻂﺋاﺮﺧ تﺎﻧﺎﻴﺒﻟ ﺔﻘﻠﻄﻤﻟا ﻢﻴﻘﻟا ﻞﺼﻔﻟ تﺎﻌﺑﺮﻤﻟا ﻞﻗأ ﺔﻘﻳﺮﻃ ماﺪﺨﺘﺳﺎﺑ ﺔﺳارﺪﻟا ﻩﺬه ﻢﺘﻬﺗ 

عﺎﻌﺷﻹا ﺔﻴﻟﺎﻋ ﻖﻃﺎﻨﻤﻟاو 

،( 

مﻮﻳرﻮﺜﻟاو مﻮﻴﻧارﻮﻴﻟاو مﻮﻴﺳﺎﺗﻮﺒﻟاو ﻲﻠﻜﻟا عﺎﻌﺷﻹا تﺎﻧﺎﻴﺑ ﻦﻣ ﻞﻜﻟ) 

يﻮﺠﻟا ﻲﻔﻴﻄﻟا 

تﺮﻴﺘﺧا ﺪﻗو . ةذﺎﺸﻟا ﻖﻃﺎﻨﻤﻟا ﻩﺬﻬﺑ ﺔﻄﻴﺤﻤﻟا رﻮﺨﺼﻟا ﻦﻣ ﺔﺠﺗﺎﻨﻟا ﺔﻴﻌﻴﺒﻄﻟا ﺔﻴﻋﺎﻌﺷﻹا ﺔﻴﻔﻠﺨﻟا ﻞﺜﻤﺗ ىﺮﺧأو 

ﺔﻘﻄﻨﻤﻟا ﻩﺬهو 

،ﺔﻴﻟﺎﺤﻟا ﺔﻘﻳﺮﻄﻟا ةءﺎﻔآ رﺎﺒﺘﺧﻻ ﺔﻨﻴﻌآ ﺔﻳﺮﺼﻤﻟا ﺔﻴﻗﺮﺸﻟا ءاﺮﺤﺼﻟا لﺎﻤﺸﺑ لﻮﺑار مأ ﻞﺒﺟ ﺔﻘﻄﻨﻣ 

رﻮﺨﺻ ﻦﻣ تﺎﻌﺑﺎﺘﺗ ﻊﻣ ٍﻖﻓاﻮﺗ ِمﺪﻋ َﺢﻄﺳ ﺔﺛﺪﺤﻣ يﺮﺒﻣﺎﻜﻟا ﻞﺒﻗ ﺎﻣ ﺮﺼﻋ ﻰﻟإ ﻊﺟﺮﺗ ﻲﺘﻟا سﺎﺳﻷا رﻮﺨﺼﺑ ﻩﺎﻄﻐﻣ 

. ﺎهﻮﻠﻌﺗ ﻲﺘﻟا ﺔﻴﺑﻮﺳﺮﻟا 

ةﺎﻴﺤﻟا ﺮﺼﻋ 

ﻞﻗأ ﺔﻘﻳﺮﻃ ماﺪﺨﺘﺳﺎﺑ ﺔﻴﻤﻴﻠﻗﻹا ﺔﺒآﺮﻤﻟا ﻞﺼﻓ ﺪﻌﺑ -ﺔﻴﻘﺒﺘﻤﻟا 

تاذﺎﺸﻟا ﻞﻴﻠﺤﺗ ﺪﻋﺎﺳ ،ﺔﺳارﺪﻟا ﻩﺬه ﻲﻓو 

ﻦﻣ ﺔﺠﺗﺎﻨﻟا ﺔﻣﺎﻬﻟا ﻲﻋﺎﻌﺷﻹا ﻒﻴﻄﻟا تاذﺎﺷ ﺪﻳﺪﺤﺗ ﻲﻓ ﻂﺋاﺮﺧ ﻰﻠﻋ ﺎﻬﻠﻴﺜﻤﺗو -( 

ﻰﻟوﻷا ﺔﺟرﺪﻟا ﻦﻣ) 

تﺎﻌﺑﺮﻤﻟا 

ﺪﻌﺑ تﺎﻧﺎﻴﺒﻟا ﻦﻣ ﺔﺠﺗﺎﻨﻟا -ﺔﻴﻘﺒﺘﻤﻟاو 

ﺔﻴﻤﻴﻠﻗﻹا ﺔﺒآﺮﻤﻟا 

ﻂﺋاﺮﺧ نأ ﺪﺟوو . ﺔﺳارﺪﻟا ﺔﻘﻄﻨﻣ ﻞﻜﻟ يﻮﺠﻟا ﺢﺴﻤﻟا 

ﻦﻣ ﺖﻘﺑﺎﻄﺗ ( مﻮﻳرﻮﺜﻟاو مﻮﻴﻧارﻮﻴﻟا مﻮﻴﺳﺎﺗﻮﺒﻟاو ﻲﻠﻜﻟا عﺎﻌﺷﻹا تﺎﻧﺎﻴﺑ ﻦﻣ ﻞﻜﻟ) 

