Interpretation of Gravity Anomalies with the Normalized Full Gradient (NFG) Method and an Example

Interpretation of Gravity Anomalies with the Normalized Full Gradient

(NFG) Method and an Example

ALI AYDIN

Abstract—The Normalized Full Gradient (NFG) method which was put forward about 50 years ago has

been used for downward continuation of gravity potential data, especially in the former Union of Soviet

Socialist Republics. This method nullifies perturbations due to the passage of mass depth during downward

continuation. The method depends on the downwards analytical continuation of normalized full gradient

values of gravity data. Analytical continuation discriminates certain structural anomalies which cannot be

distinguished in the observed gravity field. This method has been used in various petroleum and tectonic

studies. The Trapeze method was used for the determination of Fourier coefficients during the application

of this method. No other techniques for calculating these coefficients have been used. However, the Filon

method was used for the determination of Fourier coefficients during the application of the NFG method in

this work. This method, rather than the Trapeze method, should be preferred for indicating abnormal mass

resources at the lower harmonics. In this study, the NFG method using the Filon method has been applied

the first time to theoretical models of gravity profiles as example field at the Hasankale-Horasan petroleum

exploration province where successful results were achieved. Hydrocarbon presence was shown on the NFG

sections by the application of NFG downward continuation operations on theoretical models. Important

signs of hydrocarbon structure on the NFG section for field and model data at low harmonics are obtained

more effectively using this method.

Key words: Gravity anomalies, Normalized Full Gradient (NFG), Filon method, Hasankale-Horasan.

1. Introduction

Gravity and magnetic methods have been used to supplement the seismic method for

hydrocarbon exploration. The gravity field of a subsurface geological model, which is

obtained from the seismic sections, is calculated using the gravity data during these

operations. Hydrocarbon bearing structures can be determined by comparing the

calculated field with the observed gravity field. Various methods have been developed for

hydrocarbon exploration from gravity data. These include second derivatives, downward

analytical continuation, horizontal gradient vectors, the Andrew-Griffin variation method,

statistical methods and downward continuation of Normalized Full Gradient (NFG)

values of the gravity field. (GRIFFIN, 1949; ANDREEV and KLUSHIN, 1962; BEREZKIN and

Faculty of Engineering, Department of Geophysics, Pamukkale University, 20017 Kınıklı, Denizli, Turkey.

E-mail: [email protected]

Pure appl. geophys. 164 (2007) 2329–2344 � Birkhauser Verlag, Basel, 2007

0033–4553/07/112329–16

DOI 10.1007/s00024-007-0271-yPure and Applied Geophysics

BUKETOV, 1965; BEREZKIN, 1973; CIANCARA and MARCAK, 1979 MUDRETSOVA, 1984;

MOLOVICHKO et al., 1989; LYATSKY et al., 1992; AYDıN, 1997a, b; AYDıN, 2000; PASTEKA,

2000; AYDıN et al., 2002a, b).

Upward and downward analytical continuation of geophysical fields have generally

been applied to the potential field data (e.g., PAWLOWSKI, 1995; DEBEGLIA and CORPEL,

1997; XU et al., 2003). However, the method has also been successfully applied to the

seismic method as a tool of wavelet-based signal analysis which is an approximation to

seismic envelopes (KARSLI, 2001) and to electromagnetic methods (DONDURUR, 2005). In

this study, the NFG method which is used to determine the target depth using the full

gradient function. A method suggested by BEREZKIN and BUKETOV (1965), utilizing

vertical and horizontal derivatives of the potential fields, is used here. Determination of

singular points within the anomalous body center was proposed using potential field data,

and later this method was used to determine subsurface structures (e.g., BEREZKIN, 1967;

MUDRETSOVA et al., 1979; STRAKHOV et al., 1977; BEREZKIN et al., 1978; ELISEEVA, 1982;

BEREZKIN and SKOTARENKO, 1983; CIANCARA and MARCAK, 1979; AYDıN, 1997a).

