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Variations in elastic thickness and flexure ofthe Maracaibo block

ARTICLE in JOURNAL OF SOUTH AMERICAN EARTH SCIENCES SEPTEMBER 2014

Impact Factor: 1.37 DOI: 10.1016/j.jsames.2014.09.014

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Mariano S. Arnaiz-Rodrguez

Central University of Venezuela

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Franck A. Audemard

Fundacin Venezolana de Investigaciones

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Available from: Mariano S. Arnaiz-Rodrguez

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Variations in elastic thickness and exure of the Maracaibo block

Mariano S. Arnaiz-Rodrguez a, *, Franck Audemard b ,c

a Departamento de Geofsica, Escuela de Geologa, Minas y Geofsica, Facultad de Ingeniera, Universidad Central de Venezuela, Venezuelab Departamento de Ciencas de la Tierra, Fundacion de Investigaciones Simologicas (FUNVISIS), Caracas, Venezuelac Departamento de Geologa, Escuela de Geologa, Minas y Geofsica, Facultad de Ingeniera, Universidad Central de Venezuela, Venezuela

a r t i c l e i n f o

Article history:

Received 14 May 2014

Accepted 8 September 2014

Available online 30 September 2014

Keywords:

Maracaibo block

Lithosphereexure

Finite differences

Gravity

a b s t r a c t

We estimate the lateral variations of the elastic thickness of the Maracaibo block with a 3D numerical

approach by using centered nite differences. The calculation is based on solving the fourth-order partial

differential equation that governs the bending of a thin plate xed on its boundaries (zero displacement)

with variable thickness (or elastic thickness for this particular case). An initial plate-load model is built

and is iteratively modied to t the general basement conguration and gravity data. The nal result is

an elastic thickness map that covers the Maracaibo block and the surrounding sections of the South

American plate. It shows that the elastic thickness ranges from 30 km to 18 km with a mean value of

23.6 km and a mode of 26 km. The largest elastic thickness values are associated with the location of the

Santa Marta Mountains and the Barinas Apure Basin, while the smallest ones with the M erida Andes-

Maracaibo Basin exural system. The current basement conguration within the Maracaibo basin,

formed as a result of its geodynamic evolution, has affected the mechanical properties of the Maracaibo

block near the current Merida Andes position. The load of the Perija Range is compensated by a complex

stress tensor, and that of the Santa Marta Mountains does not have an isostatic root as it is held by a

relatively strong lithosphere.

2014 Elsevier Ltd. All rights reserved.

1. Introduction

A sedimentary basin is a depressed region in the Earth surface

that has been lled by sediments (Turcotte and Schubert, 2002). Aexural basin or foreland basin is a sedimentary one formed in

response to subsidence driven by vertical stress over the elastic

lithosphere (e.g.DeCelles and Giles, 1996; Watts, 2001). These ba-

sins are characterized by: (1) a thrust front of an adjacent orogen

(or load), which is responsible for the vertical stress that bends the

plate; (2) a sediment ll with a wedge shape in transverse section;

(3) the depocenter located contiguous to the thrust belt that gen-

erates the depression (e.g.Jordan,1995); and (4) aexural bulge, orforebulge, that marks the end of the basin and separates it from the

undeformed craton or plate (e.g. Karner and Watts, 1983). Typical

foreland basins are divided in four discrete sections: (a) the wedge-

top depozone that buries the active thrust front; (b) the foredeep

depozone formedby the subsidence driven by the load of the thrust

belt; (c) the forebulge, a region ofexural uplift which is the result

of a damped sinusoidal deformation; and (d) the backbulge depo-

zone, a broad region of shallow secondary exural subsidence

(DeCelles, 2012).

In Venezuela there are three foreland basins: the Eastern

Venezuela basin, the Barinas-Apure basin and the Maracaibo basin.

The two last basins are part of a double exural system driven by

the Merida Andes load. The Maracaibo basin (Fig. 1) is located

within an independent piece of crust known as the Maracaibo

block, while the Barinas-Apure Basin is situated in the South

American plate. These basins have been largely studied because of

their natural resources. Nonetheless little is known about the

behavior of the lithosphere in this region.Audemard and Audemard (2002) pointed out that both, the

Maracaibo basin and the Barinas-Apure basin, have different me-

chanical behavior, as the depocenter in the Maracaibo basin

dwhich have a major inuence over the study aread is at least

2 km deeper that in the Barinas-Apure basin.Chacn et al. (2005)

calculated the elastic thickness for the Barinas-Apure basin in

25 km, whereasMedina (2009)afrmed that the effective elastic

thickness variations within it ranged from 30 km near the craton

(Guayana Shield) to 10 km near the Merida Andes. Arnaiz-

Rodrguez et al. (2011) considered that the elastic thickness for

the Barinas-Apure basin was around 24 2 km, and estimated that,

* Corresponding author.

E-mail addresses: [email protected], [email protected]

(M.S. Arnaiz-Rodrguez).

Contents lists available atScienceDirect

Journal of South American Earth Sciences

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . co m / l o c a t e / j s a m e s

http://dx.doi.org/10.1016/j.jsames.2014.09.014

0895-9811/

2014 Elsevier Ltd. All rights reserved.

Journal of South American Earth Sciences 56 (2014) 251e264
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for the Maracaibo basin, it was around 16 2 km. Further,Arnaiz-

Rodrguez et al. (2011)pointed out that the formation of the Mar-

acaibo basin and the exural system in the Maracaibo block are not

only controlled by the Merida Andes, but also by the Perija Range

and the Santa Marta Mountains, recommending that a 3D approach

to study the exure of this microplate was necessary.Seismic anisotropy analysis suggested that SKKS split orienta-

tions at ~N45E was most likely to be caused by lithospheric

deformation parallel to the Bocono fault (Masy et al. (2011). Curie

Point Depth analysis reportedthat Maracaibo block was a thermally

stable continental basin, and that a Curie Point Depth anomaly was

due to the exure produced by the Merida Andes, or to the graben

systems located within the Barinas-Apure basin (Arnaiz-Rodriguez

and Orihuela, 2013). The studies previously referred assert that the

Maracaibo block and the South American lithospheres behave

differently.

