Layout 6

ANNALS OF GEOPHYSICS, 62, 5, GD561, 2019; doi: 10.4401/ag-8054

“EVALUATION OF DIFFERENT GRAVIMETRIC METHODS TO MOHO RECOVERY IN IRAN„
Sahar Ebadi*,1, Riccardo Barzaghi2, Abdolreza Safari1, Abbas Bahroudi1

(1) School of Surveying and Geospatial Engineering, College of Engineering, University of Tehran, Iran
(2) Politecnico di Milano, Department of Civil and Environmental Engineering, Milan, Italy
(3) School of Mining Engineering, College of Engineering , University of Tehran, Tehran, Iran

1. INTRODUCTION

The knowledge of the Mohorovičić discontinuity

(Moho) can provide valuable information to understand
some topical issues in solid Earth sciences [Sampietro,
2016]. Its knowledge in the Iran block is one of the cru-
cial issues in this region. Several unique events like tec-
tonics and orogenic activities in Iran led to a complex
geological structure of the area. Thus, it is important to
study in deep the peculiar structure of the Iranian Moho

applying different methods and different observations
in order to have a comprehensive definition of its main
features. Moho interface is commonly estimated by ei-
ther seismic or gravimetric methods. Although seismic
Moho estimates have a significant accuracy (at the level
of 1-2 km), their coverage over entire of the Earth is
quite poor. Thus, in regions where seismic data are
sparse or missing, results of gravimetric studies can be
profitably used. At global scale, this has been made pos-
sible after dedicated gravity-satellite missions, namely

Article history
Received December 12, 2018; accepted March 17, 2019.
Subject classification:
Moho, Gravimetric inverse problem, Collocation, Isostasy, Seismic data.

ABSTRACT

The complexity of geological units in Iran because of several unique events like tectonics and orogenic activities in this region led to

extensive investigations for Moho recovery by seismic methods therein. In this research, three gravimetric methods have been evaluated

by some point-wise seismic data. We applied collocation method as an iterative process as well as modified forms of Sjöberg and Jef-

frey’s theory of isostasy for local Moho depth recovery. The gravity data has been generated by GOCO03S model reduced by topogra-

phy/bathymetry, sediment and consolidated crust effects. Although the iteration process in collocation approach only slightly changed

the estimated depths, this method led to a better agreement with seismic data rather than others. Differences between collocation, Jef-

frey and Sjöberg’s solutions with seismic studies are similar but Jeffrey and Sjöberg’s methods displayed a systematic bias. The standard

deviations of the residuals among seismic data and gravimetric solutions are around 6 km. Overall, the evaluation of these approaches

indicated that Moho from gravimetric approaches reduced only slightly the standard deviation of seismic Moho estimates. Significant

discrepancies with seismic data have been detected in Makran subduction zone, Oman Sea, Persian Gulf and Caspian Sea. The explana-

tion of such inconsistency can be partially due to the poor quality of CRUST1.0 data in these areas, as this model has been used to cor-

rect the gravity values that were input in the inversion procedures.

the Gravity Recovery and Climate Experiment (GRACE)
[Tapley et al., 2004a; Tapley et al., 2004b] and the Grav-
ity field and steady-state Ocean Circulation Explorer
(GOCE) [Floberghagen et al., 2011]. These two missions
have provided global gravity field with an accuracy and
a resolution which is suitable for investigating the Moho
structure. Among successful seismic estimates, the early
results dated back to Beloussov et al. [1980]. The most
widely known crustal model based on seismic refraction
is CRUST5.1 model [Mooney et al., 1998]. Bassin et al.
[2000] further upgraded it and called the new version,
CRUST2.0. The CRUST1.0 [Laske et al., 2013] including
ice layers, water, sediments and consolidated crustal lay-
ers, is the most recent version compiled with a 1×1 arc-
deg spatial resolution. As already pointed out, because of
insufficient seismic data coverage over large areas,
gravimetric or combined gravimetric/seismic solutions
have been utilized. Based on some isostasy hypotheses
on compensating the Earth’s topographic masses, grav-
ity data can be used to determine the Moho depth. Sev-
eral basic theories were suggested to explain the
mechanism of isostasy like those proposed by Pratt-Hay-
ford [Pratt, 1855; Hayford, 1909] and Airy-Heiskanen
[Airy, 1855; Heiskanen, 1931]. Vening Meinesz [1931]
modified the Airy-Heiskanen theory by considering a re-
gional instead of a local compensation based on a thin
plate lithospheric flexure model [Watts, 2001]. Vening
Meinesz theory had been modified by Parker [1973] in
an iterative approach for Moho determination and Old-
enburg [1974] made an attempt to stabilise this method
by applying a low-pass filtering technique. The combi-
nation of these two methods was known as a Parker-
Oldenburg method and it has been generalized for the
3-D gravity inversion by Gómez-Ortiz and Agarwal
[2005] and Shin et al. [2007]. Braitenberg et al. [2000]
developed a similar method with integration of seismic
data; also they estimated variation of the Moho under
the Tibet plateau by an iterative inversion method.
Moritz [1990] improved the Vening Meinesz inverse
problem for a global compensation by adopting the
spherical approximation model of the Earth. Since there
were some theoretical deficiencies in this isostatic
method, Sjöberg [2009] reformulated Moritz’s theory and
called it as the Vening Meinesz Moritz (VMM) problem.
In this approach he solved a non-linear Fredholm’s in-
tegral equation of the first kind. Bagherbandi and
Sjöberg [2012] made a comparison between the gravi-
metric VMM and local Airy-Heiskanen methods in the
determination of Moho depth. Another approach based
on the inversion of gravity data to determining the
Moho depth is collocation method [Krarup, 1969; Tsch-
erning, 1985; Moritz, 1990]. Barzaghi et al. [1992] pro-

posed an approach based on collocation principle, which
propagate the covariance structure of the depth inter-
face to the covariance function of the observed gravity
field. Barzaghi et al. [2015] applied collocation method
by combining the global gravity-gradient information
of GOCE and local gravity data to Moho recovery. Barza-
ghi and Biagi [2014] implemented then a further version
of the collocation method by including seismic Moho
depths as input data. Braitenberg and Ebbing [2009]
studied the structure of the crust by combination of
GRACE and terrestrial gravity data. Some other scien-
tists made attempt to estimate Moho depth by applying
GOCE gravity gradient data [Braitenberg et al., 2010;
Sampietro, 2011; Sampietro et al., 2014]. Reguzzoni et al.
[2013] combined seismic and GOCE data to obtain a new
global Moho model. Tenzer et al. [2009, 2011, 2012a,
2012b] proved that applying the crustal density-contrast
stripping corrections is appropriate for a gravimetric
Moho recovery. They showed that gravitational contri-
butions of topography and major known crustal density
structures have a large spatial correlation with the Moho
geometry.

In the area under investigation in this paper, several
studies based on seismic data have been performed for
the determination of the regional Moho model. Most of
these studies concentrated on a specific area, for in-
stance profiles between Shiraz-Mashhad, Tehran-Mash-
had and Mashhad-Tabriz [Asudeh, 1982], the southern
part of the Caspian Sea [Mangino and Priestley, 1998],
Tehran region [Hatzfeld et al., 2003], Mashhad [Doloei
and Roberts, 2003; Javan Doloei, 2003], Central Alborz
and the northern Iran [Sodoudi et al., 2009… Radjaee et
al., 2010], central Zagros [Paul et al., 2006, Shad Mana-
man et al., 2011], Kopeh-Dagh [Nowrouzi et al., 2007],
Naein [Nasrabadi et al., 2008], the northwest Iran
[Taghizadeh-Farahmand et al., 2015], and Sanandaj-Sir-
jan zone [Sadidkhouy et al., 2012]. Furthermore, based
on terrestrial gravity data in this area with a quite ho-
mogenously coverage, Dehghani and Makris [1984]
combined gravimetric and seismic data to determination
of the crustal structure of Iran. Abbaszadeh et al. [2013]
compared the effective elastic thickness of the litho-
sphere estimated by terrestrial and satellite data in Iran.
Eshagh et al. [2017] reformulated two isostatic methods
for Moho recovery by considering contributions of mean
Moho over the whole Moho spectrum.