The Normalized Full Gradient (NFG) method depends on the downward analytical

continuation of normalized full gradient values of gravity data. Analytical continuation

discriminates certain structural anomalies which cannot be distinguished in the observed

gravity field. Analytical properties are lost at the singular points (±) of the borders of the

mass, giving rise to an anomaly in the gravity potentials and derivatives. Mass geometry

and location of the mass giving rise to the anomaly can be determined from the

knowledge of singular points at the mass and its borders. Downward analytical

continuation values of the observed gravity data show irregular variations during the

passage of the mass giving rise to the anomaly. The initial values of these irregular

variations describe the depth to the upper surface of the mass giving rise to an anomaly.

The application of this method is restricted since the errors in the gravity data become

more effective in the downward analytical continuation values with increasing depth

(BEREZKIN, 1988; AYDıN, 1997a).

Since residual gravity signals of oil and gas reservoirs are rather weak, gravity data

for hydrocarbon exploration purposes should be handled specifically. NFG data were

obtained from the calculations of Fourier series coefficients of the gravity data by the

Filon method (DAVIS and RABINOWITZ, 1989). The effects of hydrocarbon existence in the

NFG sections were later proposed for model calculations by utilizing the NFG data. Also

the hydrocarbon potentials of the Hasankale-Horasan area were interpreted using the

NFG method for the gravity data.

2. Method

BEREZKIN (1973) first described a full gradient function which could not be affected by

the above restrictions by utilizing horizontal and vertical derivatives of observed gravity

values. STRAKHOV et al. (1977) proved the existence of this function. The NFG method

2330 A. Aydin Pure appl. geophys.,

was successfully applied to hydrocarbon exploration in Russia, Kazakhstan and

Azerbaijan (BEREZKIN, 1973; BEREZKIN et al., 1978; MUDRETSOVA et al., 1979; BEREZKIN,

1988; MOLOVICHKO et al., 1989; BEREZKIN and FILATOV, 1992).

The NFG operator GH(x, z) is defined in two dimensions by BEREZKIN (1973) as

GHðxi; zjÞ ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

oUðxi;zjÞox

� �2

þ oUðxi;zjÞoz

� �2� �v

s

1M

P

M

i¼0

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

oUðxi;zjÞox

� �2

þ oUðxi;zjÞoz

� �2� �v

s ; ð1Þ

where M is the number of observation points, (i = 0, 1, 2, 3,. . ., M; j = 0, 1, 2,

3,. . .,z). U(xi, zi) is the function defining the gravity anomaly values along the x axis,oUðxi; zjÞ�ox and oUðxi; zjÞ�oz are derivatives of the function U(xi, zi) with respect to x

and z respectively, and m is known as the degree of the NFG operator and controls

the peak amplitude. The degree of the NFG can be taken as 1, 2, 4, etc. m = 1 is

generally used for potential field (AYDıN, 1997a) and electromagnetic data (DONDURUR,

2005) as is the case for the present study. Higher order values of the degree of the

NFG were applied in seismic applications effectively by KARSLI (2001) using the

width of the recorded signal to improve seismic resolution.

The NFG sections are computed from observed field values at several depth horizons

between the surface and a maximum depth to which the downward continuation of the

anomaly field is computed with certain intervals. For this study, a maximum depth is

taken as zm = 5 km with Dz = 0.1 km depth intervals in the NFG sections. The full

gradient term is explained in that it uses the sum of the horizontal and vertical derivatives

and the mean value of the full computed gradient is given in equation (1) over M

observation points. This processing makes the NFG value dimensionless. These values

are about 1 in areas off the anomalous body. If the contour values are identified maxima

are greater than 1 and minima are smaller than 1.

Using a Fourier series approach in such a way that the U(x, z) function along the x

axis can be given as the summation of sine and cosine functions, computation of the NFG

operator is achieved by BRACEWELL (1984). RIKITAKE et al. (1976) suggested that if the

considered data are definitive in the (0, L) interval, only the sine expansion can be used.