-تﺎﻌﺑﺮﻤﻟا 

ﻞﻗأ ﺔﻘﻳﺮﻄﺑ ﺎﻬﺘﺠﻟﺎﻌﻣ 

ﺔﻴﺋﺎﺼﺣﻹا قﺮﻄﻟﺎﺑ تﺎﻧﺎﻴﺒﻟا ﺔﺠﻟﺎﻌﻣ ﻦﻣ ﺔﺠﺗﺎﻨﻟا تاذﺎﺸﻟا ﻂﺋاﺮﺧ ﻊﻣ رﺎﺸﺘﻧﻻا ﻪﺟوو ةﺪﺸﻟاو ﻊﻗاﻮﻤﻟا ﺚﻴﺣ 

يﻷ ﺔﻴﻋﺎﻌﺷﻹا حﻮﺴﻤﻟا تﺎﻧﺎﻴﺒﻟ تاذﺎﺸﻟا ﺪﻳﺪﺤﺗ ﻲﻓ تﺎﻌﺑﺮﻤﻟا ﻞﻗأ ﺔﻘﻳﺮﻃ ماﺪﺨﺘﺳﺎﺑ ﻰﺻﻮُﻳ ﻚﻟﺬﻟ ،ﺔﻳﺪﻴﻠﻘﺘﻟا 

. ﺔﻘﻄﻨﻣ 

Paper Received 14 December 2002; Revised 25 June 2006; Accepted 8 November 2006. 

January 2007 The Arabian Journal for Science and Engineering, Volume 32, Number 1A 19


ABSTRACT 

This study deals with using the least-squares method (LSM) to separate the 

absolute aeroradiospectrometric maps (T.C., 40 K, eU, and eTh) into highly 

radioactive zones and the normal radioactive background of the host rocks. The 

Gabal Um-Rabul area, selected for testing the efficiency of the present method, 

lies in the northern part of the Eastern Desert of Egypt and is covered mainly by 

Precambrian basement rocks, which are unconformably overlain by Phanerozoic 

sedimentary successions. 

In the present study, the least-squares (first-order) residual anomaly analysis 

method was used and contour maps were drawn to delineate the significant 

aeroradiospectrometric anomalies over the study area. It was found that, the 

least-squares first-order regional and residual total-count (T.C.) and the three 

absolute radioelements (K, eU, & eTh) maps of the study area show a high 

degree of coincidence with the anomalous maps constructed by the conventional 

statistical methods in terms of the locations, intensities, and trends of anomalous 

zones. Therefore, it is recommended to apply the least squares method for 

locating radioelements anomalous zones in any surveyed area. 

Key words: Least-Square Method (LSM), Aeroradiospectrometry, Gabal Um 

Rabul, Geological setting, Normal probability plot, Regional residual separation, 

Northern Eastern Desert of Egypt. 

20 The Arabian Journal for Science and Engineering, Volume 32, Number 1A January 2007


SEPARATION OF ANOMALOUS AERIAL RADIOSPECTROMETRIC ZONES USING 

LEAST-SQUARES METHOD ON A SAMPLE AREA IN EGYPT 

INTRODUCTION 

The major objectives of aerial gamma-ray spectrometer data interpretation are the identification of anomalous 

measurements and outlining the probable boundaries of potential uraniferous provinces, in which the rocks and soils are 

preferentially enriched in uranium [1]. There are several different ways to identify and outline potential uraniferous 

provinces through the examination of the two- and three-radioelement ratios and standard deviation anomaly maps. The 

present study is a first trial to use the least square method (LSM) to identfy potential relative anomalous zones. 

Since mid-1967 high sensitive, quantitative airborne gamma-ray spectrometry has been applied extensively in 

support of geological mapping and mineral exploration, especially in regions where the geology is more complex and 

access is difficult. The method depends upon the fact that the measured absolute and relative concentrations of the 

radioelements K, U, and Th vary significantly with lithology [2]. 

The Gabal Um-Rabul study area is located in the northern part of the Eastern Desert of Egypt, to the west of Ras 

Gharib town on the western coast of the Gulf of Suez, and is bounded by latitudes 28° 07′ 30′′ N and 28° 27′ 30′′ N and 

longitudes 32° 20′ E and 32° 50′ E (Figure 1). The area is mainly covered by Precambrian igneous and metamorphic 

rocks, which constitute a part of the Arabian–Nubian Shield (Figure 2a). To the west, basement rocks are unconformably 

overlain by Phanerozoic sedimentary succession. The general topography of the eastern part of the study area is more 

rugged than its western part. In addition, the examined area includes a part of the Red Sea plain in the east. The study 

area is generally dissected by several NE, ENE, NW, and E-W trending wadis (dry drainage), which are mainly 

structurally controlled. 

