Earth and Planetary Science Letters 249 (2006) 108 – 118
www.elsevier.com/locate/epsl
Growth and characterization of complex mineral surfaces
E. Jettestuen a,⁎, B. Jamtveit a , Y.Y. Podladchikov a , S. deVilliers a ,
H.E.F. Amundsen a , P. Meakin a,b
a
Physics of Geological Processes (PGP), University of Oslo, P.O.Box 1048 Blindern, N-0316 Oslo, Norway
b
Center for Advanced Modeling and Simulation, Idaho National Laboratory, ID 83415-2211, USA
Received 1 February 2006; received in revised form 15 June 2006; accepted 25 June 2006
Editor: G.D. Price
Abstract
Precipitation of mineral aggregates near the Earth's surface or in subsurface fractures and cavities often produces complex
microstructures and surface morphologies. Here we demonstrate how a simple surface normal growth (SNG) process may produce
microstructures and surface morphologies very similar to those observed in some natural carbonate systems. A simple SNG model
was used to fit observed surfaces, thus providing information about the growth history and also about the frequency and spatial
distribution of nucleation events during growth.
The SNG model can be extended to systems in which the symmetry of precipitation is broken, for example by fluid flow. We
show how a simple modification of the SNG model in which the local growth rate depends on the distance from a fluid source and
the local slope or fluid flow rate, produces growth structures with many similarities to natural travertine deposits.
© 2006 Elsevier B.V. All rights reserved.
Keywords: rough mineral surfaces; microstructures; growth mechanism; surface normal growth; travertine
1. Introduction
Mineral deposits precipitated at the Earth's surface or
in subsurface fractures and cavities, often exhibit complex growth morphologies over a wide range of scales.
Common examples include stromatolites (e.g. Grotzinger and Rothman [1]), travertine terraces (e.g. Hammer
et al. [2] and Goldenfeld et al. [3]), and a variety of
spherulitic or ‘botryoidal’ carbonates, oxides, phosphates and other minerals. A thorough understanding of
such precipitation patterns is important because these
surfaces not only reflect the kinetics of mineral precip⁎ Corresponding author. Tel.: +47 22856033; fax: +47 22855101.
E-mail address: ejette@fys.uio.no (E. Jettestuen).
0012-821X/$ - see front matter © 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.epsl.2006.06.045
itation, but they are often the interfaces across which the
geosphere interacts with the hydrosphere and the biosphere. In some cases the biosphere may also play an
active role in shaping these interfaces. The detailed
shape of such complex surfaces may control both their
physical and chemical properties, including their reactive surface areas, their transport properties (during
surface migration of fluids, for example), and their friction properties (in fault zones, for example).
In addition to the challenges involved in understanding how such complex surfaces form, it may also be
difficult to find adequate ways of describing them in
quantitative terms. Here, we first review some simple
growth models and examine the associated microstructures and growth surface morphologies. Then we
E. Jettestuen et al. / Earth and Planetary Science Letters 249 (2006) 108–118
demonstrate how a morphologically complex carbonate surface may be accurately simulated using a simple
surface normal growth model that reproduces the observed surface topography and the most pertinent characteristics of the growth-controlled microstructure. This
model may also constrain the role of nucleation and
surface roughening during the growth process. Finally,
we explore an extension of the surface normal growth
model in which the local growth rate is affected by a
symmetry breaking processes, in this case fluid flow. We
demonstrate how some pertinent features of natural
travertine patterns can be reproduced by this model.
2. Growth models
Growth of polycrystalline materials and even single
crystals near the Earth's surface often occur sufficiently
far from thermodynamic equilibrium to generate a wide
variety of growth patterns through nonlinear coupling
between the precipitation itself and local transport processes (cf. Jamtveit and Meakin [4]).
The strategies adopted to model such growth processes
include both discrete particle models and continuum
models (Vicsek [5]; Barabási and Stanley [6]; Meakin
[7]). Selection of the modeling approach depends on the
specific problem, but in most cases relevant to natural
mineral growth it is preferable to work with models that
produce both the surface morphology and the associated
internal microstructure. Particle models produce underlying growth structures directly as a result of the way in
which discrete particles are added to the growing surface.