A downward continuation process in the wavenumber domain using a Fourier series

summation is described by JUNG (1961) as follows:

U x; zð Þ ¼X

N2

n¼N1

bnf sinpnx

L

h i

epnzL q; ð2Þ

where q is the well known parameter as BEREZKIN (1967) suggested as ‘‘Lanczos

Smoothing Term Function’’. It will be described later. bnf is the Fourier sine

coefficient, z is the plane on which the downward continuation is performed and n is

the harmonic number. The Fourier coefficient bnf can be calculated sensitively using

Vol. 164, 2007 Gravity Anomalies with the NFG Method 2331

the Filon method (FILON, 1928; DAVIS and RABINOWITZ, 1989). This method is used

to calculate integrals with rapidly varying U(x, z) sin pox and U(x, z) cos pox (FLINN,

1960; FRAZER and GUTTRUST, 1984). The U(x, z) function in window from a to b is

Z

b

a

U x; zð Þ sin p0xdx ¼ b� a

2M

X

M�1

j¼0

�

�a U xjþ1; zjþ1

cos p0xjþ1 � U xj

cos p0xj

� �

:

þ b2

U xjþ1; xjþ1

sin p0x� U xj; zj

sin pxjþ1 � cos p0xj

� �

þ sUxj þ xjþ1

2;zj þ zjþ1

2

� �

sinp0

2xj þ xjþ1

ð3Þ

whereas

a ¼ 1

e3e2 þ e sin e cos e� 2 sin2 e

b ¼ 2

e3e 1þ cos2e

� 2 sin e cos e� �

c ¼ 4

e3sin e� e cos e½ �; e ¼ pn

2 M � 1ð Þ ; p0 ¼pn

L

is described as the formulation. Depending on this formulation, by considering the zero

values at the borders of the profile of function U(x,0) the bnf coefficients according to the

Filon method are given by the equation (FILON, 1928)

bnf ¼1

M � 1bX

M�1

j¼1

U jð Þ sin2pn

2 M � 1ð Þ þs2

X

M�1

j¼1

UðjÞ þ Uðjþ 1Þð Þ"

sinpn

2 M � 1ð Þ 2jþ 1ð Þ�

:

ð4Þ

If it is calculated by the Filon formula, the mean-square error is

mbf ¼ �0:82dUffiffiffiffiffi

Mp : ð5Þ

If it is calculated by the Trapeze formula, the error is (AYDıN, 1997a)

mb ¼ �1:41dUffiffiffiffiffi

Mp : ð6Þ

As it is given here, the mean-squared error mb does not depend on the harmonic number.

In this case the calculated harmonic coefficient errors are two times less for the Filon

method. Therefore the bnf coefficients which were calculated according to the Filon

method, make possible more accurate determination of the GH(x, z) normalized full

gradient field.

Practically harmonic numbers N £ (0.1–0.25) M for bnf and N £ (0.3–0.5) for bn were

considered. bn and bnf spectra calculated for the Dg(x, 0) curves belonging to a horizontal


cylinder are given in Figure 1a. By taking M = 101, it was calculated for harmonic

window N1–N2 = 1–250. Theoretically it is possible to calculate more harmonics than

data points, as it can be seen in Figure 1 that repetitions do occur. As the pulsation in the

harmonics is determined at the value of 70 (as shown by an arrow) by the Filon formula,

it is seen everywhere in the Trapeze formula. The criterion controlling the number of

terms (N) in the summation in equation (2) will be discussed later.

The derivatives oUðxi; zjÞ�ox and oUðxi; zjÞ�ozof equation (1) can be given as follows

oUðxi; zjÞox

¼ pL

X

N2

n¼N1

nBnf cospnz

Le

pnxL ; ð7Þ

oUðxi; zjÞox

¼ pL

X

N2

n¼N1

nBnf sinpnz

Le

pnxL : ð8Þ

To stabilize the NFG operator, the U(x, z) function is multiplied by a function. Dg(x,0)

behaves stably because the data are digital in the formulation, having random errors,

having restricted observational window and similar errors. To eliminate the Gibbs effect

HARMONIC NUMBER-n

-0.08

-0.04

0.00

0.04

0.08

B(n

)

0 4 8 12 1620DISTANCE (km)

0.0

1.0

2.0

3.0

g (m

Gal

)

0-0.05

0.00

0.05

0.10

TRAPEZ

FILON

a)

b)

c)