Based on analyses and interpretation of aeroradiospectrometric survey data using conventional statistical methods, 

the interpreted radiometric–lithologic units (IRLU) map (Figure 2b) shows that, the study area comprises four basement 

rock units: Metavolcanics (11.9 Ur, and 1.9 % 40 K, 2.3 ppm eU, and 7.3 ppm eTh) , Older granites (9.95 U, 1.4 % 40 K, 

2.2 ppm eU, and 6.1 ppm eTh), Dokhan volcanics (5.1 U, 0.5 % 40 K, 1.5 ppm eU, and 3.6 ppm eTh), and Younger 

granites ( 12.6 Ur, 2.0 % 40 K, 2.4 ppm eU, and 7.4 ppm eTh). Also, the area includes five sedimentary units: Araba 

Formation ( 4.3 U, 0.4 % 40 K, 1.3 ppm, eU and 3.3 ppm eTh), Samr El-Qaa Formation (4.0 Ur, 0.4 % 40 K, 1.3 ppm eU 

& 3.0 ppm eTh), Wadi Qena Formation (3.95 U, 0.4 % 40 K, 1.5 ppm eU & 2.7 ppm eTh), Galala Formation (4.1 U, 

0.46 % 40 K, 1.35 ppm eU and 2.8 ppm eTh), and the Quaternary sediments (10.6 U, 1.7 % 40 K, 2.3 ppm eU, and 6.0 

ppm eTh)[3]. 

32N 25 E 27 29 31 

Mediterranian Sea 

Alexandria 

33 35 37 

32 

30 

28 

26 

24 

Libya 

Qattara Depession 

Siwa Oasis 

Cairo 

Study 

Area 

Suez 

Sinai 

Western Desert 

Dakhla Oasis 

kharga Oasis 

Eastern 

Desert 

Nasser Lake 

Ras Gharib 

0 100 200 km 

22 

25 27 

Sudan 

29 31 33 35 37 

January 2007 The Arabian Journal for Science and Engineering, Volume 32, Number 1A 21 

Qena 

Aswan 

Red 

Figure 1. Map of Egypt showing the location of Gabal Um Rabul 

area in the northern part of the Eastern Desert. 

Sea 

30 

28 

26 

24 

22


32 20 00E 32 50 00 

28 27 30 N 

28 27 30 

LEGEND 

Quaternary 

Sediments 

W. Ghazala 

Galala 

Formation 

N 

Wadi Qena 

Formation 

Samr El-Qaa 

Formation 

G. Um Rabul 

Araba 

Formation 

Younger 

GB 

Granites 

VD Dokhan 

Volcanics 

Older 

Granites 

28 07 30 

32 20 00 

G. Samr El-Abd 

0 2 4 6 8 km 

28 07 30 

32 50 00 

Figure 2 (a). Geological map of Gabal Um Rabul area [4]. 

32 20 00E 32 50 00 

28 27 30 N 

28 27 30 

N 

28 07 30 

32 20 00 

pz 

G. Samr El-Qaa 

W. Ghazala 

W. Hawashiya 

G. Umm Rabul 

G. Samr El-Abd 

0 2 4 6 

28 07 30 

32 50 00 

8 km 

Metavolcanics 

W. Wadi 

(Dry Valley) 

G. Gabal 

(Mountain) 

LEGEND 

Quaternary-4 

Sediments 

Quaternary-3 

Sediments 

Quaternary-2 

Sediments 

Quaternary-1 

Sediments 

Galala 

Formation-2 

Galala 

Formation-1 

Wadi Qena 

Formation-2 

Wadi Qena 

Formation-1 

Samr El-Qaa 

Formation 

Araba 

Formation 

Younger 

Granites-1 

Dokhan 

Volcanics-2 

Dokhan 

Volcanics-1 

22 The Arabian Journal for Science and Engineering, Volume 32, Number 1A January 2007 

GB-3 

GB-2 

GB-1 

VD-2 

VD-1 

Younger 

Granites-3 

Younger 

Granites-2 

Older 

Granites-4 

Older 

Granites-3 

Older 

Granites-2 

Older 

Granites-1C 

Older 

Granites-1B 

Older 

Granites-1A 

Weathered 

Older Granites-2 

Weathered 

Older Granites-1 

Metavolcanics-3 



Prospective 

pz Zone 

W. 

Wadi (Dry Valley) 

G. Gabal (Mountain) 

Figure 2 (b). Interpreted radiometric–lithologic units (IRLU) map of Gabal Um Rabul area. 