The present research is part of an ongoing multidisciplinary

effort to understand the dynamics of the Merida Andes, its adjacent

basins, structures and terranes using different approaches: GIAME

project (Geociencia Integral de los Andes de Merida-Integral Geo-

science of the Merida Andes;Schmitz et al., 2013). It focuses upon

the Maracaibo block with the purpose of estimating the lateral

variations of elastic thickness of the block and its adjacent regions

by using a 3D numerical method.

2. Tectonic setting

The Maracaibo block (Fig. 1a), an independent piece of conti-

nental crust localized in northwestern Venezuela, is limited by

three fault systems (e.g., Mann and Burke, 1984; Taboada et al.,

2000; Audemard et al., 2005): Bocono and Oca-Ancon fault sys-

tems, both with dextral strike slip; and Santa Marta-Bucaramanga

with sinistral strike slip. Its formation and expulsion (in NNE di-

rection relative to South America) are related to the compression

generated by the subduction of the Carnegie Ridge and the collision

of the Panama Arc against northern South America (e.g.

Pennington, 1981; Audemard, 1993; Kellogg and Vega, 1995). The

Maracaibo block and the Bonaire block have been overriding the

Caribbean plate, creating an ESE-dipping, amagmatic at oceanic

subduction (e.g.,Kellogg and Bonini, 1982; Freymueller et al., 1993;Van der Hilst and Mann, 1994; Kellogg and Vega, 1995; Kaniuth

et al., 1999; Taboada et al., 2000; Audemard and Audemard,

2002; Mann et al., 2006; Bezada et al., 2010 ). It is worth noting

that the northern Andes block, of which the Maracaibo block is a

piece, is bound to the N and NW by a complex deformation belt,

where the Caribbean and South American plates meet (Taboada

et al., 2000). Given the geometry of the northwestern corner of

South America, the Caribbean plate has been subducting in two

stages: an older one, found in the NW and W, began in the Eocene-

Oligocene (~50 Ma ago; e.g., Kellogg and Bonini, 1982; Kellogg,

1984; Pindell and Kennan, 2009); a younger one, found in the N,

began in the Pliocene (~5 Ma ago) from the Southern Caribbean

Deformation Belt under the Bonaire block and the Maracaibo block

(Audemard, 1991; Taboada et al., 2000; Audermard and Audemard,2002; Duerto et al., 2006; Bezada et al., 2010). Several authors have

described the older stage inuence in the Maracaibo Block geo-

dynamic evolution (e.g., Kellogg and Bonini, 1982). However, the

stage that we refer in the text is the younger one, as is the closest to

the Maracaibo Block.

Within the Maracaibo block there are three important mountain

chains: the Merida Andes, the Perija Range and the Santa Marta

Mountains. The Merida Andes is an over 400 km long and 40 km

wide mountain range with a maximum elevation of 5 km, which

has no direct genetic relationship with the rest of the Andean

Range.Colletta et al. (1997)described the internal structure of the

Merida Andes as a compressional positiveower structure that has

been assumed to be either symmetrical (e.g. Gonzalez de Juana,

1952) or asymmetrical (e.g. Audemard, 1991; Audemard y

Fig.1. (a) Shaded relief topography of the study area showing the major tectonic features in northwestern Venezuela. The red box represents the modeled study area. Abbreviations

stand for: MA, Merida Andes; PR, Perija Range; SMM, Santa Marta Mountain Range; NCA, Northern Colombia Andes; MBa, Maracaibo Basin; BABa, Barinas-Apure Basin, BF, Bocono

fault; IF, Icotea fault; SMF, Santa Marta fault; O-AF, Oca-Ancon fault. Quaternary faults fromAudemard et al. (2000)(b) Structural map of the Maracaibo block. Major structures are

the same as inFig. 1a; thin gray lines represent minor faults (French and Schenk, 2004). Red dashed lines represent sediment thickness to the top of the basement in km ( Di Croce,

1995; Parnaud et al.,1995; Laske and Masters, 1997; Ceron et al., 2007). Blue shapes denote half-graben and basement troughs while orange shapes denote basement uplifts (Erlich

et al., 1999). (For interpretation of the references to colour in this gure legend, the reader is referred to the web version of this article).

M.S. Arnaiz-Rodrguez, F. Audemard / Journal of South American Earth Sciences 56 (2014) 251 e264252
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Audemard, 2002).TheMerida Andes has also been compared to the

Laramide-Rocky Mountains; i.e. a compressive basement block

uplift overthrusting toward the adjacent basins along blind thrust

faults (Kellogg and Bonini, 1982; De Toni and Kellogg, 1993;

Audemard, 1991). The Perija Range sits between Venezuela and

Colombia with a maximum elevation of 3.6 km. This mountain belt

is characterized as an ESE dipping monocline, resulting from the

reactivation of Jurassic faults during the Cenozoic (Garrity et al.,

2004; Duerto et al., 2006). The Santa Marta Mountains is a trian-

gular shaped mountain ranged located in northern Colombia,

covering an approximate area of 3830 km2 with maximum altitude

of 5.7 km. It is usually described as an isolated uplifted massif block

of Precambrian to Mesozoic rocks that were uplifted in three pulses

from the late Maastrichtian to the Late Miocene (Cardona et al.,

2008; Ceron-Abril, 2008). These three mountains play a major

role in the exure of the lithosphere of the South American Plate

and the Maracaibo Block. Arnaiz-Rodrguez et al. (2011) proposed

that the Merida Andes load did not uniquely control the exure of

the lithosphere in the Maracaibo block, and that the Perij a Range,

the Santa Marta Mountains and the Caribbean at slab impact on

the dynamic equilibrium in the region, as well as in the basement

morphology found today.