50 100 150 200 250

0 50 100 150 200 250

B(n

)

HARMONIC NUMBER-n

Figure 1

By taking M = 101, a) Dg(x, 0) curve, bn and bnf spectra, b) Filon formula and c) trapeze formula. The arrows

show the pulsations in the harmonics.


and to increase stability the sine expansion coefficient q within the window of (0, L) the

following calculation can be made;

q ¼sin pn

NpnN

� �l

; ð9Þ

where l is any integer number and the degree of smoothing which controls the curvature

of the q function. AYDıN (1997a), DONDURUR (2005) and KARSLI (2001) suggested that

l = 1 or 2 gives reasonable results in the downward continuation, therefore, l = 1 is used

in this study. In addition, the harmonic interval in equations (2), (7) and (8) is restricted to

a lower limit of N1 and an upper limit of N2. This restricted processing was discussed by

BEREZKIN (1988), AYDıN (1997a) and DONDURUR (2005). The N1 and N2 harmonic limits

determined by these researchers were applied to gravity and electromagnetic data. This

part of this study is studied for interpreted profiles and these results will be given later.

Thus the function U(x, z) and its derivatives are defined by

U x; zð Þ ¼X

N2

n¼N1

Bnf sinpnz

Le

pnxL

sin pnN

pnN

� �l

; ð10Þ

oU x; zð Þox

¼ pL

X

N2

n¼N1

nBnf cospnz

Le

pnxL

sin pnN

pnN

� �l

; ð11Þ

oU x; zð Þoz

¼ pL

X

N2

n¼N1

nBnf sinpnz

Le

pnxL

sin pnN

pnN

� �l

: ð12Þ

H(n) is known as the linear frequency characteristic of the GH(x, z) function (BEREZKIN,

1988), which is given by

HðnÞ ¼ nepnxL

sin pnN

pnN

� �l

: ð13Þ

The q factor, however, modifies the frequency characteristic of the NFG operator by

transforming its shape into a bandpass filter, which becomes asymmetrical with

increasing depth. N1 and N2 harmonic limits determine the cutoff frequency values of this

filter (BEREZKIN, 1988; AYDıN, 1997; DONDURUR, 2005). H(n) curves are calculated without

and with a q stabilization factor for z = 1 m and z = 10 m depths (Fig. 2). H(n) curves

continuously increase with increasing n and z values without a q factor, indicating that the

effect of the H(n) function increases for large n values, which may cause unstable results

in the downward continuation process.

In order to test the efficiency of the present method in estimating the depths of the

density boundaries, the method was applied to a number of theoretical gravity anomalies.

The Fortran program TALWANI (BLAKELY, 1995), uses the theory presented by TALWANI

et al. (1959) and produces the theoretical gravity profiles on which the NFG method was

carried out.


Although setting N1 to 1 is a general convention for the potential field data to preserve

the lower frequency components, the N1 and N2 limits are generally determined by a trial-

and-error method, depending on the conditions of the problem and the characteristics of

the data. Several attempts are generally required to determine suitable values for N1 and

N2 limits. In general, several values in increasing order are tried for the determination of

N2 value (e.g., N2 = 10, 15, 20, . . ., M/2) while N1 is set to 1. After a careful examination

of NFG sections during each attempt, an appropriate value for N2 can be determined.

Then N2 is kept fixed and the same process is repeated for the determination of the N1

value. As a result, optimal limit values of the harmonics are determined.

First, in order to determine the most suitable harmonic limits, a few NFG sections

were prepared with different harmonic intervals. N1 was set to 1 for each attempt at

determining a suitable N2 value. The theoretical gravity anomalies over a geological

z=2 km

Harmonic Number-n

1.0x10-2

1.0x10-1

1.0x100

1.0x101

1.0x102

1.0x103

1.0x104

1.0x105

Fr

ah

Cyc

neu

qer

etcar

)n(

H-

citsi

20

0 20 40 60 80 100

40

60

80

100

z=1km

z=0

1

2

3

Figure 2

The variation of the frequency characteristics of the NFG operator-H(n) without q and with the q stabilization

factor for l = 2 (after BEREZKIN, 1988 and AYDıN, 1997). Curves drawn for the various harmonics, H(n),

frequency characteristics N and z = 0, 1, 2 km. There is no q multiplier for 1, 2, 3 curves. H(n) functions were

calculated at the harmonics of n = 20, 40, 60, 80 and 100 for every z by assuming l = 2.