In this paper, we adopt collocation method as well as
two isostatic approaches to determine the Moho depths
inverting gravity data over Iran. The collocation inver-
sion method for a two-layer model devised by Barzaghi
and Biagi [2014] is applied. In addition, the generalized
form of Jeffrey and Sjöberg’s method proposed by Es-

EBADI ET AL.

GRAVIMETRIC MOHO OVER IRAN

hagh et al. [2017] have been utilized in this study. These
methods have been applied to gravity from GOCO03S
gravitational model [Mayer-Gürr et al., 2012] reduced
for the SRTM30_PLUS topographic/bathymetric data
[Becker et al., 2009], the sediment and the crystalline
data of CRUST1.0 [Laske et al., 2013]. Comparisons of
these Moho depth estimates have been finally performed
with the seismic estimates available from literature.

2. THE THEORETICAL BACKGROUND

In this section, we review three gravimetric inver-

sion methods that can be successfully applied to esti-
mate the Moho depth. At first, we describe the
procedure based on the collocation principle. Subse-
quently, we also discuss two alternative isostatic ap-
proaches, which are reformulations of Jeffrey and
Sjöberg’s theories.

2.1 THE COLLOCATION SOLUTION
The collocation method for Moho estimation is based

on a stochastic approach derived from the Wiener fil-
tering and prediction theory that allows estimating the
signal correlated component based on the covariance
structure of the data [Barzaghi and Biagi, 2014]. In the
years, it has been applied to determine the gravimetric
estimate of the Moho [Barzaghi et al., 1992; Barzaghi
and Biagi; 2014, Barzaghi et al., 2015]. In this context,
the covariance structure of the Moho depth is propa-
gated to the covariance of the observed gravity in a
simple two-layer model. In order to apply collocation
for estimating the Moho depth, we should consider the
following linear relationship which holds in planar ap-
proximation [Barzaghi and Biagi, 2014]:

(1)

Δ𝑔 is the Bouguer gravity anomaly minus its mean,

G is the Newton’s gravitational constant, 𝑇₀ is the mean
Moho depth, 𝜀 is the Moho depth undulation with re-
spect ,𝑇₀, Δ𝜌 stands for the mean constant density con-
trast between the two layers and 𝑑�� = √𝑥² + 𝑦².

Also, the following conditions must be fulfilled
[Barzaghi and Biagi, 2014]:

1) 𝜀 is a weak stationary stochastic process, ergodic
in the mean and in the covariance

2) The noises in gravity and depth, n𝑔 and n𝜀 are spa-
tially uncorrelated zero mean signals

3) The cross-correlations between signals and noises
are zero

To perform the computation, the gravity auto-co-
variance and the cross-covariances between gravity and
depth are needed, i.e.:

𝐶�Δ𝑔�, Δ𝑔�� = 𝐶Δ𝑔Δ𝑔��𝑃� – 𝑃��� = 𝐶�Δ𝑔�, Δ𝑔�� (2)

𝐶�𝜀�, Δ𝑔�� = 𝐶𝜀Δ𝑔��𝑃� – 𝑃��� = 𝐶�Δ𝑔�, 𝜀�� (3)

Assuming that the observed gravity values contain a
noise component, we can write:

Δ𝑔𝑂𝐵𝑆 = Δ𝑔 + n𝑔 (4)

The collocation estimate of 𝜀 is [Moritz, 1980;

Barzaghi et al. 1992; Barzaghi and Biagi, 2014]:

(5)

With

c𝜀Δ𝑔�= 𝐶�𝜀�, Δ𝑔�� , 1 = �Δ𝑔𝑂𝐵𝑆� and C𝑙𝑙 = �𝐶Δ𝑔���Δ𝑔����.

As the first step to use this approach, the empirical

covariance function of Δ𝑔𝑂𝐵𝑆 should be estimated and
modelled with appropriate positive definite model func-
tions [Moritz, 1980]. Under the hypotheses previously
stated, the empirical covariance can be estimated as
[Barzaghi et al., 1992]:

(6)

Also, auto and cross-covariance models must be de-

fined in order to derive the estimator of 𝜀 for Moho de-
termination. One possible model for the auto covariance
of Δ𝑔 [see Barzaghi and Biagi, 2014] is:

(7)

Where 𝐽₁(�) is the first order Bessel function.
If this auto-covariance is considered, one can prove

[Barzaghi et al., 1992] that:

(8)

which can be evaluated by numerical integration meth-
ods.

The parameters A and 𝛼 are determined so that the
model (7) fits the empirical estimated covariance val-
ues of Δ𝑔. After deriving 𝐶𝜀Δ𝑔�𝑃, 𝑄� by the expression

𝑅2
Δ𝑔�𝑥,𝑦,0� = 𝐺∬𝑑𝑥𝑑𝑦 Δ𝜌

��[𝑇2 +𝑑2 ]3/2
𝜀𝑇₀

₀

𝜀̂ = �c𝑇 �C–1l𝑙𝑙𝜀Δ𝑔

𝐶�Δ𝑔Δ𝑔(Δ𝑃𝑘) = � �Δ𝑔𝑂𝐵𝑆 �𝑄��Δ𝑔𝑂𝐵𝑆 �𝑄��

𝑃𝑘–1 <�𝑄� – 𝑄��<𝑃𝑘 , Δ𝑃𝑘 = 𝑃𝑘 – 𝑃𝑘–1

𝑁
1 �

𝑖=1
𝑁�
1 ��

𝑗=1

𝐶Δ𝑔Δ𝑔(𝑟) =
𝐴𝐽₁�𝛼𝑥�

𝛼𝑥

𝐶𝜀Δ𝑔�𝑃, 𝑄� = �
𝛼

𝑑𝑘𝑘𝑒𝑘𝐻�𝐽0�𝑘�𝑃–𝑄��2π𝐺𝜌̄𝛼
𝐴

EBADI ET AL.

above, we can then obtain by applying formula (5). The
final Moho estimate is then given as 𝑇 = 𝑇0 + 𝜀.

Also, in order to refine the estimate, iterations on
gravity residuals can be performed so that the final so-
lution is obtained as 𝑇 = 𝑇0 + 𝜀1 + ... + 𝜀𝑛 . Usually two
or three iterations are computed.

2.2 THE JEFFREY’S SOLUTION
Jeffrey [1976] has solved the problem of isostasy

for Moho modelling in a very similar way to the
VMM method [Sjöberg, 2009]. Eshagh and Hussain
[2016] proposed a different modelling of the isostatic
gravity disturbance 𝛿gI by considering the gravita-
tional effects of topography and bathymetry, sedi-
ments and consolidated crystalline basement as
follows:

𝛿gI = 𝛿g – 𝛿gTB – 𝛿gS – 𝛿gCrys+𝛿gC (9)

In this equation, 𝛿g denotes the observed gravity

disturbance which is the difference between measured
and normal gravity at a computation point on the
Earth, 𝛿gC is the compensation attraction, 𝛿gTB is the
topographic/bathymetric effect on 𝛿g, 𝛿gS and 𝛿gCrys
represent the gravitational effects of sediment and
consolidated crust, respectively. Moritz [1990] and
Sjöberg [2009] applied this equation as a fundamental
condition to solve the VMM problem. In order to de-
fine the compensation potential in equation (2-10), Es-
hagh et al. [2017] arranged the formula in Jeffrey
[1976] in the following way:

(10)

As stated before, 𝜀 is the variation of the Moho

depths relative to the mean value indicated by T0. In
this equation, R is the radius of the Earth, 𝜎 is the unit
sphere, 𝑟’ denotes the geocentric distance of the in-
finitesimal mass element while d𝑟’ and d𝜎 = sin𝜃d𝜃d𝜆
are the radial and the surface integration elements,
𝑃𝑛(cos𝜓) is the Legendre polynomial of degree n for
the argument of the geocentric angle 𝜓. 𝜃 and 𝜆 rep-
resent the spherical co-latitude and longitude of the
element, l is the Euclidean spatial distance which is a
function of the 𝑟’ (see. Heiskanen and Moritz [1967]).