Adjacent to the northern foothills of the Merida Andes, lays theMaracaibo basin, a foreland basin resulting from the loading of the

Merida Andes and Perija Range (e.g., Audemard and Audemard,

2002; Audemard, 2003). The Maracaibo basin is a small basin

with a deep asymmetric depocentre (Fig. 1b) and the apparent

absence ofexural bulge (Mann et al., 2006). The great depth of this

basin (at least 9 km), in comparison with the Barinas-Apure basin

(at least 4.5 km) shows either that the Maracaibo block has a

different elastic thickness than the rest of the South American plate

(Audemard and Audemard, 2002; Arnaiz-Rodrguez et al., 2011) or

that the basement thrusting in the Merida Andes was asymmetric

(De Toni and Kellogg, 1993).

3. Gravimetric and isostatic setting

Gravimetric studies of the Maracaibo basin and the Merida

Andes have been carried out since the 70s, and most of them have

come to similar results in terms of the gravity and the isostasy in

the region (e.g.,Folinsbeei, 1972; Kellogg and Bonini, 1982; Escobar

and Rodrguez, 1995; Chacn et al., 2005; Arnaiz-Rodrguez et al.,

2011). In this section, we present gravimetric maps of the Mar-

acaibo block with a brief discussion on the signicant anomalies to

illustrate its isostatic state. The free air anomaly (Sandwell and

Smith, 2009) and the total Bouguer anomaly map (Arnaiz-

Rodrguez and Garzon, 2012) of the region are shown inFig. 2.

The free air anomaly of the Maracaibo block ranges from

593 mGal to 149 mGal, with mean values of 16.3 mGal (Fig. 2a).

Positive values are associated with the topography of the mountain

ranges in the area, while negative values are associated with the

adjacent foreland basins. Differences in the negative free air

anomaly values at the northern and southern foothills of the

Merida Andes show the discrepancy between the depocenter

depths of the Maracaibo basin (9 km) and the Barinas-Apure basin

(4.5 km). This difference is associated with the lateral variations of

mechanical properties between the Maracaibo block and South

America and to the asymmetric distribution of the masses (loads)

within the Merida Andes structure (Audemard and Audemard,

2002; Arnaiz-Rodrguez et al., 2011). Positive free air anomaly

values show complex distribution of loads in the area. Four

mountain ranges load the lithosphere: the Merida Andes, PerijaRange, Santa Marta Mountains and the Northern Colombian Andes.

The Merida Andes seems to be the most signicant of these, as the

depocenter for the Maracaibo basin is immediately adjacent to

them; however, the Perija Range and the Northern Colombian

Andes clearly bound the basin on its western side. The deepest

section of the Barinas-Apure basin is linked to the joint contribu-

tion of the Northern Colombian Andes and the Merida Andes

(Arnaiz-Rodrguez et al., 2011).

The Bouguer anomalies range from 265 mGal to 145 mGal,

with a mean of45 mGal (Fig. 2b). The highest values are associ-

ated with the Santa Marta Mountains and Perija Range, indicating

that they lack local isostatic compensation (e.g.Kellogg and Bonini,

1982). Other positive anomalies are likely related to upper crust

density contrast, basement uplift (Fig. 1b), or shallow basement inthe Barinas-Apure basin and the Maracaibo basin. Watts (2001)

proposes that positive values of Bouguer anomaly often indicate

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Fig. 2. (a) Free air anomaly map of the studied region (Sandwell and Smith, 2009). (b) Complete Bouguer anomaly map of the studied region, reduced with 2.67 g/cm 3 Bouguer

density (BA;Arnaiz-Rodrguez and Garzon, 2012). Quaternary faults fromAudemard et al. (2000). Both contour maps are colored in the same color scale and contours are every

50 mGal. Gravimetric positive anomalies in the Santa Marta and Perija mountains indicate absence of isostatic compensation, while displacement to the northwest of the

gravimetric low that could be associated with the Merica Andes isostatic root reveals a complex regional compensation system. (For interpretation of the references to colour in this

gure legend, the reader is referred to the web version of this article).

M.S. Arnaiz-Rodrguez, F. Audemard / Journal of South American Earth Sciences 56 (2014) 251 e264 253
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buried loads (density contrasts in the subsurface), and thus, those

within the Merida Andes and the Northern Colombian Andes, can

be considered as indicative of this sort of loads. Regarding the low

Bouguer anomalies, these are associated with basin regions:

notable negative values are located over the depocenters for the

Maracaibo basin and Magdalena Basin. One of the most important

characteristics of the Bouguer anomaly map is that the gravimetric

low that characterizes an isostatically compensated mountain is

displaced over the northern foothills of the Merida Andes. The

negative gravimetric anomalies are most likely due to the sum-

mation of deep (Moho) and mid-depth (basement) effects (Arnaiz-

Rodrguez et al., 2011), and not to the position of the Merida Andes

isostatic root.

Fig. 3 exhibits the radially averaged power spectrum of the

Bouguer anomaly. From the slopes of this spectrum we estimate the

depth to three mayor sources of gravimetric anomalies: the Moho,

the upper crust-lower crust boundary and the basement, using a

horizontal prism model (e.g.Spector and Grant, 1970). The longest

wavelength is associated with interfaces between 50 and 40 km,

which limit the gravimetric interpretation to crustal depth. Filtering

all but the longest wavelength with a band-pass algorithm (Fig. 4),

we produce a regional map (Fig. 4a) and a residual map (Fig. 4b).

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45 5 km (Moho depth)

17.4 2 km (Upper Crust - Lower Crust)

9.5 1 km (Basement/ Maracaibo Basins depocenter)

Bandpass filter (wavelenght = 0.0105883 radians/km)

0.15 0.2 0.250.1

-5

-10

Wavenumber(Radians/km)

log(Powe

r)

Fig. 3. Radially averaged power spectrum of the complete Bouguer anomaly -BA-showing the source depths estimated from the slopes of the curve. The largest wavelength

component is most likely associated with the Moho discontinuity, the mid wavelength component with the lower cruste

upper crust boundary and, the shortest one, with thebasement.