In the present study, the least-squares method was applied on the total-count (T.C.) survey data of the 

aeroradiometry, aeroradiospectrometric potassium ( 40 K%), equivalent uranium (eU), and equivalent thorium (eTh). The 

application of least-squares residuals technique in aeroradiospectrometric data may be of interest especially in the field 

of aerial radiospectrometric exploration. T.C., 40 K%, eU, and eTh maps were subjected to a separation technique using 

the least-squares method to separate the highly radioactive zones from the normal radioactive background of the host 

rocks. Regional components of the first, second, third, fourth, and fifth orders were fitted to the input data. Correlation 

coefficients between successive residual maps were computed in order to determine the optimum order of the regional 

surface to be used. The regional field in this particular area can be represented as first-order, because the first order gave 

a good correlation factor in each case. 

The least-squares method (LSM) was used to construct the first-order regional and residual total-count (T.C.) and 

the three absolute radioelements (K, eU, & eTh) maps of the study area. The produced residual radiospectrometric maps 

were compared with the point (local) anomaly maps, produced by the conventional statistical methods. The present study 

delineates some locations of high and very high aerial radiospectrometric levels which identify and outline 

aeroradiospectrometric significant anomalies all over the study area . 

GEOLOGICAL SETTING 

The rocks exposed in Gabal Um-Rabul area can be grouped according to their mode of occurrence and their mutual 

relationships from top to bottom as the following sequence (Figure 2a) [4].


Phanerozoic Rocks 

The Phanerozoic sedimentary rocks which are represented in the western part of the area under investigation, are 

descried briefly in the following paragraphs. 

Quaternary Sediments (Quaternary – QW) 

According to the geological map (Figure 2a) of the study area, the undifferentiated Quaternary Sediments (QW) are 

situated in four localities. The average T.C. radioactivity of Quaternary sediments is 10.6 U [3]. They are classified into 

four interpreted radiolithologic units (IRLU) QW-1, QW-2, QW-3 and QW-4 as seen in Figure 2b. Quaternary deposits 

consist mainly of wadi aluvium deposits which is composed of loose rock fragments from the surrounding rocks. 

Galala Formation (Cenomanian–Early Turonian – KUG) 

According to (Figure 2a), the Galala Formation (KUG) is exposed in the western part of the the study area in two 

localities and is mainly composed of limestone, some dark browin grey sandstone, and clay bands intercalations. As a 

result of the application of the conventional statistical methods of analysis, Galala Formation was treated as two 

independent IRLU (KUG-1 and KUG-2) (Figure 2b). The average T. C. radioactivity of Galala Formation is 4.1 Ur, 

[3]. 

Wadi Qena Formation (Early Cretaceous – KLQ) 

The Wadi Qena Formation (KLQ) is located in three localities in the western part of the study area (Figure 2a). This 

formation is composed of sandstones which was deposited during Albian Cenomanian age. The application of the 

convensional statistical analysis prove that the Wadi Qena Formation was involved in two IRLU (KLQ-1 & KLQ-2, 

Figure 2b). The average T. C, radiactivity of the Wadi Qena formation is 3.95 Ur. 

Samr El-Qaa Formation (Carboniferous – CQ) 

The Samr El-Qaa (CQ) Formation is exposed in only one locality within the study area (Figure 2a). It is mainly 

composed of Carboniferous age shale deposites. This formation yielded a T.C. average value of 4.0 U. 

Araba Formation (Cambrian – ES) 

The Araba Formation (ES) is exposed in two localities: one locality in the northwestern part and the other in the 

southwestern part of the study area. This unit is mainly composed of sandstones of Cambrian age. The previous 

statistical analysis of the aeroradiometric data indicated that the Araba Formation in both localities represent a single 

IRLU. The average value of T.C. of this IRLU is 4.3 U. 

Precambrian Basement Rocks 

Younger Granites (GB) 

In the present study area uounger (pink) granites (GB) are represented by the calc- alkaline members [6]. Their 

composition ranges from monzogranite to ideal granite. This type of granites are more resistant to weathering and 

occupy terrains of higher relief than the older granite (GA). Three (IRLUs (GB-1, GB-2, and GB-3) have been in this 

rock unit (Figure 2b) 

Dokhan Volcanics 

Typical sequences of this rock unit are composed of intermediate to acidic volcanic rocks with their pyroclastic 

equivalents. They are divided, petrographically, into andesite, quartz andesite, dacite, ryholite, quartz trachyte, and 

pyroclastics [7]. Typical outcrops of the Dokhan volcanics are seen at Gabal Samr El-Qaa and two other occurrences are 

located in the southwestern part of the basement complex outcrop in the study area. Dokan volcanics comprise two 

IRLUs (VD-1 and VD-2) as seen in Figure 2b. 