model with and without oil were given with different harmonics sections. Profile lengths

were selected as L = 20 km and the theoretical anomalies are shown in Figure 3 together

with their corresponding NFG sections computed for different harmonic intervals as N1–

N2 = 1–10, 1–12, 1–15, 1–18, and 1–20. It is seen that the principal characteristics of the

NFG sections in Figure 3a are that there is one main local maximum and two flanking

minima enclosures in the first gravity profile.

Both of these maxima are located at the beginning and end points of the sides of the

reservoir at 2-km depth on the top of the anticline. It is concluded that the method creates

two maxima at these points (z = 2 km) because the maximum anomaly gradients also

occur around these points.

The depths of the maximum points in each NFG section in Figure 3 correspond to the

estimated depth values which are indicated by a maximum closing count on the NFG

sections. In the cases of multiple maxima, both maxima suggest the same depth estimate,

a)

b)

c)

Figure 3

An application of the NFG method to the gravity model obtained from a complex geological structure, a) Dg(x,z)

curves calculated for the geological models with and without hydrocarbons, b) NFG sections calculated for N1–

N2 = 1–10, N1–N2 = 1–12, N1–N2 = 1–15, N1–N2 = 1–18 and N1–N2 = 1–20 harmonics, and c) geological

models with and without hydrocarbons.


and therefore, one can estimate the depth value using any of the multiple maxima on the

NFG sections. The depth values estimated from the NFG sections are compared with

the actual theoretical model depths. The depth values estimated using N1–N2 = 1–10, 1–15

and 1–20 indicate that N1–N2 = 1–15 provides the most suitable harmonics (Table 1).

3. Applications

3.1. Theoretical Data Examples

Calculated Dg(x,0) curves and GH(x,z) sections are given in Figure 3 for the cases

with and without reservoirs in anticline structure in the layered media. The top of the

anticline is 1 km and the density differences are given in Figure. 3. The theoretical model

was calculated by the method of Talwani (TALWANI et al., 1959) for an arbitrary shaped

2D body. Although Dg(x,0) curves are similar in shape and value, there is no sign of the

effect of reservoir structure. The obvious observable characteristics of the geological

model which does not have a reservoir, are the depths of the maximum singular points in

the calculated NFG sections for the various harmonics, and these indicate the tops of the

anticlines. The effects of the primary and secondary anticlinal structures, and the vertical

fault at the right side of the model and the normal fault at the left side were observed in

the NFG sections obtained from the model section which has various structures. The most

suitable harmonics were chosen from Table 1 as N1–N2 = 1–15, and it is the maximum

singular point at a horizontal distance of 10 km for the depth of about 3 km that suggests

a model without hydrocarbons. This singular point represents the effects of the anticline

structures in the NFG sections. Minimum singular closures at x = 3 and 7 km which are

at 4 km depth, indicate the effects of the normal fault which underlie the anticlinal

structure. Also the effects of the vertical fault at 14 km in the geological model are

observed at similar distances and at 4 km depth in the NFG sections. This situation was

also observed for the geological model with a hydrocarbon reservoir for the sections

calculated for the harmonics of N1–N2 = 1–15, N1–N2 = 1–18 and N1–N2 = 1–20. In the

case of a structure with a hydrocarbon reservoir, the effects of the reservoir can be

observed in all NFG sections. The observed minimum singular point between two

maxima, was observed in the harmonics N1–N2 = 1–12 at the top of the reservoir, and the

Table 1

Comparison of the estimated and actual model depths derived from Figures 3a and 3b using n = 1–10, 1–15 and

1–20 harmonic intervals for the model depths of z = 2, 3 and 4 km.