Further, Eshagh et al. [2017] solved the radial inte-
gral and expanded 𝛿gC in a spectral form according to
the Heiskanen and Moritz [1967] scheme:

(11)

Where 𝐾= 1– .

Also Eshagh et al. [2017] approximated the term

[𝜀/(𝑅‐𝑇0)]n+3 by a binomial series and after simplifica-
tion, (2-11) reduces to:

(12)

They wrote this equation according to Laplacian har-

monics of Δ𝜌𝜀:

(13)

By considering Eq. (2-9) and inserting (2-13) into

that, they got:

(14)

Eshagh et al. [2017] took the summation from both

sides of Eq. (2-14) and extract 𝜀 from the resulting ex-
pression and finally arrived at:

(15)

Since 𝜀 is the undulation of Moho depths with re-

spect to 𝑇0 , the total Moho depth is given as 𝑇 = 𝑇0 + 𝜀.

2.3 THE SJÖBERG’S SOLUTION
The Vening Meinesz Moritz (VMM) inverse problem

of isostasy [Sjöberg, 2009] has been developed and ap-
plied successfully over different areas of the Earth. The
main difference between Jeffrey and Sjöberg’s method
is how to write the compensation potential. Sjöberg
[2009] used the compensation potential VC derived by
Moritz [1990]:

(16)

Eshagh et al. [2017] solved the integrations by as-

suming T = T0 and obtained the compensation attrac-
tion of the gravity disturbance as follows:

𝑉C = 𝐺�� �

d𝑟’d𝜎 =
σ 𝑅–𝑇0 –𝜀

𝑅–𝑇0

𝑙
Δ𝜌𝑟’2

σ 𝑛=0 𝑅–𝑇0 –𝜀

𝑅–𝑇0

𝑟𝑛+1
Δ𝜌∞

= 𝐺��� � 𝑟’𝑛+2d𝑟’𝑃𝑛(cos𝜓)d𝜎

𝑇0
𝑅

𝛿gC = � (𝑛+1) 𝐾𝑛+3 �� (Δ𝜌𝜀) 𝑃𝑛 (cos𝜓)d𝜎
σ𝑅–𝑇0

𝐺𝑅 ∞

𝑛=0

𝛿gC,𝑛

= 4𝜋𝐺 𝐾𝑛+2 (Δ𝜌𝜀)𝑛2𝑛+1

𝑛+1

(Δ𝜌𝜀)𝑛

= 𝐾–(𝑛+2) �𝛿gn – 𝛿gTB – 𝛿gS – 𝛿gCrys�

4𝜋𝐺
1

𝑛+1
2𝑛+1

n n n

𝜀

=– � 𝐾–(𝑛+2) �𝛿gn – 𝛿gTB – 𝛿gS – 𝛿gCrys�

4𝜋𝐺Δ𝜌
1

𝑛+1
2𝑛+1

n n n

∞

𝑛=0

𝛿gC�
𝑟=𝑅

=𝐺�� Δ𝜌� 𝐾𝑛+3

×�1–�1 – �
𝑛+3

�𝑃𝑛(cos𝜓)d𝜎
𝜀

𝑅–𝑇0

𝑛+3
𝑛+1∞

𝑛=0

𝑉C =𝐺Δ𝜌���

𝑃𝑛(cos𝜓) � � 𝑟’𝑛+2d𝑟’– � 𝑟’𝑛+2d𝑟’�d𝜎
σ 𝑅–𝑇

𝑅

𝑅–𝑇0

𝑅1
𝑟𝑛+1

∞

𝑛=0

GRAVIMETRIC MOHO OVER IRAN

(17)

Furthermore, they considered the spectral form of

𝛿gC and got:

(18)

Where .

They proved by inserting Eq. (18) into (9) that the

Moho depth can be obtained as:

(19)

Where .

As it can be seen in Eq. (19), T0, besides the zero-de-

gree term, affects all frequencies.

3. THE IRAN CASE STUDY

In this section, we present the Iran case study and

the application of the three methods previously de-
scribed to the gravimetric estimate of the Moho in
Iran. We divide this section into four parts. In section
3.1 we present a brief geological structure of the area.
The used gravity data are described in section 3.2
while in section 3.3 the local gravity Moho estimates
over the study area by collocation, the Jeffrey and
Sjöberg methods are presented. Finally, in section 3.4
comparisons among different gravimetric and seismic
derived Moho values are shown.

3.1 THE STUDY AREA
All methodologies have been applied in Iran over

an area limited by the parallels 20° and 45° North and
the meridians 40° and 65° East (see Figure 1). Several
unique events like tectonics and orogenic activities
led to complicated structural units in this area. By
considering the geological features of Iran, some
models and interpretations have been proposed for
this region [Nabavi, 1976; Eftekharnezhad, 1980;
Alavi-Naini, 1993; Aghanabati, 2004; Ghorbani,
2013]. According to these studies, a geological setting
of this area showing a geological classification of var-
ious structural zones of Iran has been devised and is

presented in Figure 1, superimposed on the regional
topography. Topography/bathymetric heights were
generated by the SRTM30_PLUS model to degree and
order 2160 with a resolution of 5'×5' over the study
area [Becker et al., 2009]. As seen in Figure 1, the
ranges of topography vary from -3182 to 4142 m.
Significant topography is seen over the Alborz and
Zagros mountains which continues from West-North
until East-South. Most of Iran is surrounded by a
rough topography except for southern border of
Caspian Sea, Central Iran, Lut Block, Jazmourian and
Makran basins.

The convergence of the Arabia-Eurasia plate led to
the complex features in the Iranian crust and litho-
spheric mantle. The closure of Tethys Ocean and col-
lision of Arabian-Eurasian plates caused the
formation of Iranian plateau during the Mesozoic and
Cenozoic period [Berberian and King, 1981; Berberian
et al., 1982]. Some active and young tectonic struc-
tures consist of the collision zones in Zagros, Alborz,
Kopeh-Dagh and subduction zones in the Makran and
South Caspian Basin were formed as a result of the
Arabia-Eurasia convergence [Shad Manaman et al.,
2011]. This convergence led to formation of the two
tectonometamorphic and magmatic belts of Sanan-
daj-Sirjan zone and the Urumieh-Dokhtar magmatic
assemblage.

Central Iran is a triangle located in the middle and
bordered by the Alborz Mountains in the North, Lut
Block in the East and Urumieh-Dokhtar in the South.
In this zone, there are rocks of all ages, from Precam-
brian to Quaternary, and several episodes of orogeny,
metamorphism and magmatism. Sanandaj-Sirjan is lo-
cated to the South-West of Central Iran and the North-
East of Zagros Mountains. A remarkable feature of this
zone is the presence of immense volumes of magmatic
and metamorphic rocks of Paleozoic and Mesozoic
eras. Zagros ranges separate the Arabian Block from
the rest of Eurasian tectonic plate. In this area, there
are no abundant outcrops of Paleozoic rocks and the
area is without magmatic and metamorphic events. Al-
borz range is located in North of Iran, parallel to the
Southern margin of Caspian Sea. This mountain is
characterized by different sedimentary rocks. The
Kopeh-Dagh Mountains and basin consist largely of
extrusive igneous rocks belong to Paleogene volcanic
areas. Makran is separated from Jazmourian depres-
sion by a long range of ophiolites extending from
West to East [cf. Ghorbani, 2013].