(mGal)

Gravity Anomaly

74 73 72 71 70

7

8

9

10

11

100 50 0 50 100

100

10

0

50

50

50

50

0

0

0

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0

0

0

0

0

0

0

0

0

0

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0

0

50

50

50

50

(a) (b)

Fig. 4. (a) Regional map from ltering the longest wavelength of the complete Bouguer anomaly map showing gravimetric anomalies due to Moho and basement variations. (b)

Residual map from ltering the longest wavelengths of the complete Bouguer anomaly map showing the gravimetric anomalies due to the density contrast in the upper crust and to

some structures shown inFig. 1b (half-graben and basement troughs). Quaternary faults from Audemard et al. (2000).

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6/15

The regional map (Fig. 4a) presents the gravimetric contribution

of the deeper structures, particularly the Moho. The Moho depth in

the area varies from 25 km in the Santa Marta Mountains to 45 km

intheMerida Andes northern foothills (Ceron et al.,2007). Niu et al.

(2007) suggested that the Moho in the region has a maximum value

of 49 km, while the mean Moho value is around 42 km. Positive

values in the regional map reect the location of thinner crust as

well as the Santa Marta Mountains, which is congruent with the

values proposed by Ceron et al. (2007). Negative values

under 50 mGals most likely correspond to the extent of the

regional exure due to the load distribution. Those zones with

anomalies below100 mGals may be related to places where the

crust and/or the sedimentary section are thicker.

The residual map (Fig. 4b) displays the gravimetric signature of

all the shallower structures such as basement uplifts, troughs and

faults. Some positive anomalies (exceptionally within the center of

the Merida Andes)are associated with some of the basement uplifts

inFig. 1b, although those within the Barinas-Apure Basin do not

seem to have a clear gravimetric response. Other signicant re-

sidual positive anomalies are associated with the Perija Range and

the Santa Marta Mountains. This couldbe related to Paleozoichigh-

density rocks and deformed basement present in those mountain

ranges. We do not consider here that some of these positiveanomalies represent small-buried loads, but it cannot be ruled out.

Some negative values can be linked to the locations of the basement

troughs (Fig. 1b), though not as clear as the anomalies produced by

uplifts. Other residual positive and negative values are related to

smaller structures and density contrasts that go beyond our aims.

4. Methodology

4.1. Mechanical background

Inexural studies, the lithosphere is usually represented as a 2-

D elastic beam that lays over a viscous medium (Watts, 2001). This

beam is then deformed by vertical stresses linked to the existence

of a vertical column of mass laying over it (thrust belts, ice caps,

sedimentary layers, etc). Assuming the absence of horizontal stress,

two models have been largely applied: the innite plate model (e.g.

Watts et al., 1985) and the broken plate model (e.g. Karner and

Watts, 1983a,b). The rst one is applied in cases where the load is

located relatively far away from a plate margin, while the second

one is applied when the loads are set near the limit of the plate. In

the rst scenario, the deformation is computed by solving the

fourth-order differential equation (Equation(1))

Dd4w

dx4

pq

0

p rmwg

q r inwg

(1)

where:

w is the deection of the beam

p Winkler foundation term

q Sedimentary load termrm Mantle density

rin Sediments density

g Gravity aceleration

D Flexural rigidity

D, in Equation(2),depends on the efcient elastic thickness (Te,

how much of the lithosphere behaves elastically), the Young

modulus (E) and the Poisson radius (y) of the beam (Watts, 2001).

D ETe3

12

1 y2 (2)

These equations have been widely used to study, withina simple

approach, the behavior of the lithosphere, assuming that D and Te

are constants. When more complex situations are presented, and it

is notpossible to assume Te as a constant, a numerical approach can

be used to compute the deection of a beam with variable me-chanical parameters (e.g., Bodine, 1981). The problem becomes

much more intricate when the exure of the lithosphere cannot be

simplied into a 2-D elastic beam.

In a 3-D scenario, an elastic plate is used to represent the lith-

osphere (rather than a beam), and the deformation is computed by

solving the fourth-order partial differential equation with variable

coefcients that governs the bending of a thin plate xed on its

boundaries and variable thickness (Equation (3); Eq (3.83) in

Ventsel and Krauthammer, 2001).

DV2V2w 2vD

vx

v

vx

V

2w 2

vD

vy

v

vy

V

2wV2D

V

2w

1 y!v2D

vx2

v2w

vy2 2

v2D

vxvy

v2w

vxvy

v2D

vy2

v2w

vx2! P

(3)

Wherewrepresents the bending of a plate, whose thickness varies

gradually (there is no abrupt variation in thickness). P represents

thesystem of transverse loads applied to the plate. D is describedby

Equation(4)

DETex;y3

12

1 y2 (4)

To perform the mechanical modeling it is necessary to solve

Equation(3).At this point the boundary conditions imposed to the

equation are: (1) the boundaries of the plate are xed

(displacement 0) and are far away (at least 100 km) from the

loads, and (2) the thickness of the plate (that represents the elasticthickness of the lithosphere) is variable but cannot vary abruptly.

Two more boundary conditions must be imposed, related to the

geologic situation at hand: (3) the plate sits over a Winkler foun-

dation that represents the mantle, and (4) the depression after the

exure is ll with sediments.Cardozo (2009)developed a code to

solve Equation (3) by using centered nite differences, and

considering the parameters and conditions previously specied. To

compute w(x,y), the distribution of loads P(x,y) and the variations of

the elastic thickness of the plate Te(x,y) are needed. The parameters

of the mantle and inll material (rm, r in) are also required.

4.2. The Maracaibo block scenario and modeling approach

Arnaiz-Rodriguez et al. (2011) pointed out from a series ofsimple 2D models that: (a) the Maracaibo block and the South

American plate cannot behave as a plate with constant elastic

thickness, (b) the Maracaibo block exure depends on the loads

distribution, and (c) elastic thickness variations must exist in the

region to explain the current basement morphology. They

concluded that is was necessary to apply 3D modeling to estimate

the elastic thickness lateral variations in the region. Considering the

mountain belt distribution (Fig. 1a), and given the fact that it is

difcult to establish the physical limit between both plates, we

chose to model the Maracaibo Block-South America interaction

region with a single continuous plate with variable elastic thickness

and xed boundaries.