Model depth z (m) 2 3 4

n 1–10 1–15 1–20 1–10 1–15 1–20 1–10 1–15 1–20

Estimated depth (m) 2.3 2.0 1.7 3.2 3.1 2.8 4.3 4.0 3.9

Error (%) 15 0 15 7 3 7 8 0 3


depth obtained for harmonics of N1–N2 = 1–15 was congruent with the reservoir depth.

Maximum singular point values due to the anticline structure, are 2.37, 2.68, 3.13, 3.42

and 3.40 for the harmonics of N1–N2 = 1–10, 1–12, 1–15, 1–18 and 1–20, respectively, in

the NFG sections (Fig. 3a). If the structure has a reservoir, the maximum closures have

the values of 2.88, 1.73, 2.11, 2.10 and 2.07. The same harmonic minima between two

maxima were (no value for N1–N2 = 1–10 harmonics), 0.25, 0.22, 0.11 and 0.10

(Fig. 3b). The reservoir structure is well observed in the NFG sections at the harmonics

of N1–N2 = 1–15, 1–18 and 1–20 for the structure with hydrocarbons. There is a

minimum singular point between maxima for two singular points in these sections, and

the depth of minimum closure is the same as the reservoir structure depth at the

harmonics of N1–N2 = 1–18.

3.2. Field Data Examples

3.2.1 Geology of the Hasankale-Horasan Region. Geological studies were carried out by

the Turkish Geological Survey (MTA) and the Turkish Petroleum Company (TPAO) in

the study area. The results of those studies showed possible existence of petroleum source

rocks (PELIN et al., 1980; SAROgLU and GUNER, 1981). Geologic and location of the study

area are given in Figure 4.

The basement rocks consists of ophiolites and ophiolithic melanges which make up

the Kop and Palandoken mountains in the study area. On the top of the basement units,

from the Eocene to the Quaternary with various lithologies take place. The Narman

formation which is made up of volcanics and volcanoclastics is transgressive with the

Eocene-aged Bulkasım Formation, which was formed as flyshe facies in the area. Near

Pasinler, the Miocene-aged Gulluce Formation overlies the Narman and Bulkasım

Formations unconformably. The units belonging to the Benek and Kumurlu members

which are made up of coarse gravel, sandstones and shades deposited in the fluvial and

lagunal environments, and are overlain by a shallow marine-lacustarine sedimentary unit

of the Miocene-aged Askale Formation which is synchronous with the Gulluce Formation.

The Pliocene-aged Aras Formation, which is made up of volcanics, volcanoclastics and

marl-gravelstones, covers the other units unconformably. At the top, the Quaternary-aged

alluvial deposits, which is comprised of gravelstones, mudstones, and sandstones, covers

all units unconformably. The sediment thickness, which is the sum of all six stratigraphic

units, is about 6.5 km in the region (SAROGLU ve GUNER, 1981).

In order to show the effectiveness of the joint utilization of the NFG method with

other geological and geophysical methods to the observed data in the petroleum

exploration work, it was applied to the two test profiles chosen in the Hasankale-Horasan

basin. The seismic work was carried out and the exploration wells were drilled along the

profiles by TPAO. The work which have been carried out in the Hasankale-Horasan basin

where the crystalline basement depth reaches 6.5 km, have shown that this region is very

promising with respect to hydrocarbon prospects (PELIN et al., 1980; SAROGLU and GUNER,

1981).


From these studies the targeted levels are the limestone and dolomitic micrites which

are within the Karakurt and Zırnak formations and void of marly layers. These were

targeted before the Horasan I and Pasinler III boreholes were drilled. Though signs of

petroleum were observed in the Horasan I borehole, the well was dry. Two profiles were

selected in which A-B and C-D were given in Figure 4. The A-B profile which is 30 km

long in the Erzurum-Hasankale-Horasan region is concurrent with the SW-NE trending

seismic section. The entire profile which overlies the Jurassic Mudurnu Formation is

overlain conformably by the Cretaceous Sakaltutan Ophilites which forms the top of the

alluvial units. The beginning of the profile is comprised of the faulted Eocene Bulkasım

Formation which is overlain unconformably by the Pliocene Karakurt Formation, and the

latter one is covered up jointly by the Aras Formation and Quaternary alluvium. The C-D

profile which is 28 km in length approximately in the N-S direction is concurrent with the

seismic section is shown in Figure 4. The profile crosses the Pliocene Karakurt and Aras

Tn

Plk-Ba

Pm

Kus

Pla

Tg

Tb

Tgu

Plk-Ba

TbTn Tn

Tg

PASINLER

HORASAN

HORASAN-I

Q-al

P-1

P-2

0 6 12 km

TURKEY

BLACK SEA

MEDITERRANEAN SEA

STUDY AREA

A

B

C

D

N EXPLANATIONS

Gumusali Fm.Tgu

Aras Fm

Karakurt Fm.