σ
𝛿gC = 𝐺Δ𝜌���(𝑛+1) �1 –(𝑛+2)

�𝑃𝑛 (cos𝜓)d𝜎 –
∞

𝑛=0 𝑅
𝑇

2𝑅
𝑇

∞

𝑛=0 (𝑛+3)
(𝑛+1)

– 𝐺Δ𝜌��� �1–𝐾𝑛+3�𝑃𝑛(cos𝜓)d𝜎

𝛿gC,𝑛 = 4𝜋𝐺Δ𝜌𝛽𝑛 𝑇𝑛– �1–𝐾𝑛+3�𝛿𝑛0
2𝑛+1
𝑛+1

3
4𝜋𝐺𝑅Δ𝜌

𝛽𝑛 = 1–(𝑛+2)
2𝑅
𝑇0

𝑇 = 𝐴C0+ � 𝛽 –1�𝛿gTB + 𝛿gS – 𝛿gCrys – 𝛿gn�
4𝜋𝐺Δ𝜌

𝑛+1
2𝑛+1

nn n n
𝑛=0

∞

𝐴C0 = (1–𝐾3)� �𝑅–𝑇0
𝑅

3
𝑅

3.2 THE GRAVITY DATA SET
In this study, the considered gravity data have been

synthetized from the GOCO03S gravitational model up
to degree and order 180 and were computed on a
0.5×0.5 arc-deg surface grid. In order to obtain the to-
pography/bathymetry (TB) corrections, we applied the
spherical harmonics expansion of digital elevation
model from SRTM30_PLUS to degree and order 180
consistent with the resolution of CRUST1.0 model.
Moreover, for computing the gravity corrections due to
sediment and consolidated crustal layers, we used the
Earth’s crustal model CRUST1.0, which in this area gives
mean densities values for the sediments and the con-
solidated crustal layers that are, respectively, 2060 kg m-
3 and 2670 kg m-3 (see Figures 2b and 2c). By applying
all these corrections we obtained the gravity data that
were used in the inversion procedures. Figure 2d repre-
sents the map of the refined Bouguer gravity, in unit of
mGal, reduced for the gravitational contribution of
crustal density heterogeneities over the study area. This
illustrates the largest and positive value at Oman Sea
and the negative one over the Zagros and Sanandaj-

Sirjan belts and in the North-East part of Iran around its
border to Azerbaijan and Turkey and in the south part
in Bam. All the mentioned corrections are displayed in
Figure 2 and the related statistics are given in Table. 1.

EBADI ET AL.

FIGURE 1. Topography heights and geological setting of the study area of Iran [km].

Max Mean Min STD

TB 227.3 -35.0 -371.1 96.7

sediments 183.5 66.0 3.9 34.5

crust 46.5 -199.5 -424.7 84.2

total 486.8 230.6 -195.1 123.2

TABLE 1. Statistics of the TB, sediment and consolidated crust
corrections to gravity disturbances [mGal].

3.3 THE GRAVIMETRIC MOHO ESTIMATES
The three methods described in section 2 for deter-

mination of Moho were applied in the study area. The
computations were accomplished by setting 𝑇0 = 44 km,
which is the mean of depths estimated from seismic
studies [Mangino and Priestley, 1998; Paul et al., 2006;
Taghizadeh-Farahmand et al., 2010; Radjaee et al.,
2010; Tatar and Nasrabadi, 2013; Taghizadeh-Farah-
mand et al., 2015; Motaghi et al., 2015; Abdollahi et
al., 2018].

As stated above, the collocation approach in planar
approximation has been applied to GOCE derived re-
duced Bouguer gravity, i.e. Bouguer gravity anomalies
reduced for sediment and consolidated crust effects.
Moho depths have been determined with respect to

mean value 𝑇0 while the 𝜀 values have been obtained
according to the scheme described in section 2. In this
computation, the constant density contrast between
crust and mantle has been set to 600 kg m-3. The grav-
ity data, obtained by applying combined topogra-
phy/bathymetry gravitational effect from
SRTM30_PLUS data and corrections for the sediment
and consolidated crust data generated from the
CRUST1.0, has been re-gridded on a regular (x, y) grid
in the investigation area (see Figure 3).

The collocation procedure has been then applied it-
eratively. The behaviour of the empirical covariance
function of gravity data and the best-fit model with the
related parameters can be seen in Figure 4 for the three
steps that have been performed to get the final estimate.

GRAVIMETRIC MOHO OVER IRAN

FIGURE 2. a) the TB gravitational effect; b) the gravitational effect of sediments; c) the gravitational effect of consolidated crust;
d) the reduced Bouguer gravity anomalies [mGal].

a) b)

c) d)

EBADI ET AL.

FIGURE 3. Bouguer gravity anomaly reduced by topography/bathymetry, sediment and consolidated crust corrections on a (x,y) grid
[mGal].

In this figure, parameter A is the covariance value in
the origin, 𝛼 is the scaling factor for argument of Bessel
function and 𝜎�̂�2 is the noise variance, i.e. the difference
between the empirical value and the model function at
the origin. A and 𝛼 are found by letting the first em-
pirical zero coincide with the zero of the model function
and assuming the model function coincide with the em-
pirical one at the second point [Barzaghi et al., 1992].
In the first step, the model function which best de-
scribed the empirical values is J1 Bessel function divided
by its argument, with A=14000 mGal2 and parameter
�̂� =0.0055 km-1. A value is sufficiently close to initial
one of empirical function, which is 14815 mGal2. The
difference between the two values in the origin, i.e. the
noise variance, has been fixed to 815 mGal2. In the sec-
ond step, residuals of gravity from the first inversion
step have been used as input data. As can be seen in
Figure 4 the variance of these residuals, i.e. the value
in the origin of the empirical function, decreased dras-
tically to 3490 mGal2 and the signal variance, i.e. the

A value, has been set to 3200 mGal2. The �̂� and 𝜎̂𝑛2
quantities have been fixed at 0.0135 km-1 and 290 mGal2,
respectively. Furthermore, in third step, based on the
residual gravity from the second iteration, model co-
variance parameters were fixed at 𝐴�𝛿𝑔 =900 mGal2,
�̂� =0.0317 km-1, 𝜎�̂�2 =192 mGal2. This iterative process
has been stopped at the third iteration since the co-
variance function of the third step residuals has a cor-
relation length (the distance at which the covariance
function is half of its value in the origin) that is com-
parable with the grid step. Results of this procedure are
shown in Figure 5 and related statistics are summa-
rized in Table 2.

The final estimate (see Figure 5c), obtained by
adding the values coming from the iterative procedure
to the mean depth 𝑇0 =44 km, shows maximum depths
under the Zagros Mountain, the Sanandaj-Sirjan and
the Urumieh-Dokhtar belts with spread under the Al-
borz Mountain and Kopeh-Dagh, while the minimum
depth is under the Oman Sea and the border of Caspian.

GRAVIMETRIC MOHO OVER IRAN

FIGURE 4. The empirical covariance function of the gravity data and the best−fit model.
a) First step: 𝐴�𝛿𝑔 14000 mGal2, �̂� = 0.0055 km−1, 𝜎�̂�2 = 815 mGal2.
b) Second step: 𝐴�𝛿𝑔 3200 mGal2, �̂� = 0.0135 km−1, 𝜎�̂�2 = 290 mGal2.
c) Third step: 𝐴�𝛿𝑔 900 mGal2, �̂� = 0.0317 km−1, 𝜎�̂�2 = 192 mGal2.

Collocation
Method

Step Max Mean Min STD

First step 49.0 44.0 35.5 2.4

Second step 51.9 44.0 32.8 3.0

Third step 54.6 44.0 31.6 3.4

TABLE 2. Statistics of Moho depth computed according to the collocation method [km].

In first step it can be observed that the Moho depth
varies between 35.5 km and 49.0 km and in most areas,
depth of Moho is below 40 km. In second step, statistics
are similar to previous with a slight increase of the stan-
dard deviation of the estimated Moho depths. As seen
in Fig. 5c the Moho depths coming from the third step
are more high frequency (standard deviation increases
to 3.4 km) and ranges between 31.6 km and 54.6 km.