Continuum models focus on surface advancement, but
local growth trajectories can still be constructed to
produce a ‘microstructure’ behind the growth surface. In
both cases an advancing ‘active zone’, in which growth
occurs, leaves behind a ‘frozen’ internal structure.
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The structure of a rough polycrystalline surfaces may
be affected by several processes including: diffusive and
advective mass transport in front of the advancing surface, surface attachment kinetics, and surface diffusion
or any other surface-smoothening processes. Rapid,
transport-controlled growth will generally produce a
surface that is rough even at microscales (cf. Meakin [8]).
Slower growth with increasing effects of surfacesmoothening processes, will lead to a loss of roughness at increasingly larger scales. Temporal variation in
growth rate, may lead to transitions between microscopically rough and smooth surface growth.
In this section, we describe two well-known particle
models that produce rough surfaces, the Eden model and a
‘ballistic’ deposition model, and a simple continuum
model based on growth normal to the surface — the
surface normal growth (SNG) model. The Eden model
(Eden [9]) was originally developed to simulate the
growth of cell colonies, but it has been demonstrated to
have a much wider range of applications. The growth
surface evolves by randomly filling unoccupied sites on
the growth surface with equal probability. This creates a
compact and spatially homogeneous growth structure
shown in Fig. 1a). However, the surface morphology is
rough and it has nontrivial scaling properties (Meakin [7]).
In the Ballistic growth model (Vold [10,11]) particles
‘rain down’ on a growing surface where they may stick
to one or several nearest neighbors depending on the
chosen growth rules. This process may cause shadowing
effects and produce a richer internal structure than the
uniformly dense structure generated by the Eden model.
For the ballistic growth model, the internal structure is
uniform on a large scale, but on small length scales a
fan-like ‘microstructure’ is formed (Fig. 1b). The Eden
model and the ballistic growth model produce rough
surfaces with self-affine scaling properties. Even though
Fig. 1. Cross section for three growth models: a) Eden growth on a square lattice; b) ballistic deposition on a square lattice; c) normal growth with
continuous addition of nucleation sites and visualization of growth directions. The interfaces between the red and blue colors indicate the surfaces at
different stages during the growth process.
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E. Jettestuen et al. / Earth and Planetary Science Letters 249 (2006) 108–118
their internal morphologies are different, computer
experiments and theoretical analysis indicate that their
surface roughness have the same scaling properties,
implying that these models belong to the same universality class (Meakin [7]).
Continuum models have previously been used to
model complex carbonate structures. Grotzinger and
Rothman [1] suggested that the stochastic differential
equation known as the KPZ-model (Kardar et al. [12])
might provide an adequate description of the growth of
stromatolites. This model belongs to the same universality
class as the ballistic growth and Eden growth models and
thus produces a complex fractal growth surface with the
same scaling properties. An alternative and more general
continuum model that we will study in some detail in this
paper is based on surface normal growth.
In a surface normal growth model the evolution of the
surface is determined when the growth velocity perpendicular to the surface is prescribed. The evolution of a
surface with a constant growth velocity is described by the
equation
Ah
¼ Vn
At
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 þ jjhj2 ;
ð1Þ
where h is the height of the surface, Vn is the growth
velocity in the normal direction, and |∇h| is the absolute
value of the gradient of the height (the slope of the
surface). This is a nonlinear equation which develops
cusps separating smooth spherical caps, but valid numerical schemes that allow tracking of the growth surface
do exist (Sethian [13]). The KPZ equation can be derived
from the normal growth equation (Eq. (1)) by assuming
small surface slopes |∇h|, replacing the square root in Eq.
(1) by the first order Taylor expansion 1 + 1/2|∇h|2,
adding a Laplacian term, and finally adding an uncorrelated noise term.
Many natural growth surfaces of interest are generated
by discontinuous growth with intermittent hiatuses and
multiple nucleation events that leads to surface roughening
during the growth. In the SNG model, we represent the
nucleation (roughening) events by locally increasing the
surface height at randomly selected positions. The
geometry of the growth surface and the associated
microstructure in a cross section for the surface normal
growth model is shown in Fig. 1c. The ‘microstructure’ is
obtained by including short line segments that show how
points on the surface propagated during the growth process.