Zirnak Fm.

Gulluce Fm.Hundul Fm.

Pla

Plk-Ba

Tz

TgTgh

AlliviumQ-al

Bulkasim Fm.

Narman Fm.

Sakaltutan Fm.

Akdag Fm.

Pulur Fm.

Tn

Tb

Kus

PMa

Pm

Seismic Line

Gravity Profile

Fault

WellP-1

PASINLER-III

Figure 4

Geology of the survey area, locations of the interpreted seismic sections (two bold solid lines) and Dg(x,z)

gravity progiles (two dotted lines) (SAROGLU et al., 1981). Gravity profiles, interpreted seismic sections,

geological sections (based on interpreted seismic sections) and various harmonics of the NFG sections will be

used in Figure 5.


Formations starting from the south and partly traverses the alluvia at the northern end.

Stratigraphically the Jurassic Mudurnu Formation is overlain conformably by the

Cretaceous Sakaltutan Ophiolite Formation. As it is with Profile A-B, the beginning of

the profile constitutes the faulted Eocene Bulkasım Formation which is overlain

unconformably by the Pliocene Karakurt Formation. The latter is covered jointly by the

Aras Formation and Quaternary alluvium.

3.2.2 A-B Profile. A 50 mGal anomaly that increases along the entire profile (Fig. 5a)

corresponds with a change in the basement topography. This is obvious in Figures 5a and

5b as representing the geology and seismics. The observed faults and the formation

boundaries are clearly indicated in these sections. The anticlinal structure in the first 2 km

of the section corresponds to borehole Horasan I drilled by TPAO. Due to faulty seismic

data, the middle part of the section could not be interpreted. However, the general

formation boundaries could be followed quite well in both sections. A high large density

increases is indicated by the interpreted seismic and geological sections in the middle part

of the profile. Henceforth, the information which has been put forward by the NFG

sections obtained from gravity field values of the A-B profile shall be considered under

the light of complete geological and geophysical knowledge.

From the relationship between optimum profile length and depth such as in Table 1,

N1–N2 = 1–20, N1–N2 = 1–25 and N1–N2 = 1–30 profiles were considered for the

interpretation of the NFG sections.

The NFG sections of the A-B profile were calculated and drawn for the harmonics of

N1–N2 = 1–10, N1–N2 = 1–15, N1–N2 = 1–20, N1–N2 = 1–25, N1–N2 = 1–30 and N1–

N2 = 1–35 (Fig. 5d). The effect of the rise in the middle of the profile was shown as the

minima closing area between two maxima at the N1–N2 = 1–10 harmonics. This effect

was observed as well at all the other harmonics. A characteristic minimum singular point

was observed at 6 km for the anticlinal area for N1–N2 = 25 harmonics. This situation

was also observed in the harmonics of N1–N2 = 1–25, N1–N2 = 1–30 and N1–N2 = 1–35.

The depth of a structure which could be considered as reservoir is 2 km. A minimum

singular point was observed at the harmonics of N1–N2 = 1–20, N1–N2 = 1–25, N1–

N2 = 1–30 and N1–N2 = 1–35 at 27 km of the profile and the depth of this point is about

2–2.5 km. These parts are against the limestone units in the interpreted seismic and

geological sections. The parts shown with the shaded rectangles and ellipses (in the

Figs. 4 and 5) were considered as the areas with reservoir characteristics.

The Pasinler III borehole which was drilled at 2 km alone the A-B profile is not a

suitable place according to the NFG data, whereas the place of 6 km is the better area.