Based on gravity disturbance data, coming from the
GOCO03S, completed to degree and order 180, we then
estimated the Moho depth over Iran with the gravimet-
ric approaches devised by Sjöberg and Jeffrey. As done
in the collocation solution, the mean Moho depth has
been set to 44 km. Also, the constant density contrast
between crust and mantle has been set to 600 kg m-3 and
corrections including topography/bathymetry, sediment
and consolidated crust has been accounted as well. The

results are plotted in Figure 6 and the summary of sta-
tistics is given in Table. 3. These solutions show a simi-
lar pattern with a large Moho depth under Zagros and
Alborz mountains and also along Sanandaj-Sirjan and
Urumieh-Dokhtar belts and Kopeh-Dagh. The areas with
minimum depth are under the Oman Sea, some parts of
Caspian and Persian Gulf while central Iran, Tabas and
Lut block have relatively shallow Moho depth. As seen
in Figure 6, Sjöberg method gives a smoother solution
than the one based on Jeffrey method.

Minimum Moho depths in both these methods are
lower than minimum depths estimated using the collo-
cation method. Statistics in Table. 3 show a minimum
Moho depth of 17.6 km and 33.9 km for Jeffrey and
Sjöberg methods, respectively. Also, the maximum
Moho depth according to Jeffrey solution seems to be
overestimated since this method has given a depth

EBADI ET AL.

FIGURE 5. Map of Moho model derived from collocation method in a) First step b) Second step c) Third step [km].

a) b)

around 67.4 km near the northwest of Iran. On the con-
trary, by applying the Sjöberg method, the maximum
Moho depth in Iran has been estimated to 59.6 km.

3.4 COMPARING GRAVIMETRIC AND SEISMIC MOHO

ESTIMATES
To validate the gravimetric Moho solutions, we com-

pared them with existing regional seismic studies for
Iran [Mangino and Priestley, 1998; Paul et al., 2006;
Taghizadeh-Farahmand et al., 2010; Radjaee et al., 2010;
Tatar and Nasrabadi, 2013; Taghizadeh-Farahmand et
al., 2015; Motaghi et al., 2015; Abdollahi et al., 2018]. A
compilation of these numerous seismic datasets has been
prepared and checks for their consistency were per-
formed. In this way, we defined a selected collection of
seismic Moho values in the Iran area, which consists of
277 points. These models are shown in Figure 7 and their
statistics are given in Table 4. The maximum Moho
depth is located under the Sanandaj-Sirjan zone and sur-
rounding mountains. By seismic estimates, the minimum
depth of Moho is under the Oman Sea and Makran sub-
duction zone. As it can be seen, Moho depths derived
from seismic studies varies between 18.5 km and 66 km.

These seismic values were then compared with the
gravity derived estimates. In order to perform the com-
parison, we interpolated the gridded gravity estimates
on the sparse seismic point using linear interpolation.

The differences are plotted in Figure 8 and the statis-
tics of the differences are summarized in Table. 5. As
one can see in Figure 8a, the differences between the
collocation solution and seismic data are between -17
km and 21.9 km. The differences between Jeffrey’s and
Sjöberg’s solutions and seismic data range from -11.1
km to 22.2 km and -10.8 km to 23.4 km, respectively
(see Figures 8b and 8c). As it can be seen in Table 5, the
STDs of the differences with respect to seismic data are
around 6 km, the smaller STD values being obtained by
the Sjöberg estimate. Since the STD of seismic data 8.2
km (see Table 4), we can conclude that the gravimetric
Moho estimates are not so highly correlated with the
seismic estimates. Furthermore, the statistics show that
Jeffrey and Sjöberg’s method give estimated Moho va-
lues that have biases with respect to the seismic values
larger than collocation. This reflects in the RMSs values
that show how collocation gives a Moho estimate which
is, overall, closer to the seismic values.

GRAVIMETRIC MOHO OVER IRAN

Max Mean Min STD

Jeffrey 67.4 44.9 17.6 7.2

Sjöberg 59.6 46.6 33.9 3.7

TABLE 3. Statistics of Moho depth computed according to Jeffrey and Sjöberg’s method [km].

FIGURE 6. Bouguer gravity anomaly reduced by topography/bathymetry, sediment and consolidated crust corrections on a (x,y) grid [mGal].

a) b)

This overall analysis can be further specified for dif-
ferent sub-areas in the Iran region where existing re-
gional seismic solutions are available.

Central Zagros and specifically Sanandaj-Sirjan zone
are regions where the maximum depth of Moho has
been revealed therein. According to our computations,
collocation solution indicated a 55 km Moho depth for
this area. Sjöberg and Jeffrey’s methods also indicated
Moho depths at the level of 55 km and 60 km for this
zone, respectively. Dehghani and Makris, [1984] by
using integrated gravity and seismic data estimated a
crustal thickness beneath the central Zagros in 55 km,
which fully agrees with the results of collocation and
Sjöberg’s methods. Hatzfeld et al. [2003] proposed a
depth of 46 km for the crustal thickness at the single
station close to the town of Ghir in central Zagros.

Another investigation of the lithospheric structure
of the Iranian Plateau has been performed by Asudeh
[1982] along three profiles connecting Mashhad to Shi-
raz, Tehran to Mashhad and Shiraz to Tabriz. He re-
ported crustal thickness along these profiles 43, 45 and
46 km, respectively. Doloei and Roberts [2003] and
Javan Doloei and Ghafory-Ashtiany [2004] have pro-
posed 52 km for depth of Moho in Mashhad. By collo-
cation solution, depth of Moho in Mashhad has been
estimated in about 52 km which is in agreement with
Javan Doloei [2003] and Javan Doloei and Ghafory-

Ashtiany [2004] results. Also, Sjöberg and Jeffrey’s
method estimated the Moho depth of about 52 and 56
km in Mashhad, respectively. Doloei and Roberts [2003]
used seismic data and suggested a crustal thickness of
46 km in Tehran located southern part of the central
Alborz. Results of collocation, Sjöberg and Jeffrey’s
method gave values of Moho depths of 43, 45 and 47
km in Tehran, respectively.

Dehghani and Makris [1984] showed that the crustal
thickness varies from 35 km beneath Alborz Mountains
to 54 km in central Alborz. Sobouti and Arkani-Hamed
[1996] identified a 45 km crustal thickness along the
Alborz Mountains. In the analysis of 290 teleseimic
events carried out by Sodoudi et al. [2009] at 12 short-
period stations of the Tehran telemetric network, an av-
erage depth of 44-46 km for Moho under central Alborz
has been estimated. Radjaee et al. [2010] reported the
crustal thickness 48 km under the northern part of the
central Iranian Plateau. Also, they found a variable
crustal thickening between 55 and 58 km under central
Alborz. Shad Manaman et al. [2011] estimated a thick
Moho with 55-60 km depth beneath the central Alborz.
Jiménez-Munt et al. [2012] and Taghizadeh-Farahmand
et al. [2015] estimated crustal thickness 50 and 54 km
in central Alborz, respectively. The results of colloca-
tion and Sjöberg’s method indicated depth of Moho in
that area around 53 km which is close to the values re-

EBADI ET AL.

FIGURE 7. Moho derived from seismic results [km].

Max Mean Min STD

Seismic data 66.0 44.0 18.5 8.2

TABLE 4. Statistics of Moho depth from Seismic estimates [km].

ported by Dehghani and Makris [1984], Radjaee et al.
[2010] and Shad Manaman et al. [2011]. The estimation
of Jeffrey’s method has given a quite overestimated
depth of 60 km in this area.

Paul et al. [2006] estimated crustal thickness beneath
Urumieh-Dokhtar magmatic area around 42 km.
Nasrabadi et al. [2008] indicated that Moho depth is 40
km beneath Maku station in northwest of Iran.

Taghizadeh-Farahmand et al. [2010] applied P and S
seismic waves to recover the crustal thickness around
48 km in this area. According to Taghizadeh-Farah-
mand et al. [2015], the average of Moho depth varies
from 41 km in the northwest Iran to 45-49 km in the
northeast. Jiménez-Munt et al. [2012] estimated the
crustal structure from combination of the geoid height
and elevation data with thermal analysis.