Older granites (GA) 

Older granites (GA) are grey synorogenic and range in composition from quartz diorites to granodiorites and locally 

monzonites [6]. Commonly, this type of granite occurs in the form of elongated large bodies parallel to the NW–SE 

regional structural trend. GA-granite is easily susceptible to weathering, and occupies low-lying terrains strewn with 

small hillocks and traversed by wide sandy wadis. Weathered older granites (GAW) are mapped separately in Figure 2a. 

The application of the conventional statistical methods of analysis [8] differentiated the older granites in the present 

area into eight subunits (GAW-1, GAW-2, GA-1A, GA-1B, GA-1C, GA-2, GA-3, GA-4). as shown in Figure 2b. 

January 2007 The Arabian Journal for Science and Engineering, Volume 32, Number 1A 23


Metavolcanics 

These rocks are interpreted as the products of volcanic activity during eugeosyncline subsidental phase [8]. The 

metavolcanics in the Eastern Desert are generally subdivided into three classes: 

1. Intermediate to acidic metavolcanics and metapyroclastics. 

2. Ophiolitic metavolcanics. 

3. Metavolcanics, undifferentiated. 

Ophiolitic metavolcanics and undifferentiated metavolcanics, are not represented in the study area. Metavolcanics in 

the study area belong to the intermediate to acidic metavolcanic and metapyroclastics (MVA) class. Typical outcrops are 

seen around Gabal Samr El-Abd (Figure 2a). They are intimately associated with sediments [6] that are largely 

composed of tuffs and volcanogenic greywackes. The intermediate to acidic metavolcanic and metapyroclastics are 

essentially composed of meta-andesites and metadacites together with subordinate amounts of metabasalts and 

metarhyolites. According to the radiometric survey, this unit is divided into three subunits (MVA-1, MVA-2 & MVA- 

3), in Figure 2b. 

AERORADIOSPECTROMETRIC SURVEY AND DATA PRESENTATION 

In 1984 Western Geophysical Company of America carried out aeroradio spectrometric and aeromagnetic surveys 

for most of the surface area of the Eastern Desert of Egypt under a joint venture of the Egyptian General Petroleum 

Corporation (EGPC) and the Egyptian Geological Survey and Mining Authority (EGSMA). 

The aeroradiospectrometric survey was conducted along parallel flight lines oriented in a NE–SW direction at 1.5 

km spacing. A high-sensitivity 256-channel airborne gamma-ray spectrometer (AGRS) system was used for gamma-ray 

measurements. For safety reasons, the flight altitude was 92m in flat terrains and 122m in mountainous terrains [10]. The 

data were corrected and plotted as aeroradiospectrometric contour maps and profiles. In the present study, the digitizing 

process follows the basic acquired analog profiles of the flight lines drawn on the map and color image techniques were 

used in the interpretation of aerial gamma ray spectrometric data [11]. 

Consequently, the digitized total-count radiometry in Ur (radioactivity of 1 ppm of uranium), potassium in 

percentage, equivalent uranium & equivalent thorium contents in ppm, were plotted in the form of filled-color image 

maps (Figures 3– 6). 

The colored image maps, which are generated by assigning different colors to each grid element based on some 

attribute such as intensity, are more adequate for the human visual system interpretation of images than line drawings. 

Displaying geophysical data in color image form can often reveal information that is hidden in contour or profile maps 

[11–14]. Type and number of the used colors are determined according to the numerical range of the data. It is better to 

use a set of standard colors to avoid confusion when interpreting numerous images [15]. 

32 20 00E 32 50 00 

28 27 30 N 

28 27 30 

N 

28 07 30 

32 20 00 

0 2 4 6 8km 

28 07 30 

32 50 00 


L5 

L4 

L3 

L2 

L1 

32 

30 

28 

26 

24 

22 

20 

18 

16 

14 

12 

10 

8 

6 

4 

T. C. in Ur 

Figure 3. Filled-contour image map of the aerial total-count aero radiometric data.

32 20 00E 

28 27 30 N 

N 

28 07 30 

32 20 00 


0 2 4 6 8 

Figure 4. Filled-contoured image anomaly map of the aero radio spectrometric potassium. 

32 50 00 

28 27 30 

32 50 00 

28 07 30 


km 

(0.1 %) 

L5 

L4 

L3 

L2 

L1 

32 

30 

28 

26 

24 

22 

20 

18 

16 

14 

12 

10 

8 

6 

4 

2 

K 0.1 % 

32 20 00E 32 50 00 

28 27 30 N 

28 27 30 

N 

28 07 30 

32 20 00 

0 2 4 6 8km 

32 50 00 

Figure 5. Filled-color contour image of the aeroradiospectrometric equivalent uranium. 