The internal structure formed by this model exhibits a
characteristic ‘feather-like’ pattern, and the growth surface
consists of spherical caps meeting along sharp cusps. The
morphology of the growth surfaces as well as the internal
microstructure will be controlled by the frequency of
nucleation or roughening events relative to the growth rate.
Fig. 2 shows how the morphology of the surface changes
with increasing frequency of nucleation events. Decreasing
the nucleation frequency produces more prominent ‘fanlike’ microstructures. Rare nucleation produces a few
spherical growth structures with a radial internal microstructure, i.e. a botryoidal morphology.
3. Characterization of a natural carbonate surface
In the following we describe an examination of a
naturally grown carbonate surface from the Pleistocene
Sverrefjell volcano in Svalbard (located at 79° 23′ N,13°
26′E; Skjelkvåle et al. [14]). At this location Ca, Mgcarbonates formed a crust within pipe-like chimney
structures (Fig. 3a) and this is interpreted in terms of
precipitation from pipe-filling fluids under low temperature conditions (H.E.F. Amundsen, personal communication). The carbonate crust is typically a few cm thick and
forms a layered structure with alternating layers of
complexly intergrown dolomite, huntite and magnesite.
The external growth surface has a cauliflower-like structure with spherical caps separated by cusps (Fig. 3b).
In a very porous inner layer almost spherical carbonate
grains (10–20 μm across) form dendritic structures (Fig.
3c,i). Such textures are usually interpreted as evidence for
rapid nucleation and transport-controlled far-from-equilibrium growth (cf. Roselle et al. [15]). Only during the
last stages of growth do some of the grains form facets
(Fig. 3c,ii). Further toward the surface, the layered
carbonate crust becomes less porous and the microstructures of the individual layers appear to have been
formed by complex surface-directed growth (Fig. 3d).
Fig. 2. Surfaces generated by the SNG-model with random nucleation. The
nucleation rate increase by a factor of 100 from a) to b) and by a factor of
100 from b) to c). Dark colors indicate low elevation while light colors
indicate high elevation. The height difference between the lowest and
highest point for each of the surfaces is approximately 10% of the shortest
boundary.
E. Jettestuen et al. / Earth and Planetary Science Letters 249 (2006) 108–118
111
Fig. 3. Ca, Mg-carbonate coatings from the Sverrefjell volcano at Svalbard. a)Hollow chimney-like structure coated by Ca, Mg-carbonates. b) Hand
specimen from the chimney shown in (a) displaying a layered internal structure. c) Backscattered electron (BSE) images of the microstructures of the
inner porous layer of the sample shown in (b). Scale bars: in (c,i) 500 μm; in (c,ii)50 μm. d) Microstructure of one of the intermediate layers shown in
(b). Scale bar 500 μm.
A Roland Active Piezo Sensor touch scanner with
vertical resolution of 0.025 mm was used to measure the
topography of a carbonate surface like that shown in
Fig. 3b. A 3-D digitized version is displayed on a
0.1 mm grid in Fig. 4b. Although this surface appears
relatively rough on the scales observable by eye, its
scaling properties (obtained both by correlation function
and wavelet analysis) are essentially those of a bumpy
two-dimensional surface. This is not consistent with any
of the discrete growth models presented above. However, the growth surface as well as the observed microstructures have many similarities with the structures
generated by the surface normal growth model (SNG),
including surfaces consisting of spherical caps separated
by cusps. To test whether the SNG-model is adequate
for the carbonate growth, we first determined if the
SNG-model can accurately reproduce the observed surface. This analysis is divided into two parts; the first is to
identify regions bound by cusps, and the second is to fit
these regions to spheres.
Cusps can be identified in vertical cuts through the
surface as points where the local slope changes discontinuously from negative to positive. In practice, cusps are
found by comparing left-and right-hand finite differences
in vertical cuts through the surface. Points on cusps will
have a larger right-hand difference than left-hand
difference, and vice versa for off-cusps points, as Fig. 4a,
i illustrates. A network of cusps is built up by marking the
cusp-points for different cross sections through the sample.
The white grid in Fig. 4b shows the directions of the cross
sections that were made to generate a cusp network.