GRAVIMETRIC MOHO OVER IRAN

TABLE 5. Statistics of differences between gravimetric Moho estimates and seismic results [km].

a) b)

Max Mean Min STD RMS

Collocation
Method

21.9 2.4 -17.0 6.3 6.7

Jeffrey Method 22.2 5.7 -11.1 6.1 8.3

Sjöberg Method 23.4 5.2 -10.8 6.0 7.9

FIGURE 8. Differences between seismic data and Moho derived from a) Collocation method b) Jeffrey’s method c) Sjöberg’s
method [km].

Their results showed the crustal thickness of 50 km
beneath the Alborz and Kopeh‐Dagh mountains. By our
gravimetric solutions depth of Moho in Kopeh‐Dagh
has been estimated slightly more than 50 km.

Mangino and Priestley [1998] estimated the Moho
depth at 30‐33 km beneath the South Caspian Basin.
Also, Shad Manaman et al. [2011] estimated similar val‐
ues for Moho depth in this area. Our results from gravi‐
metric methods there indicate the Moho depth of about
37, 38 and 33 km by collocation, Sjöberg and Jeffrey’s
methods, respectively.

Shad Manaman et al. [2011] investigated the Moho
depth through the Makran subduction zone and re-
ported values around 25-30 km for the Oman seafloor
and Makran. Taghizadeh-Farahmand et al. [2015] pre-
sented a depth of 35 km over this area. Abdollahi et al.
[2018] reported range of Moho from 18 to 28 km in
Oman Sea. The collocation solution gave the Moho
depth at around 33 km in Oman Sea. Also, results of
Jeffrey and Sjöberg’s methods has led to depth values of
20 and 34 km in this area, respectively. Our estimations
by collocation and Sjöberg’s method are different from
the results of seismic studies at the subduction zone and
the tectonic border in the Oman Sea. This could be re-
lated to the procedure that we adopted for correcting
the gravity values. Indeed, Eshagh et al. [2017] con-
cluded that the sediment and crystalline corrections
computed using the CRUST1.0 have a low quality in
oceanic areas.

Dehghani and Makris [1984] reported that the crustal
thickness varies between 45 and 48 km in the eastern
Iran. Nowrouzi et al. [2007] estimated depth of Moho
around 44-50 km under Kopeh-Dagh. Jiménez-Munt et
al. [2012] suggested Moho depth minima of about 36
km beneath the Lut block. According to Shad Manaman
et al. [2011], Moho depth varies from 35 km to 40 km
in central Iran and Lut block. Nasrabadi et al. [2008]
mentioned that the crustal thickness deepens up to 56
km under the Naein station in central Iran. The results
of Sadidkhouy et al. [2012] showed that depth of Moho
in Isfahan area is variable between 38.5 and 43 km. Our
solutions by gravimetric methods give the Moho depth
ranging from 47 km in central Iran to 44 km in Lut
block, which is in a good agreement with Paul et al.
[2006] and Sadidkhouy et al. [2012]. In the coast of the
Persian Gulf, a Moho depth of about 25 km has been
suggested by Paul et al. [2006] where we have different
values (here our estimates are around 35 km). All these
comparisons between seismic estimates and regional
Moho depths obtained from the different gravimetric
inversion methods for each of the different sub‐areas
have been summarized in Table. 6.

All in all, these comparisons show that our results
are in most cases in the same range with seismic esti‐
mations in literature. By considering the effects of sed‐
iment and consolidated crust we provided satisfactory
results for most of the continental crust where our es-
timates have a relatively good agreement with local
seismic studies.

Larger discrepancies are present between seismic and
gravimetric estimates in the offshore area around 22 de-
grees of latitude. This problem has to be further inves-
tigated also following the discussion presented in
Eshagh et al. [2017].

4. SUMMARY AND CONCLUDING REMARKS

In this study, we applied collocation method as well

as two approaches based on isostasy principle pre-
sented by Sjöberg and Jeffrey for estimating the re-
gional Moho in Iran using gravity observations. For
this purpose, we considered the data of the GOCO03S
satellite only global geopotential model that were sub-
sequently reduced by topography/bathymetry, sediment
and crystalline crust data effect by using the
SRTM30_PLUS DTM and the CRUST1.0 model. The
three different gravimetric approaches gave coherent
estimates. The estimated Moho depths obtained using
collocation, Jeffrey and Sjöberg’s approaches proved
to be statistically equivalent when compared to seis-
mic derived values. The collocation method has been
applied iteratively in three steps and the numerical
computations showed that an iterative process in col-
location method could not change the results signifi-
cantly even though the Moho estimate based on
collocation method in the third step contains more high
frequency details. Furthermore, the collocation solu-
tion proved to be less biased than those based on Jef-
frey and Sjöberg’s methods when considering
discrepancies with respect to seismic Moho estimates.
To evaluate our results, we have compiled a 277 points
collection of local seismic estimations in this area. The
overall standard deviation of the differences between
the results of the collocation, Sjöberg and Jeffrey’s
methods and the seismic estimates is around 6.0 km.

The minimum RMS of differences is between collo-
cation estimates and point-wise seismic data since, as
mentioned, collocation led to less biased discrepancies
with the considered seismic values.

Although the application of sediment and consoli-
dated crust corrections in our solutions provides a rea-
sonable agreement with point-wise seismic data over
most of continental areas like central Zagros, Sanan-

EBADI ET AL.

daj-Sirjan, Kopeh-Dagh and Alborz Mountains, this
leads to unrealistic estimates under the Makran sub-
duction zone, Oman Sea, Persian Gulf and Caspian Sea.
This can be the effect of the poor quality of the
CRUST1.0 data in this region [see Eshagh et al., 2017].

The comparisons performed in this paper prove that
further analyses are needed to come to a better consis-
tency between gravity and seismic derived Moho depths
in Iran before computing any joint seismic/gravimetric
estimate.

GRAVIMETRIC MOHO OVER IRAN

Region Reference
Moho
Depth
(km)

Differences between gravimetric solutions and regional
seismic Moho depths

Collocation Jeffrey Sjöberg

STD RMS STD RMS STD RMS

Central Zagros

Dehghani and Makris (1984)
Hatzfeld et al. (2003)
Motaghi et al. (2015)
Tatar and Nasrabadi (2013)

55
46
49
47

3.2 3.3 5.3 6.2 5.5 5.3

Central Alborz

Dehghani and Makris (1984)
Sobouti and Arkani-Hamed (1996)
Sodoudi et al. (2009)
Radjaee et al. (2010)
Shad Manaman et al. (2011)
Jiménez-Munt et al. (2012)
Taghizadeh-Farahmand et al. (2015)

35
45

44-46
55-58
55-60

50
54

3.5 5.6 4.2 4.3 3.2 3.2

Northwest of Iran
Nasrabadi et al. (2008)
Taghizadeh-Farahmand et al. (2010)
Taghizadeh-Farahmand et al. (2015)

40
48
41

4.8 5.0 4.7 9.9 4.3 5.9

Northeast of Iran

Dehghani and Makris (1984)
Doloei and Roberts (2003)
Javan Doloei and Ghafory-Ashtiany
(2004)
Nowrouzi et al. (2007)
Jiménez-Munt et al. (2012)
Taghizadeh-Farahmand et al. (2015)

45-48
52
52

44-50
50

45-49

1.6 2.3 2.9 6.3 1.8 5.3

Lut Block
Shad Manaman et al. (2011)
Jiménez-Munt et al. (2012)
Taghizadeh-Farahmand et al. (2015)

40
36
41

3.0 7.4 5.5 13.0 3.5 11.2

Yazd Block
Nasrabadi et al. (2008)
Motaghi et al. (2015)
Taghizadeh-Farahmand et al. (2015)

56
38
42

2.3 8.1 4.3 11.8 2.2 10.8

Central Iran
Paul et al. (2006)
Shad Manaman et al. (2011)
Sadidkhouy et al. (2012)

41
35

38.5-43
1.1 5.3 1.2 8.2 0.5 6.4

South Caspian Basin
Mangino and Priestley (1998)
Shad Manaman et al. (2011)

30-33
30-33

10.5 7.6 10.4 7.6 13.9 10.9

Urumieh-Dokhtar
and

Sanandaj-Sirjan

Paul et al. (2006)
Motaghi et al. (2015)
Taghizadeh-Farahmand et al. (2015)

48 59 48 6.0 6.1 6.1 6.8 6.3 6.5

Oman Sea Floor
and

Makran

Shad Manaman et al. (2011)
Taghizadeh-Farahmand et al. (2015)
Abdollahi et al. (2018)

25-30
35

18-28
5.0 8.2 6.0 9.5 4.8 9.9

Coast of the
Persian Gulf

Paul et al. (2006) 25 1.6 3.2 2.6 8.1 3.9 5.0

TABLE 6. The regional seismic Moho depths in sub−areas of Iran and differences with gravimetric solutions in this area [km].