L5 

L4 

L3 

L2 

L1 

28 07 30 

75 

70 

65 

60 

55 

50 

45 

40 

35 

30 

25 

20 

15 

10 

5 

eU in ppm multiplied by 10


32 20 00 

32 50 00 

28 27 30 28 27 30 

N 

28 07 30 28 07 30 

32 20 00 

0 2 4 6 8 km 

32 50 00 

Figure 6. Filled-color image of the aeroradiospectrometric equivalent thorium. 

LEAST-SQUARES METHOD 

The least squares method (LSM) is usually used in estimating the residual component of Bougeur [16], magnetic 

[17], and self-potential [18] anomalies. In the present study, the authors tried to apply the LSM approach followed by 

Nettleton [19] and Abdelrahman [20] to separate the radioactive anomalous bodies from the normal radiation of the host 

rocks. 

The method consists of fitting a mathematical surface that approximates the regional component of the 

aeroradiospectrometric data. In all cases, the condition of the least–squares solution is: 

2 

∑R 

= minimum (1) 

where R denotes the residual component and is given as: 

with ∆ g being the observed aerospectrometric values, and z the regional surface aero-radiometric value. 

R =∆g −z, 

(2) 

Generally, both orthogonal polynomials [21–23] and as non-orthogonal polynomials [24–27] have been used for the 

least-squares determination of residual anomalies. In the latter method, the regional surface aeroradiospectrometric value 

is represented by the polynomial: 

Condition (1) is fulfilled, when the partial derivatives with respect to each of the an-s,s are zero. This gives 

½(p+1)(p+2) simultaneous linear equations from which the ½(p+1)(p+2) different values of an-s,s can be determined. 

Here, , 

p n 

Z ( x, y) n s 

a x y 

(3) 

− 

= ∑ ∑ 

n= 0 s= 

0 

n−s, s 

a n− s s are 1/2( p + 1)( p + 2) , coefficient p is the order of the two-dimensional (2-D). polynomial, and x and y are 

the coordinates. 


s 

L5 

L4 

L3 

L2 

L1 

75 

70 

65 

60 

55 

50 

45 

40 

35 

30 

25 

20 

15 

10 

5 

eU in ppm multiplied by 10


The least–squares method is known to produce both positive and negative residuals, even when the true residuals 

are positive. The residual map is usually balanced between positive and negative areas [28]. 

The optimum order of the least-squares regional surface, is obtained by applying the correlation factor criteria 

between successive least-squares residual anomalies [20], when subtracted from the observed aerial radiospectrometric 

survey data. This produces the least distorted residual component of the field. 

Accordingly, the absolute aeroradiospectrometric maps (T.C., 40 K, eU, and eTh) were subjected to a separation 

technique using the least-squares method to separate the highly-radioactive zones from the normal radioactive 

background of the host rocks. Regional components of the first, second, third, fourth, and fifth orders were fitted to the 

input data. Correlation coefficients between successive residual maps were computed in order to determine the optimum 

order of the regional surface to be used (Table 1). The regional field in this particular area can be represented as firstorder, 

because the first good correlation factor in each case is r12 (Table 1). 

The least-squares method (LSM) was used to construct the first-order regional and residual total-count (T.C.) and 

the three absolute radioelements ( 40 K, eU, and eTh) maps of the study area (Figures. 7 to 14). 

Table 1: Numerical Values of Correlation Coefficients Between Successive Residual Maps. 

N 

28 07 30 

rj,j+1 

T.-C. (in Ur) 

40 K (in %) eU (in ppm) eTh(in ppm) 

r12 0.92 0.92 0.95 0.94 

r23 0.90 0.85 0.98 0.97 

r34 0.88 0.86 0.96 0.92 

r45 0.97 0.02 0.99 0.99 

rj,j+1= correlation factor between jth order residual rj and the next higher order rj+1. 

32 20 00E 32 50 00 

N 

28 27 30 

32 20 00 

0 2 4 6 8km 

Figure 7. Filled-color contoured anomaly map of the first-order regional total-count 

(T.C.) aeroradiometric data (contour lines in Ur). 

32 50 00 

T. C. (Ur) 

28 07 30 


17.0 

16.5 

16.0 

15.5 

15.0 

14.5 

14.0 

13.5 

13.0 

12.5 

12.0 

11.5 

11.0 

10.5 

10.0 

9.5 

9.0 

8.5 

8.0 

7.5 

7.0 

6.5 

6.0 

5.5 

5.0 

4.5 

4.0 

3.5 

T. C. in Ur


32 20 00E 32 50 00 

28 27 30 N 

28 27 30 

N 

28 07 30 

32 20 00 

0 2 4 6 8 

Figure 8. Filled-color contoured anomaly map of the first-order residual total-count 

(T.C. ) aeroradiometric data (contour lines in Ur). 