Larger-scale structures can be identified by increasing
the intervals used to calculate the finite differences, so that
a hierarchal structure can be obtained, as shown in Fig. 4a,
ii. Fig. 4c illustrates this by showing the accumulation of
cusp points found by increasing the coarsening. Largescale structures are bounded by thicker lines indicating
that they are located on many scales.
When well-defined ‘cap-regions’ have been identified
between the cusps, spherical surfaces can be fitted to the
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E. Jettestuen et al. / Earth and Planetary Science Letters 249 (2006) 108–118
Fig. 4. This figure illustrates the analysis applied to the carbonate surface; Part a,i) shows how cusp points are found by comparison of left and right
hand finite differences, which are given by the slope of the red lines. The red lines are drawn between the point under study and the intersections
between the circle and the surface. The lengths of the arc segments provide a measure of the coarseness, r; Part a ii) shows how different coarseness
scales pick up different structures in the cusp hierarchy; Part a iii) illustrates the steepest descent method. An arbitrary initial point is selected, the
value of Eq. (2) is evaluated for points in a small neighborhood of the selected point and the neighboring point with the smallest value is selected. This
process is repeated until a local minimum is reached; Part b) shows the directions of the vertical cuts, marked as white lines, that were used to find the
cusp network; Part c) shows the cusp network generated by superposition of cusps found for different coarsening scales.
natural caps. This is accomplished by using the equation
for a circle, j rY − rY j−R ¼ 0, where R is the radius, and
rY0 is the origin of the circle, and finding the origin of the
sphere rY0 that minimizes
rs − rY0 jis Þ2 is ;
d ¼ hðj Y
rs − rY0 j−hj Y
ð2Þ
where rYs are the points in a cap region, and ⟨⋯⟩s denotes
averaging over the cap region. Thus hjrYs −rY0 jis is the
estimated radius of the corresponding sphere, fitted to the
cap, with an origin at rY0 . Eq. (2) gives the standard
deviation between the actual surface and a sphere with
origin at rY0 over the spherical cap region bounded by
cusps. A local minimum of d (Eq. (2)) is obtained by
using a steepest descent method (see Fig. 4a,iii). Fig. 5a,b
shows a comparison between the observed surface and the
surface that is reconstructed from the cusps, and Fig. 5c
shows the difference between the two surfaces. Three
quarters of the fitted surface lies within the mean deviation
Fig. 5. Botryoidal carbonate textures showing: a) natural carbonate surface; b) surface reconstructed from the spherical surface found by cusp
network detection, using a coarsening window of 1.2–1.8 mm; c) the difference between the natural surface and the reconstructed surface.
E. Jettestuen et al. / Earth and Planetary Science Letters 249 (2006) 108–118
between the natural and fitted surface which is 1% of the
height difference between the lowest and highest points
on the surface. This maximum height difference is
approximately 18 mm, so the fit is accurate to within
b 0.2 mm.
If the surface normal growth rate is constant across
the entire free surface, the distribution of sphere sizes
reflects the distribution of nucleation events in time (the
radius of the spherical cap is proportional to the time
lapse between the nucleation time and the time at which
growth stopped). Moreover, the origins of the spheres
are the nucleation sites. The temporal distributions of
nucleation events for different stages of growth are
shown in Fig. 6. This figure suggests that nucleation is
not continuous, but occurs in bursts. This observation is
consistent with intermittent growth of new carbonate
layers interrupted by hiatuses in the growth process.
A final test of the SNG model was conducted by
prescribing the nucleation sites and the timing of new
nuclei formation and running the model to regenerate
the observed growth surfaces starting from an initially
flat surface. The various stages in the growth process are
shown in Fig. 7, which confirms that the model
adequately reproduces the observed calcite surface. By
drawing local growth trajectories during the growth
processes the corresponding microstructure can also be
obtained. This structure is shown in Fig. 8. The agreement between the structure of the natural surface and the
structure of the model surface decreases as older layers
of the sample are examined. There are two primary
causes of this: 1) The addition of new layers and nucleation sites covers and obscures older surface structural
113
features. 2) The appearance of cusps creates singularities on the surface at which the slope is not well
defined. Thus, we need to find weak solutions of Eq. (2)
(see [13]) and this results in loss of information about
the surface prior to cusp formation.