Thus, we build an initial model taking into consideration the

area inFig. 1a and the main loads within it (M

erida Andes, Perij

a

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7/15

Range, Santa Marta Mountains and Northern Colombian Andes).

These loads were initially represented from the down-sampled

topographic grid extracted from the V15 Global Topography

(Sandwell and Smith, 2009). Mechanical parameters needed for the

model (r, m E) as well as initial values of elastic thickness were

extracted from previous research; they can be seen in Fig. 5 (Chacn

et al., 20 05; Medina, 2009; Arnaiz-Rodrguez et al., 2011). Once the

initial model was built, the exure was computed using Cardozo's

(2009)code. Loads and elastic thickness were iteratively modied

in small steps so that the plate would t the general basement

conguration; and the residual topography, would t the down-

sampled topography. A owchart illustrating this process is pre-

sented inFig. 5.

Fig. 6presents some steps of the modeling process: the rst is

the exure of the initial model; the second is a middle step; the

third is the nal model. Finally, we computed the gravity anomaly

of the model to compare it to the regional component of the

observed total Bouguer anomaly using the Oasis Montaj 3D GM-SYS

module (Geosoft, 2007). The residual topography and gravimetric

anomaly of the nal model are presented inFig. 7; the resulting

elastic thickness map, inFig. 8.

5. Results

The elastic thickness within the Maracaibo block (Fig. 8) ranges

from 30 km to 18 km, with a mean value of 23.73 km and a mode of

26 km (Fig. 9). The orientation of the elastic thickness contours is

roughly N45E, similar to the Merida Andes and the Bocono fault

System. The largest elastic thickness values (higher than 26 km) are

associated with the location of the Santa Marta Mountains, and

with the deformed Guayana Shield to the southeast (Barinas Apure

Basin). The smallest values (less than 20 km) are associated with

the Merida Andes-Maracaibo basin exural system. Elastic thick-

ness minimum values appear in the northern ank of the Merida

Andes and the Bocono fault, which is congruent with the gravi-

metric data of the area, where the Bouguer anomaly minimum

(that characterizes a locally compensated mountain) is displaced tothe north (Fig. 2b).

The residual topography, i.e. the height of the topographic load

after the exure, ts the real downsampled topography with rela-

tively low deviations. The largest difference is of 172 m, which

represents 3.7% of the real topography (Fig. 7a).Fig. 6(III) presents

the exure of the mechanical model in meters. The exure of the

modeled plate is similar to the real basement conguration within

the basins. Accordingly, the model ts the morphologic data; the

error of the estimation is difcult to judge, since the modeling and

data-tting is done manually. The modeling process showed that

values in the center of the model, near the Merida Andes, were

more sensitive to the variations of elastic thickness and load size (as

would be expected) suggesting that the error in this area should be

small (1.0 km) due to the relatively good t of the plate congu-

ration to the basin's basement, and the insignicant difference

between the residual topography and the real topography. Larger

errors (2.5 km) can be expected near the edges of the region

considered for the modeling (Fig. 1).

6. Discussion

The results of the mechanical model prove that the basement

conguration within the Maracaibo basin is controlled by two

important load systems: the Merida Andes and the Perija Range-

Northern Colombian Andes. The Merida Andes is clearly the

largest load in the system as the orientation of the elastic thickness

contours is similar to the one of this mountain range. This afr-

mation is supported by gravimetric data, as previously discussed.

After having compared the elastic thickness gradients on both sides

of the Merida Andes foothills, we propose that elastic thickness

variations in the Barinas-Apure basin (from 27 to 24 km) are most

likely due to the exure caused by the Merida Andes load over the

relatively stable South American lithosphere (Arnaiz-Rodrguez

et al., 2011); while elastic thickness variations within the Mar-

acaibo basin (from 24 to 18 km) are due to lithospheric weakening

caused by different processes from the Jurassic extension (and

graben formation) to the present compression (uplift of the Merida

Andes and convergence between the Maracaibo block and South

America;Audemard and Audemard, 2002).

Regarding the Merida Andes isostatic state, it is evident from

gravimetric data that local isostasy is not the compensation

mechanism that supports this range (Kellogg and Bonini, 1982;Escobar and Rodrguez, 1995). Flexural evidence, regional gravi-

metric anomalies (Fig. 4a) and elastic thickness gradients adjacent

to the mountain (Fig. 8) suggest a regional compensation mecha-

nism (e.g.,Chacn et al., 2005; Arnaiz-Rodrguez et al., 2011). In a

regional isostasy scenario, we propose that the Maracaibo block

Initial model

Initial Loads:downs-sampled topographic grid

(Sandwell and Smith, 2009) Parameters:Mantle Density: 3.3 g/cm3Sediments Density: 2.4 g/cm3

Poissons Ratio: 0.25

Youngs Modulus: 100e9 Pascal

Initial constant Te: 25 kmMrida Andes

Perij Range

Santa Marta Mountains

Northern Colombian Andes Compute 3D Flexure of a thin plate using

centered finite differences (Cardozo, 2009)

Input model

Compare results to basement configuration

and calculate residual topography

Does the mechanical model

fit the geology?

Does the mechanical model

fit geophysical data?

Compute gravity

of the model

YES!YES!

NO

Endmodelling!

Modify

Loads

and/or Te

Fig. 5. Flowchart describing modeling approach. First, an initial model is created with assumed parameters (downsampled topography and mechanical parameters) and constant

elastic thickness (25 km). Then, the model is tested in the nite difference code (Cardozo, 2009). Flexure of the plate is compared to the basement morphology and residual

topography is compared to the real downsampled topography. The model is updated and tested until it ts the geological data. The gravimetric response of the best model is

computed and compared to the regional gravimetric anomaly; if the model roughly

ts the data, the modeling is

nished, if not the model is modi

ed again.