32 50 00 

28 07 30 

32 20 00E 32 50 00 

28 27 30N 

28 27 30 

N 

(b) 

28 07 30 

32 20 00 

0 2 4 6 8km 

Figure 9. Filled-color contoured anomaly map of the first-order regional 

aeroradiospectrometric potassium, K (contour lines in 0.1%). 


km 

25 

9 

7 

5 

3 

1 

-1 

-3 

-5 

8 

6 

4 

2 

28 07 30 

32 50 00 

T. C. in Ur 

32 

30 

28 

26 

24 

22 

20 

18 

16 

14 

12 

10 

K % multiplied by 10


32 20 00E 32 50 00 

28 27 30N 

28 27 30 

N 

(b) 

28 07 30 

32 20 00 

0 2 4 6 8 km 

Figure 10. Filled-color contoured anomaly map of the first-order residual aeroradiospectrometric 

potassium, K (contour lines in 0.1 %.). 

28 07 30 

32 50 00 

32 20 00E 32 50 00 

28 27 30 N 

28 27 30 

N 

28 07 30 

32 20 00 

0 2 4 6 8 


aero radiospectrometric equivalent uranium eU (contour lines in 0.1 ppm). 


km 

32 50 00 

18 

16 

14 

12 

10 

8 

6 

4 

2 

0 

-2 

-4 

-6 

-8 

K % multiplied by 10 

-10 

-12 

30 

29 

28 

27 

26 

25 

24 

23 

22 

21 

20 

19 

18 

17 

16 

15 

14 

28 07 30


32 20 00E 32 50 00 

28 27 30 N 

28 27 30 

N 

28 07 30 

32 20 00 

0 2 4 6 8km 

28 07 30 

32 50 00 

Figure 12. Filled-color contoured anomaly map of the first- order residual aero radiospectrometric equivalent uranium eU (contour 

lines in 0.1 ppm). 

32 20 00E 32 50 00 

28 27 30 N 

28 27 30 

N 

28 07 30 

32 20 00 

0 2 4 6 8 


aeroradiospectrometric equivalent thorium eTh (contour lines in ppm.). 


km 

28 07 30 

32 50 00 

55 

50 

45 

40 

35 

30 

25 

20 

15 

10 

5 

0 

-5 

9.0 

8.5 

8.0 

7.5 

7.0 

6.5 

6.0 

5.5 

5.0 

4.5 

4.0 

3.5 

3.0 

2.5 

-10 

-15 

eU in ppm multiplied by 10 

eTh in ppm


32 20 00E 32 50 00 

28 27 30 N 

28 27 30 

N 

28 07 30 

32 20 00 

0 2 4 6 8 

km 

Figure 14. Filled-color contoured anomaly map of the first-order residual 

aeroradiospectrometric equivalent thorium eTh (contour lines in ppm). 

28 07 30 

32 50 00 

DISCUSSION 

The first-order least-squares regional aeroradiometric and aeroradiospectrometric anomaly maps show the firstorder 

least-squares regional level as straight lines (or colored zones). Figures 7, 9, 11, and 13 show that these first-order 

least-squares regional lines trend NNW-direction in both aeroradiometric and aeroradiospectrometric potassium maps 

(Figures 7 and 9), N–S in the aeroradiospectrometric equivalent uranium anomaly map (Fig. 11), and NNE in 

aeroradiospectrometric equivalent thorium anomaly map (Figure 13). 

Generally, in the first-order least-squares regional aeroradiometric map and the aeroradiospectrometric maps 

(Figures. 7, 9, 11, and 13) the levels of radiation increase in intensity from the west (sedimentary section) to the east 

(basement rocks) of the sample area. The first-order least-squares residual maps (Figures 8, 10, 12, and 14) are in 

principle different from the original colored radiometric and radiospectrometric contour and image maps (Figures 3–6). 

The high radiation levels on these residual maps correspond to previously-defined (Figure 2b) interpreted radiolithologic 

units (IRLU) and structures [8]. 

The first order least-square areoradiometric total count (T.C.) map (Figure 8) shows that there are high and distinct 

radiation levels. The highest radiation zones correspond to western and southern parts of the Older (Grey) granite (GA- 

1C) radiometric-lithologic unit. In addition, an other relatively high radioactve zone appears at the western part of the 

map, which coincides with the northern part of the Araba Formation (ES) as a distinct interpreted radiometric–lithologic 

unit IRLU. 