REFERENCES

Abbaszadeh, M., M. Sharifi, and M. Nikkhoo (2013). A

comparison of the estimated effective elastic thick-
ness of the lithosphere using terrestrial and satel-
lite-derived data in Iran, Acta Geophysica, 61,
638-648.

Abdollahi, S., V.E. Ardestani, H. Zeyen and Z.H. Shomali
(2018). Crustal and upper mantle structures of
Makran subduction zone, SE Iran by combined
surface wave velocity analysis and gravity model-
ing, Tectonophysics, 747, 191-210.

Aghanabati, A. (2004). Geology of Iran, Geological sur-
vey of Iran.

Airy, G.B. (1855). On the computation of the effect of
the attraction of mountain-masses, as disturbing
the apparent astronomical latitude of stations in
geodetic surveys, 145, 101-104.

Alavi-Naini, M. (1993). Paleozoic stratigraphy of Iran,
Treatise on the Geology of Iran, 5, 1-492.

Asudeh, I. (1982). Seismic structure of Iran from surface
and body wave data, Geophys. J. Int., 71, 715-730.

Bagherbandi, M. and L.E. Sjöberg (2012). Non-isostatic
effects on crustal thickness: a study using CRUST2.
0 in Fennoscandia, Phys. Earth Plan. Int., 200, 37-
44.

Barzaghi, R., A. Gandino, F. Sanso and C. Zenucchini
(1992). The collocation approach to the inversion
of gravity data, Geophys, prospect,, 40, 429-451.

Barzaghi, R. and L. Biagi (2014). The collocation ap-
proach to Moho estimate, Annals of Geophysics,
57, 0190.

Barzaghi, R., M. Reguzzoni, A. Borghi, C. De Gaetani, D.
Sampietro and A. Marotta (2015). Global to local
Moho estimate based on GOCE geopotential model
and local gravity data. in VIII Hotine-Marussi
Symposium on Mathematical Geodesy, 275-282,
Springer.

Bassin, C., G. Laske and G.J.E. Masters (2000). The cur-
rent limits of resolution for surface wave tomog-
raphy in North America, 81.

Becker, J., D. Sandwell, W. Smith, J. Braud, B. Binder, J.
Depner, D. Fabre, J. Factor, S. Ingalls and S. Kim
(2009). Global bathymetry and elevation data at
30 arc seconds resolution: SRTM30_PLUS, Marine
Geod., 32, 355-371.

Beloussov, V., N. Belyaevsky, A. Borisov, B. Volvovsky,
I. Volkovsky, D. Resvoy, B. Tal-Virsky, I.K. Kham-
rabaev, K. Kaila, and H.J.T. Narain (1980). Struc-
ture of the lithosphere along the deep seismic
sounding profile: Tien Shan—Pamirs—Karakorum—
Himalayas, 70, 193-221.

Berberian, F., I. Muir, R. Pankhurst and M. Berberian
(1982). Late Cretaceous and early Miocene An-
dean-type plutonic activity in northern Makran
and Central Iran, J. Geol.. Soc., 139, 605-614.

Berberian, M. and G. King (1981). Towards a paleo-
geography and tectonic evolution of Iran, Cana-
dian J. Earth Sci., 18, 210-265.

Braitenberg, C. and J. Ebbing (2009). New insights into
the basement structure of the West Siberian Basin
from forward and inverse modeling of GRACE
satellite gravity data, J. Geophys. Res.: Solid Earth,
114.

Braitenberg, C., P. Mariani, M. Reguzzoni and N. Ussami
(2010). GOCE observations for detecting unknown
tectonic features. in Proc. of the ESA Living Planet
Symposium, 151-165.

Braitenberg, C., M. Zadro, J. Fang, Y. Wang and H. Hsu
(2000). The gravity and isostatic Moho undula-
tions in Qinghai–Tibet plateau, J. Geodyn., 30,
489-505.

Dehghani, G. and J. Makris (1984). The gravity field and
crustal structure of Iran, Neues Jahrbuch für Ge-
ologie und Paläontologie-Abhandlungen, 215-
229.

Doloei, J. and R. Roberts (2003). Crust and uppermost
mantle structure of Tehran region from analysis
of teleseismic P-waveform receiver functions,
Tectonophysics, 364, 115-133.

Eftekharnezhad, J. (1980). Subdivision of Iran into dif-
ferent structural realms with relation to sedimen-
tary basins (in Farsi), Bulletin of the Iranian
Petroleum Institute, 82, 19-28.

Eshagh, M., S. Ebadi and R. Tenzer (2017). Isostatic
GOCE Moho model for Iran, J. Asian Earth Sci.,
138, 12-24.

Eshagh, M. and M. Hussain (2016). An approach to
Moho discontinuity recovery from on-orbit GOCE
data with application over Indo-Pak region,
Tectonophysics, 690, 253-262.

Floberghagen, R., M. Fehringer, D. Lamarre, D. Muzi, B.
Frommknecht, C. Steiger, J. Piñeiro and A. Da
Costa (2011). Mission design, operation and ex-
ploitation of the gravity field and steady-state
ocean circulation explorer mission, J. Geod., 85,
749-758.

Ghorbani, M. (2013). A summary of geology of Iran. in
The Economic Geology of Iran, 45-64, Springer.

Gómez-Ortiz, D. and B.N. Agarwal (2005). 3DINVER. M:
a MATLAB program to invert the gravity anomaly
over a 3D horizontal density interface by Parker–
Oldenburg's algorithm, Comput. Geosci., 31, 513-
520.

EBADI ET AL.

Hatzfeld, D., M. Tatar, K. Priestley and M. Ghafory-Ash-
tiany (2003). Seismological constraints on the
crustal structure beneath the Zagros Mountain belt
(Iran), Geophys. J. Int., 155, 403-410.

Hayford, J.F. (1909). Geodesy: The Figure of the Earth
and Isostasy from Measurements in the United
States, US Government Printing Office.

Heiskanen, W. (1931). Isostatic tables for the reduction of
gravimetric observations calculated on the basis of
Airy's hypothesis, Publ. Isos. Inst. IAG (Helsinki),
No. 2, 30, 110-153.

Heiskanen, W.A. and H. Moritz (1967). Physical geodesy,
edn, Vol. 86, pp. Pages, Bulletin Géodésique.

Javan Doloei, G. (2003). Transfer/Receiver Functions and
its Application on Crustal Structure of Uppsala,
Tehran and Mashhad Area, Ph. D Thesis, Interna-
tional Institute of Earthquake Engineering and
Seismology (IIEES).

Javan Doloei, G. and M. Ghafory-Ashtiany (2004).
Crustal structure of Mashhad Area from time do-
main receiver functions analysis of teleseismic
earthquake, Res. Bull. Seismol. Earthquake Engi.
30-38.

Jeffrey, H. (1976). The earth. Its origin, history and phys-
ical constitution, 6th edition, Cambridge, Cam-
bridge University Press.