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8/15

may support the northern half of the Merida Andes, which is the

highest one, while South America supports the southern half. If we

consider that a low angle thrust is more efcient for overthusting

than shortening, and because shortening in the northern foothills

of the Merida Andes (~40 km) is far greater than in the southern

foothills (10e

12 km; Audemard and Audemard, 2002), then we

may expect that the overthrusting in the North to be much smaller

than the one in the South. The asymmetry implied by the short-

ening/overthrusting relation, previously proposed byColletta et al.

(1997), induces more uplift on the northern side than in the

southern side. Therefore the relatively weak lithosphere of the

Maracaibo block is holding a tall and narrow load that produces a

2000

2500

24

24

74 72 70

8

10

500

10001

000

1000

1000

1000

1500

1500

1500

2000

2000

2000

2500

74 72 70

8

10

1000

1500

1500

1500

150

0

2000

2000

200

2000

2000

2500

2500

2500

2500

250

0

3000

3000

3000

3000

3000

3500

350

3500

3500

4000

4000

4000

450045

00

4500

5000

74 72 70

8

10

2000

4000

4000

4000

6000

6

6000

6000

8000

8000

10000

10000

10000

12000

15 20 25 30

(km)

Elastic Thickness (Te)(km)

Loads Height

6

4

2 0 2 4 6

(I)

Topographic

LoadElastic Thickness Flexure due to Load

(II)

(III)

Fig. 6. Some steps of the exural model. From top to bottom three examples are presented: (I) is the initial model where the load is the same as the down-sample topography, Te is

25 km, the exure does not t the basement conguration. (II) is an intermediate step where the load is larger than the topography in the mountains and the same in the basins, Te

is different for SA (24e26 km) and for the MB (18e22 km), the exure has a similar shape to the basement conguration but the depth does not t. (III) is the nal model where the

topographic load is larger than the topography (dark red squares represents regions where the load is at least 3 km larger than the topography), Te gradients exist in all the area and

the exure roughly ts the depth and shape of the basement conguration. Quaternary faults from.Audemard et al. (2000).(For interpretation of the references to colour in this

gure legend, the reader is referred to the web version of this article).

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9/15

large exure (9 km at the Merida Andes northern foothills), while

the strong South American lithosphere holds a widespread load

that causes a minor exure (4.5 km at the Merida Andes southern

foothills). This interpretation supports the asymmetry of the

mountain chain masses, rst proposedby De Cizancourt (1933); the

asymmetric orogenic oat model anticipated by Audemard and

Audemard (2002); and the unevenness of the Merida Andes load

distribution over the Maracaibo Block and South America. It is also

consistent with the 20e30 dipping blind thrust and 10 km uplift of

basement rock described byDe Toni and Kellogg (1993).Further-

more, Fig. 10 shows the relation between crustal thickness

(modeled from the regional Bouguer anomaly,Fig. 4a) and elastic

thickness. The region with thicker crust is related to the weakestlithosphere, but they are also associated to the highest sections of

the Merida Andes, as well as the deepest sections of the Maracaibo

100 0

74 72 70

8

10

(km)Residual Topography

6 4 2 0 2 4 6

Gravity Anomaly(mGal)

74 72 70

8

10

100

100

50

(a) (b)

Fig. 7. (a) Residual topography of the nal model; the largest value is 172 m, which represents 3.7% of the real topography. (b) Gravimetric anomalies due to the exure beam and

the masses of the modeled exural loads. The anomaly produced by the exure is similar to the regional gravimetric anomalies (Fig. 4a).

74 73 72 71 70

7

8

9

10

11

15 20 25 30

20

20

20

24

24

24

(km)

Elastic Thickness (Te)

Fig. 8. Contour map showing the lateral variations of the elastic thickness (Te) of the

MB. Largest values (>26 km) are associated with the undeformed shield to the SE and

the SMM to the NW. Small values (


10/15

basin, both acting as large but narrow loads over a weakened

lithosphere with small elastic thickness.

Other important loads are the Perija Range and the Northern

Colombian Andes, which limits the basin on its western margin.

The Perija Range hardly distorts the pattern of the elastic thickness

contours, which implies that it is in isostatic equilibrium. Since

there is no gravimetric evidence (Figs. 2 and 4) that shows the

existence of an isostatic root (e.g. Kellogg and Bonini, 1982), andelastic thickness values are not particularly large (Fig. 8), another

mechanism must be present for this equilibrium to exist. Generally,

when considering isostasy, other stresses beyond those produced

by a vertical load are not taken under consideration in the model.

One could think that horizontal stresses due to compression and

plate interaction, particularly related to the convergence between

the Maracaibo block, the Caribbean plate and South America, could

be enough to hold such load as the Perija Range in dynamic equi-

librium. Another possibility is that, given the fact that the Mar-

acaibo block is a small plate, the large subsidence of the lithosphere

caused by the Merida Andes could force the crustal block to tilt

towards the SE, uplifting the NW side. Since the Perija Range and

the Santa Marta Mountains are on this side, they might hold the

plate from rising, and therefore be on some state of dynamicequilibrium driven by a vertical (upward vs. downward) stress.

Most likely a blend between both cases exists, causing the Perija

Range not to have an isostatic root.

Larger elastic thickness values in the northwest, going from

26 km to 30 km, particularly near Santa Marta Mountains, would

explain why this mountain does not have sign of been isostatically

compensated (as free air and Bouguer anomalies are positive,

Fig. 2). This could be related to the convergence and coupling be-

tween the South American and the Caribbean plates. We cannot

rule out that a process similar to the one associated with the Perija

Range state could also play a signicant role in the Santa Marta

Mountains isostatic state.