4. Patterns in a flow system
Mineral growth at the Earth's surface often occurs
from flowing supersaturated fluids. In such cases
precipitation is controlled by cooling or by loss of gas/
vapor. Familiar examples include the growth of
travertine and geyserite around hot springs, and the
precipitation of Fe-oxides and other minerals in acidmine runoffs. In most cases, precipitation of solids from
a thin layer of flowing fluids produce spectacular
‘cockle’ or ‘terrace’-shaped morphologies (Ford and
Williams [16]). Fig. 9a shows travertine terraces around
the Troll thermal spring located near the Sverrefjell
volcano (see above) in Svalbard (Jamtveit et al. [17]).
The terraces have flat tops and a convex shapes that are
generated during a process that involves ‘coarsening’ of
the terrace pattern. Such terrace patterns have been
successfully modeled by coupling fluid flow to the local
surface growth velocity (Hammer et al. [2] and Goldenfeld et al. [3]). The microstructure of natural travertines is often similar to structures generated by surface
normal growth. The outer rim of advancing travertine
steps or terraces are usually comprised of feather-like
‘ray-crystals’ (Fig. 9b) directed perpendicular to the
advancing outer surface (cf. Folk et al. [18]). In the
following we will show that some of the characteristics
features of these precipitation patterns can be modeled
by simple extensions of the surface normal growth
model, with a local growth rate that depends on the local
slope and the distance from the fluid source.
Travertine growth from fluids ejected on a horizontal
surface may produce cone-shaped morphologies like the
famous 11-meter tall Liberty Cap at Mammoth Hot
Springs (Fig. 9c). The geometry of this cone clearly
suggests that the precipitation rate of travertine decrease
strongly away from the fluid outlet. The shape of the
Liberty Cap can be modeled by a surface normal growth
process with a growth velocity (Vn in Eq. (1)) that
depends on the distance from the fluid outlet, s,
measured along the surface.
4.1. Calibration of the growth velocity
Fig. 6. The distribution of the spherical surface element radii found
using different coarsening windows. r is defined in Fig. 4a and is
measured in millimeters. The gray rectangles mark the four regions
that were recognized as local maxima at different coarsening scales,
representing bursts of nucleation.
Among a variety of different simple functional forms for
the dependence of Vn on the distance from the outlet, s, we
found that the best visual agreement between the shape
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E. Jettestuen et al. / Earth and Planetary Science Letters 249 (2006) 108–118
Fig. 7. a) to c) shows the evolution of the modeled surface, where c) is the final stage. d) shows the difference between the model surface in c) and the
natural surface in Fig. 5a.
of Liberty Cap and the shape generated by the model
was obtained using
Vn ~
1
;
1 þ cd s
ð3Þ
where c = 0.07. Fig. 10 shows the outline of the Liberty
Cap from Fig. 9c together with a sequence of surface
profiles generated during the evolution of a SNGmodel. The shape of the top part of surface generated by
the model is very similar to the shape of Liberty Cap.
The lower part of Liberty Cap is altered due to weathering. However, the shape of the lower part of the
Fig. 8. The microstructure of the upper layers revealed by a cut through
the modeled sample marked by the white line in Fig. 7c.
surface generated by the SNG-model is similar to the
envelope of the Liberty Cap.
4.2. Travertine terrace formation
The formation of steps or terraces during surface
normal growth arises naturally in a model in which the
local precipitation rate is positively correlated with the
local slope of the surface. This correlation is consistent
with observations in a variety of systems in which steps
are formed, although there is no consensus concerning
the underlying mechanism (cf. Zaihua et al. [19]; Chen
et al. [20]; Hammer et al. [2]; Goldenfeld et al. [3]). In
travertine spring deposits, the growth rate is negatively
correlated with the distance from the outlet because of
the depletion of carbon dioxide and dissolved calcium as
the fluid flows over the surface of the travertine deposit,
and this is supported by observations such as the shape
of the Liberty Cap.