The first-order least-squares residual aeroradiospectrometric equivalent uranium (eU) map (Fig. 12) shows a high 

radiation zone corresponding to Wadi Hawashiya and the wadis passing through the nondifferentiated Quaternary 

sediments (QW-4) IRL unit and a high radiation level at the far western part of the map, to the east of the contact zone 

between the sedimentary Araba Formation (ES) IRLU and the basement rocks. The very low level equivalent uranium in 

the southwestern part of the area is attributed to the presence of the sedimentary Galala formation, which is made up 

mainly from limestone. 

Figures 15–18, show that the locations and the relative intensities of the anomalous zones outlined by the present 

least square technique coincide with the anomalous zones (triangular sympol) that are defined using the conventional 

statistical methods [3]. Therefore, the least-squares method (LSM) is considered as an additional and modern technique 

for identification of radioactive anomalous zones, its results were compared with the results acquired from the 

traditional statistical analysis method. 


25 

24 

23 

22 

21 

20 

19 

18 

17 

16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

1 

0 

-1 

-2 

-3 

-4 

eTh in ppm


32 20 00E 32 50 00 

28 27 30 N 

28 27 30 

N 

28 07 30 

32 20 00 

T.C.-aeroradiometric survey data > X+3S 

0 2 4 6 8km 

28 07 30 

32 50 00 

Figure 15. Total-count (T.C.) aeroradiometric point (local) anomaly map superimposed 

on the first-order residual aeroradiometric total-count (T.C.) color image anomaly map 

32 20 00E 32 50 00 

28 27 30 N 

28 27 30 

N 

28 07 30 

32 20 00 

K - aeroradiospectrometric survey data > X+3S 

0 2 4 6 8 

32 50 00 

Figure 16. Potassium (K) point (local) anomaly map superimposed on the first-order 

residual aeroradiospectrometric potassium (K) colored image anomaly map. 


km 

24 

22 

20 

18 

16 

14 

12 

10 

8 

6 

4 

2 

0 

-2 

-4 

-6 

28 07 30 

T. C. in Ur 

18 

16 

14 

12 

10 

8 

6 

4 

2 

0 

-2 

-4 

-6 

-8 

K % multiplied by 10 

-10 

-12


32 20 00E 32 50 00 

28 27 30 N 

28 27 30 

(0.1 ppm) 

N 

28 07 30 

32 20 00 

eU- aeroradiospectrometric survey data > X+3S 

0 2 4 6 8 

32 50 00 

Figure 17. Equivalent uranium (eU) point (local) anomaly map superimposed 

28 07 30 


km 

on the first-order residual aeroradiometric equivalent uranium (eU) 

colored image anomaly map. 

32 20 00E 32 50 00 

28 27 30 N 

28 27 30 

N 

28 07 30 

32 20 00 

eTh- aeroradiospectrometric survey data > X+3S 

0 2 4 6 8 km 

Figure 18. Equivalent thorium (eTh) point (local) anomaly map superimposed 

on the first-order residual aeroradiometric equivalent thorium (eTh) 

colored image anomaly map. 

32 50 00 

55 

50 

45 

40 

35 

30 

25 

20 

15 

10 

5 

0 

-5 

eU in ppm multiplied by 10 

-10 

-15 

eTh (ppm) 

28 07 30 

24 

22 

20 

18 

16 

14 

12 

10 

8 

6 

4 

2 

0 

-2 

-4 

eTh in ppm


CONCLUSIONS 

In this study the least-squares method was applied on the total-count (T. C) and aeroradiospectrometric data. 

Constructed T.C., 40 K, eU, and eTh maps of a selected sample area were subjected to a separation technique using the 

least-squares method to separate the highly radioactive zones from the normal radioactive background of the host rocks. 

Regional components of the first, second, third, fourth, and fifth orders were fitted to the input data. Correlation 

coefficients between successive residual maps were computed in order to determine the optimum order of the regional 

surface to be used. The regional field in this particular area can be represented as first-order, because the first order 

analysis gave a good correlation factor in each case. 

The residual T. C. map and three maps of radioelements ( 40 K, eU, and eTh) of the study area were prepared using 

the least–squares method. This method was applied on a aeroradiometric and aeroradiospectrometric data (T.C., 40 K, 

eU, and eTh) of Gabal Um-Rabul area in the northern part of the Eastern Desert of Egypt to separate the highlyradioactive 

zones from the normal radioactive background of the host rocks. The applied method can be successfully 

used to define the local aeroradiometric and aeroradiospectrometric anomalous zones in the area. The locations of these 

anomalous zones coincide with those defined prevously using conventional interpretation methods. 

The least-squares method is considered as an additional and modern technique for identification of radioactive by 

anomalous zones. It is recommended to apply this method for locating the most prospective anomalous zones of 

radioelements in any surveyed area, because it is easier, simpler, faster, more feasible, and applicable on all acquired 

data when compared to the conventional statistical-point (local) anomaly method. 

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