The residual Bouguer anomaly map combined with the base-

ment topography can be used to differentiate the four sections of

the Maracaibo basin (Fig. 11). The wedge-top depozone is located

next to the Merida Andes. This depozone is expected to be narrow

due to the relationship between overthrusting and shortening in

the Merida Andes northern foothill. The foredeep depozone is

present further to the NW and is characterized by a steep basement

from 9 km to 4.5 km depth. The Position of the forebulge crest

(shown in a bold line in Fig. 11) is indicated by a cluster of 4.5 km

contours and by a positive residual Bouguer anomaly. The forebulgeof the basin has not been located before, and was thought to be

absent (Mann et al., 2006; Arnaiz-Rodrguez et al., 2011). Because

this particular forebulge shows no topographic expression (is

buried by 4 km of sediments), the Maracaibo basin is in an over-

lled state (DeCelles, 2012). Furthermore, the relative proximity

between the forebulge and the thrust front supports low elastic

thickness values found within the basin (


11/15

the Icotea fault, a left-lateral strike slip fault, also distorts the

pattern of the elastic thickness contours in the direction of its

displacement. Therefore, the Icotea fault has, at least, a crustal in-

uence, as suggested by seismicity in its vicinities, with events up

to 40 km deep (Audemard and Audemard, 2002). Moreover, this

distortion has the appearance of continuing to the southeast, which

is compatible with the idea of itsconvergence with the Bocono fault

at some point (e.g.Beltran, 1994), or at least that it does not end in

the Maracaibo Lake area as proposed byCastillo and Mann (2006).

As the loads within the Maracaibo block have different ages, we

will briey discuss the time dependent exure of the lithosphere.

Based on the viscoelastic plate model (Walcott, 1970), two char-

acteristics of the load are important: the age and the width (Watts,

2001). Young loads are mostly correlated to high values ofexuralrigidity, while older ones tend to produce lower exural rigidity

values. Wide loads cause the lithosphere to approach faster to a

hydrostatic state (Airy's isostasy model) than a narrow load. The

Merida Andes, within the Maracaibo block exural system, can be

considered as a relatively young and narrow load that produces a

short wavelength and deep exure over the lithosphere. Such cir-

cumstances would suggest that the instantaneous exural rigidity

of the plate (and therefore its elastic thickness) should be less than

the standards values for continental lithosphere. In fact, there is no

simple relationship between instantaneous exural rigidity, the

elastic thickness variations and the age of a load (Watts, 2001), so

we cannot directly determine how much of the subsidence and

elastic thickness variations are produce by the Merida Andes load,

nor how much is inherited from previous process.

6.1. Flexural history of the Maracaibo Block

Based on the results of this research and on previous in-

terpretations of the geodynamic evolution of the Maracaibo Block,

its orogens and basins, we present a schematic portrayal of the

geodynamic history of the region (Fig.12), with particular emphasis

on the different exural stages deforming this microplate:

a. Originally, the Maracaibo block was part of the South American

plate. This lithosphere probably had a relatively large and con-

stant elastic thickness (>30 km), as suggested by regional ex-

ural studies about South America (e.g. Watts et al.,1995; Stewart

and Watts, 1997; Perez-Gussinye, 20 07).

b. In the Late Jurassic, rifting between North and South Americacreated the Proto-Caribbean seaway (e.g. Pindell and Barrett,

1990), as well as a passive margin along northern South Amer-

ica. This process would have reduced the elastic thickness to-

wards the divergent margin. Eventually, extension of the

lithosphere created a series of grabens and half grabens in the

South American crust (Parnaud et al., 1995); their formation

would have weakened the lithosphere and signicantly reduced

the elastic thickness near these structures, as suggested by

Audemard and Audemard (2002).

c. During the Cretaceous, sediments were deposited over the

continental platform causing subsidence in the lithosphere

(Duerto, 1998). In the late Maastrichtian the uplift of the Santa

Marta Mountains began, which might have affected the elastic

thickness in an uncertain way. During this period, thermal

3.0

1.0

2.0

1.5

3.0

3.0

4.5

4.5

4.5

4.5

3.0

4.5

6.

0

6.0

7.

5

7.5

74 73 72 71 70

7

8

9

10

11

6.

0

WED

GE-TOP

DEPOZ

ONE

FORE

DEEP

DEPOZ

ONE

BACKBU

LGE

FOREBULGE

(mGal)

Gravity Anomaly

100 50 0 50 100

Fig. 11. Forebuldge position and depozones of the Maracaibo basin on top of the residual Bouguer anomaly and major structures in the study area. The forebulge is located within a

set of 4.5 km contours and associated to some positive residual anomalies within the basin.

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12/15

equilibrium of the lithosphere drove thermal subsidence in the

Maracaibo Block, similar to the process described in the Eastern

Cordillera in Colombia (e.g. Sarmiento, 2002), certainly reducing

the elastic thickness.

d. The rstexural deformation stage of the Maracaibo basin was

associated with the collision of the The Great Caribbean Arcwith northern Venezuela from the Paleocene to the early Eocene

(Lugo and Mann, 1995). Throughout this period, some portions

of

The Great Caribbean Arc

collided and overthrust the passive

margin. Shortening related to this process led to the Lara nappe

emplacement (Stephan, 1985) that caused subsidence in

northwestern Venezuela, reducing the elastic thickness in

northern South America, similar to the lithospheric weakening

produced by nappe emplacement described in the East Carpa-

thians (e.g.Artyushkov et al., 1996).

e The Oligocene represents an important orogenic stage because

of the uplift of the Colombian Andes and the Perij a Range, as

well as a second pulse of the Santa Marta Mountains uplift. The

Fig. 12. Geodynamic evolution of the MB, its orogens and basins, based on the reconstruction proposed by different authors, see text for details. The dotted red line shows the

variation of the elastic thickness (Te) through time (not at true vertical scale). MA current structure is based on Arnaiz-Rodrguez et al. (2011)andMonod et al. (2010)models. The

age of the stages described are as follow: (a) Pre-Jurassic, (b) Late Jurassic, (c) Cretaceous, (d) Paleocene, (e) Oligocene, (f) Middle Moicene, (g) Pliocene. In Fig. 12g, S stands for

shortening and Ot for overthusting. Thick arrows show the direction of stress (either compression or extension) and the small arrow marks the forebulge. (For interpretation of the

references to colour in this gure legend, the reader is referred to the web version of this article).