Jiménez-Munt, I., M. Fernandez, E. Saura, J. Vergés and
D. García-Castellanos (2012). 3-D lithospheric
structure and regional/residual Bouguer anomalies
in the Arabia—Eurasia collision (Iran), Geophys. J.
Int., 190, 1311-1324.

Krarup, T. (1969). A contribution to the mathematical
foundation of physical geodesy, Geod. Inst. Copen-
hagen, Medd., 44.

Laske, G., G. Masters, Z. Ma and M. Pasyanos (2013). Up-
date on CRUST1. 0—A 1-degree global model of
Earth’s crust. in Geophys. Res. Abstr, pp. 2658EGU
General Assembly Vienna, Austria.

Mangino, S. and K. Priestley (1998). The crustal structure
of the southern Caspian region, Geophys. J. Int.,
133, 630-648.

Mayer-Gürr, T., D. Rieser, E. Höck, W.-D. Schuh, I. Kras-
butter, J. Kusche, A. Maier, S. Krauss, W. Hausleit-
ner and O. Baur (2012). The new combined satellite
only model GOCO03S. in GGHS2012, Venice.

Mooney, W.D., G. Laske and T.G.J.J.o.G.R.S.E. Masters
(1998). CRUST 5.1: A global crustal model at 5× 5,
103, 727-747.

Moritz, H. (1980). Advanced physical geodesy, Karlsruhe
: Wichmann ; Tunbridge, Eng. : Abacus Press, 1980

Moritz, H. (1990). The figure of the Earth, Wichmann,
Karlsruhe, 353.

Motaghi, K., M. Tatar, K. Priestley, F. Romanelli, C. Do-
glioni and G. Panza (2015). The deep structure of
the Iranian Plateau, Gondwana Res,, 28, 407-418.

Nabavi, M. (1976). History of Iran Geology, Geological
Survey Mineral Exploration Country.

Nasrabadi, A., M. Tatar, K. Priestley and M. Sepahvand
(2008). Continental lithosphere structure beneath
the Iranian plateau, from analysis of receiver
functions and surface waves dispersion. In 14th
World Conference on Earthquake Engineering, 17.

Nowrouzi, G., K.F. Priestley, M. Ghafory-Ashtiany, G.J.
Doloei and D.J. Rham (2007). Crustal velocity
structure in Iranian Kopeh-Dagh, from analysis of
P-waveform receiver functions, J. Seismol. Earth-
quake Engi,, 8, 187-194.

Oldenburg, D.W. (1974). The inversion and interpreta-
tion of gravity anomalies, Geophysics, 39, 526-
536.

Parker, R. (1973). The rapid calculation of potential
anomalies, Geophys. J. Royal Astron. Soc., 31,
447-455.

Paul, A., A. Kaviani, D. Hatzfeld, J. Vergne and M.
Mokhtari (2006). Seismological evidence for
crustal-scale thrusting in the Zagros mountain belt
(Iran), Geophys. J. Int., 166, 227-237.

Pratt, J. (1855). On the attraction of the Himalaya
Mountains, and of the elevated regions beyond
them, upon the plumb-line in India, 145, 53-100.

Radjaee, A., D. Rham, M. Mokhtari, M. Tatar, K. Priest-
ley and D. Hatzfeld (2010). Variation of Moho
depth in the central part of the Alborz Mountains,
northern Iran, Geophys. J. Int., 181, 173-184.

Reguzzoni, M., D. Sampietro and F. Sanso (2013). Global
Moho from the combination of the CRUST2. 0
model and GOCE data, Geophys. J, Int., 195, 222-
237.

Sadidkhouy, A., Z. Alikhani and F. Sodoudi (2012). The
variation of Moho depth and V P/V S ratio be-
neath Isfahan region, using analysis of teleseismic
receiver function, J. Earth Spa Phys., 38, 15-24.

Sampietro, D. (2011). GOCE exploitation for Moho mod-
eling and applications. In Proceedings of the 4th
international GOCE user workshop.

Sampietro, D. (2016). Crustal modelling and Moho esti-
mation with GOCE gravity data. In Remote sens-
ing advances for earth system science, 127-144,
Springer.

Sampietro, D., M. Reguzzoni and C. Braitenberg (2014).
The GOCE estimated Moho beneath the Tibetan
Plateau and Himalaya. In Earth on the Edge: Sci-
ence for a Sustainable Planet, 391-397, Springer.

Shad Manaman, N., H. Shomali and H. Koyi (2011). New

GRAVIMETRIC MOHO OVER IRAN

constraints on upper-mantle S-velocity structure
and crustal thickness of the Iranian plateau using
partitioned waveform inversion, Geophys. J. Int,,
184, 247-267.

Shin, Y.H., H. Xu, C. Braitenberg, J. Fang and Y. Wang
(2007). Moho undulations beneath Tibet from
GRACE-integrated gravity data, Geophys. J. Int.,
170, 971-985.

Sjöberg, L.E. (2009). Solving Vening Meinesz-Moritz in-
verse problem in isostasy, Geophys. J. Int., 179,
1527-1536.

Sobouti, F. and J. Arkani-Hamed (1996). Numerical
modelling of the deformation of the Iranian
plateau, Geophys. J. Int., 126, 805-818.

Sodoudi, F., Yuan, X., Kind, R., Heit, B. & Sadidkhouy,
A., 2009. Evidence for a missing crustal root and
a thin lithosphere beneath the Central Alborz by
receiver function studies, Geophys. J. Int., 177,
733-742.

Taghizadeh-Farahmand, F., N. Afsari and F. Sodoudi
(2015). Crustal thickness of Iran inferred from con-
verted waves, Pure Appl. Geophys., 172, 309-331.

Taghizadeh-Farahmand, F., F. Sodoudi, N. Afsari and
M.R. Ghassemi (2010). Lithospheric structure of
NW Iran from P and S receiver functions, J. Seis-
mol., 14, 823-836.

Tapley, B.D., S. Bettadpur, J.C. Ries, P.F. Thompson and
M.M. Watkins (2004a). GRACE measurements of
mass variability in the Earth system. Science, 503-
505.

Tapley, B.D., S. Bettadpur, M. Watkins and C. Reigber
(2004b). The gravity recovery and climate exper-
iment: Mission overview and early results. Geo-
phys. Res. Lett., 31, 9, doi: 10.1029/2004GL019779

Tatar, M. and A. Nasrabadi (2013). Crustal thickness
variations in the Zagros continental collision zone
(Iran) from joint inversion of receiver functions
and surface wave dispersion, J. Seismol., 17, 1321-
1337.

Tenzer, R. K. Hamayun and P. Vajda (2009). Global maps
of the CRUST 2.0 crustal components stripped
gravity disturbances, J. Geophys. Res.: Solid Earth,
114.

Tenzer, R., P. Novák and V. Gladkikh (2011). On the ac-
curacy of the bathymetry-generated gravitational
field quantities for a depth-dependent seawater
density distribution, Studia Geophysica et Geo-
daetica, 55, 609.

Tenzer, R., P. Novák, V. Gladkikh and P. Vajda (2012a).
Global crust-mantle density contrast estimated
from EGM2008, DTM2008, CRUST2.0, and ICE-
5G, Pure Appl. Geophys., 169, 1663-1678.

Tenzer, R., P. Novak and G. Vladislav (2012b). The ba-
thymetric stripping corrections to gravity field
quantities for a depth-dependent model of seawa-
ter density, Marine Geod., 35, 198-220.

Tscherning, C. (1985). Local approximation of the grav-
ity potential by least squares collocation, Proc, Int.
Summer School on Local Gravity Field Approxi-
mation, 277-362.

Vening Meinesz, F.A. (1931). Une nouvelle methode
pour la reduction isostatique regionale de l’inten-
site de la pesanteur, Bull. Geodes., 29, 33-51.

Watts, A.B. (2001). Isostasy and Flexure of the Litho-
sphere, Cambridege: Cambridge University Press.

*CORRESPONDING AUTHOR: Sahar EBADI,

School of Surveying and Geospatial Engineering,

College of Engineering, University of Tehran, Iran,

EBADI ET AL.