The effects of horizontal layering and faults can be observed in the NFG sections for the

parts of the profile at 10–25 km. This interval is not suitable for hydrocarbon prospecting

according to the NFG sections. However, a minimum closure between two maxima

observed at 27 km represents quite well the reservoir characteristics. The extent of a

limestone layer in the geological structure and the small anticlinal structure indicates the

formation of reservoir structure there.


3.2.3 C-D Profile. There is about 17 mGal gravity value variation in this profile which is

intersected by the Profile A-B towards the end (Fig. 5a). There is a sign of low density

rise in the middle of the profile as indicated by the interpreted seismic and geological

sections. Faults are present at 12, 14 and 16 kms.

The NFG sections of A-B profile were calculated and drawn for the harmonics of

N1–N2 = 1–10, N1–N2 = 1–15, N1–N2 = 1–20, N1–N2 = 1–25, N1–N2 = 1–30 and

N1–N = 1–35 (Fig. 5c). The effect of the rise in the middle of the profile was shown

as the minimum area between two maxima at the N1–N2 = 1–10 harmonics for the two

anticlines. Although this effect was observed at the harmonics of N1–N2 = 1–20 and

N1–N2 = 1–25, it is congruent with the depths of the structures. A characteristic minimum

singular point was also observed at 22 km for the anticlinal area for N1–N2 = 1–18

harmonics. This part is just north of the Horasan I borehole and the depth of this structure

is about 2 km. A singular point with depth between 1 and 2 km was observed at 8 km

along the profile for the harmonics of N1–N2 = 1-30 and N1–N2 = 1–35. These parts lay

against the limestone units in the interpreted seismic and geological sections. These parts

Figure 5

An application of the NFG method to the A-B and C-D profiles. a) Observed gravity field curves Dg(x,z), b)

Interpreted seismic section approximately goes parallel and close to the gravity lines and c) NFG sections for

N1–N2 = 1–10, N1–N2 = 1–15, N1–N2 = 1–18, N1–N2 = 1–20, N1–N2 = 1–22 and N1–N2 = 1–25. The ellipsoids

correspond to anomalies where most likely reservoirs can be found.


which are made of sandstones (Fig. 3), as observed from the interpreted seismic and

geological sections, were considered as the areas having reservoir characteristics of an

anticlinal structure.

The observed structures which were indicated by the NFG method are at the

intersectional area towards the end of the profiles. It is necessary to drill a new

exploratory borehole there, since these effects were observed along both of the profiles.

This is also supported by the interpreted seismic and geological sections as having

reservational characteristics.

4. Results

The NFG values, which are obtained from the downward continuation of gravity field

data, provide direct information about the hydrocarbon content of reservoirs. By using the

Filon method for the calculation of the Fourier series coefficient, singular points were

determined at the lower harmonics with better precision. Density variations which are

caused by the presence of hydrocarbons make up the minimum closure between two

maxima for the reservoir. The results which were obtained by the application of the NFG

method to the observed gravity data of the profiles trending SW-NE and E-W respectively,

have shown that the NTG method could be used effectively for hydrocarbon exploration.

After evaluation of the NFG method, and the seismic and geological sections at the area of

the intersection of the two profiles, an exploratory borehole was proposed. These

advantages were put forward by the NFG method for hydrocarbon exploration. This

method has shown that it could be used at the initial and final stages of the hydrocarbon

exploration by applying it to the gravity data for the promising areas. This method

therefore can be used to determine the areas for detailed seismics and borehole sites.

Acknowledgements

The author would like to warmly thank Prof. Dr. Fahrettin Kadirov and Prof. Dr.

Mustafa Ergun and Dr. Derman Dondurur for thoughtful reviews, many helpful sug-

gestions preparing the manuscript and the English language and comments. The work

reported here was supported by Research Foundation of Karadeniz Technical University

(Project No: 96.112.007.2) and seismic and gravity data were supported by TPAO. Final

English corrections on the proof article by Prof. Dr. Kadir Gurgey are greatly appreciated.

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(Received November 6, 2006, accepted August 2, 2007)

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Interpretation of Gravity Anomalies with the Normalized Full Gradient (NFG) Method and an Example