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rst and second were related to the Nazca Plate subduction,

while the third to the at subduction of the Caribbean Plate

(Kellogg, 1984; Van der Hilst and Mann, 1994; Taboada et al.,

2000). Flat subduction of the Caribbean plate that started in

the NW at this period might have help support the load in the

Maracaibo block along the Perija Range and the Santa Marta

Mountains. It is worth noting that the crustal structure of the

Perija Range is not well known, therefore, in our reconstruction

we take the one proposed byAudemard and Audemard (2002).

f In the Middle Miocene, stress produced by the Panama Arc

collision with northern South America forced the inversion of a

Jurassic graben that led to the uplift of the Merida Andes (e.g.

Audemard and Audemard, 2002; Monod et al., 2010) and drove

the exural subsidence of the region, as well as the creation of

the large depocenter on the northern foothills of the Merida

Andes (Audemard, 2003). The formation of this foreland basin is

recorded by normal faults within it with an average trend of

S37E (Castillo and Mann, 2006). The large load of the Merida

Andes might have reduced the elastic thickness in the Mar-

acaibo basin and the Barinas-Apure basin through its uplift to

some extent, and formed the incipient forebulge of the Mar-

acaibo basin.

g. Ultimately, in the last 5 Ma, the compression generated by thePanama arccollision and the subduction of the Carnegie Ridge at

the Ecuador trench in northern South America produced the

escape of the Maracaibo block and the northern Andes and the

Bonaire block (Egbue and Kellogg, 2010). As both overrode the

Caribbean Plate, a south-dipping amagmatic at oceanic sub-

duction was created in the Southern Caribbean deformation belt

(e.gAudermard, 2009). The current uplift of the Merida Andes

and the Perija Range is driven by oblique convergence and

resulting transpression between South America and the Mar-

acaibo block (Audemard and Audemard, 2002) affecting the

exural system in an uncertain way.

7. Conclusions

Numerical modeling of the complex load system within the

Maracaibo block has allowed us to estimate the lateral variations of

the exural thickness in the region. Based on the elastic thickness

variations, we can draw the following conclusions:

1. The use of a 3D numerical approach is valid to roughly estimate

the variations of the elastic thickness of the continental litho-

sphere. This method is applicable as long as the boundary

conditions and limitations expressed by the equations are

respected, and satisfy the overall geodynamic setting.

2. The elastic thickness in the study area ranges from 30 km to

18 km, with a mean value of 23.7 km, a mode of 26 km. The

orientation of the elastic thickness contours is roughly N45E,

similar to the Merida Andes, indicating that this is the most

important load within the Maracaibo block. Large elastic thick-

ness values (higher than 26 km) are associated with the location

of the Santa Marta Mountains and with the deformed Guayana

Shield. The smallest values (less than 20 km) coincide with the

Merida Andes-Maracaibo basin exural system. Estimated er-

rors range from 1.0 km to 2.5 km.

3. The basement conguration within the Maracaibo basin seems

to be controlled by the Merida Andes (which is clearly the

largest load) and by the Perija Range-Northern Colombian

Andes (which limits the basin on its western margin).

4. The elastic thickness map shows that the 20 km contour has a

similar orientation than the Bocono fault system; this could

imply that the mechanical and geodynamic limit between the

Maracaibo block and South America is in some way associated

with this structure, even though it is improbable the fault dis-

places the Moho.

5. The Perija Range barely distorts the pattern of the elastic

thickness contours and lacks an isostatic root. There may be two

possible explanations for this: (a) horizontal stresses due to

compression and plate interaction hold the Perija Range load, or

(b) the large subsidence of the lithosphere caused by the Merida

Andes could force the Maracaibo Block to tilt towards the SE;

this would have caused the west side of the block to be uplifted

but the Perija Range and the Santa Marta Mountains prevent it

from rising. A mixture of both should not be discarded.

6. Contiguous 4.5 km contours and positive residual Bouguer

anomaly within the basin indicate the forebulge crest of the

Maracaibo basin. It shows no topographic expression as it is

buried by 4 km of sediments, which implies that the basin is in

an overlled state. Moreover, the distance between the fore-

bulge and the northern thrust front support low elastic thick-

ness values found within the basin.

7. The Santa Marta Mountains region has larger elastic thickness

values (from 26 km to 30 km). This could be related to the

convergence of South America and the Caribbean plate (CP) and

the coupling related to this process. The scenarios proposed for

the Perija Range might play a role on the Santa Marta Mountainsisostatic equilibrium as well. Moreover, the fact that the Santa

Marta Mountains was uplifted far from the region affected by

graben formation suggests that elastic thickness values in this

region were unaffected by pre-orogenic processes.

8. When looking at the full picture of the geodynamic evolution of

the Maracaibo block, it is clear that, even though the Merida

Andes is the most important load in the system, its orogenesis is

not the only process that produced the current elastic thickness

gradients within it. Consequently, the Te values within the

Maracaibo basin (from 24 to 18 km) are likely the response to

different stages in the Maracaibo block history. Particularly

Jurassic extension could have affected and weakened the lith-

osphere. Subsequently, the uplift and overthrusting of the

Merida Andes over the weak Maracaibo block lithosphere pro-duced the deep Maracaibo block.

Further work

As noted previously in this paper, classic exural studies take

into consideration vertical stresses related to the loads over the

lithosphere. Horizontal (either compression or extension) stresses

are not, but are often mentioned in the interpretation of the re-

sults obtained. As the Maracaibo block represents a region with a

relatively complex stress eld, compressional stress must be

considered. Further work will include modeling the geodynamic

situation with the nite element method so the horizontal stress

eld can be taken into account, as well as viscoelasticdeformation.

Acknowledgments

The authors would like to thank the Project GIAME and its team

for support during the research, Nestor Cardozo for designing al-

gorithms freely available to the geoscientic community, and

Michael Schmitz and James Kellogg for their thoughts on previous

stages of the research and their motivation to nish the work.

Finally, we would like to thank the reviewers whose notes, com-

ments, corrections, recommendations and thoughts greatly

improved the quality of the original manuscript, and once again to

James Kellogg Editor-in-Chief for his comments that helped us

improve the manuscript and interpretations.

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