The most plausible cause of the observed correlation
between local surface slope and growth velocity is
enhanced degassing (CO2-loss) in regions with high
fluid flow velocities due to the rapid vertical transport of
CO2 by turbulent eddy diffusion. Previous models for
travertine terrace formation assume a linear relation
between the slope, or fluid flow rate, and the growth rate
(Hammer et al. [2], Goldenfeld et al. [3]). However,
fluid flow on gentle slopes is mainly laminar whereas
flow on steep slopes will be affected by turbulence, and
it is conceivable that the rate of degassing is a strongly
nonlinear function of slope. To simulate terrace growth,
E. Jettestuen et al. / Earth and Planetary Science Letters 249 (2006) 108–118
115
Fig. 9. a) Travertine deposit (100 m across) formed by calcite precipitation from fluid emanating from the Troll thermal spring, Svalbard (spring
source located in the upper left part of the picture). b) Microstructure of a travertine sample from the front part of one of the main travertine terraces at
the Troll spring. The growth direction is upward. Note several nucleation events during growth with regeneration of feather-like calcite crystals. Scale
bar: 1 mm. c) The 11 m high Liberty Cap travertine deposit located at the Mammoth Hot Springs in Yellowstone, USA.
we assumed that the rate of degassing and thus the rate
of normal growth is zero at small slopes, where the flow
in laminar, and has a finite value (that depends only on
the distance to the fluid source) on steep slopes. This can
be expressed by the growth equation:
(
Vn ðsÞ ¼
; if jjhj jjhjc
1
;
; if jjhj jjhjc
1 þ cd s
0
ð4Þ
where |∇h|c is the critical slope at which the transition
from laminar to turbulent flow takes place.
Eq. (4) would produce the shape of the Liberty Cap,
but would need an initial height perturbation on the
surface with slopes greater than |∇h|c. Despite its
simplicity, this model generates growing surfaces with
some of the characteristic features, such as terraces,
commonly observed in travertine deposits. For steep
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
slopes, where jjhj 1; 1 þ jjhj2 cjjhj and Eq.
(4) can be approximated by
Ah
−Vn ðsÞjjhj ¼ 0:
At
ð5Þ
This equation describes the evolution of the so-called
indicator function in level set (cf. Sethian [13]) calculations of the motion of one-dimensional interfaces in twodimensional space. In such calculations, the indicator
function (which corresponds to the height field in this
case) is used to differentiate between the two sides of the
interface. In most cases, the indicator function has a value
of zero at the interface, and it is positive on one side of the
interface and negative on the other side. However the locus
of points at any height corresponds to an interface at that
height. The one-dimensional interface surface (the level
set) in each horizontal cut moves with a velocity of Vn.
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E. Jettestuen et al. / Earth and Planetary Science Letters 249 (2006) 108–118
Fig. 10. The outline of the Liberty Cap (in circles) together with the
evolution of the SNG-model with a velocity function given by Eq. (3).
The final surface is marked by a thick stippled line, and the evolution
of the surface at constant time intervals are marked by solid lines.
At a constant local precipitation rate, the radius of a
travertine terrace is proportional to the product of the age
of the travertine system and the local precipitation rate.
Thus variation in terrace radii can provide independent
information about the spatial dependence of the Vn(s).
4.3. Simulation of terrace evolution
In Fig. 11 we show the evolution of an initially tilted
rough surface, by using the model described by Eq. (5),
and the horizontal distance from the upper boundary at the
right-hand-side is used as the distance from the fluid
Fig. 12. The evolution of a horizontal cut midway through the model
show in Fig. 11.
outlet, s. Reflective boundary conditions were used in the
lateral directions (the front and back planes in Fig. 11).
The initial surface height was given by
ho ðx; yÞ ¼ hjhix þ gðx; yÞ;
ð6Þ
where ⟨∇h⟩ is the average slope of the surface (⟨∇h⟩) and
η(x,y) is a spatially random perturbation. In the simulation
shown in Fig. 11, the average slope ⟨∇h⟩ and the critical
slope, |∇h|c, were both set to unity. The random
perturbation was a 2 + 1-dimensional Brownian process
(correlated vertical fluctuations about a flat two-dimensional surface, with a Hurst exponent of 1/2). The evolving
surface includes terrace-like features similar to those in
natural travertine deposits. Simulations with average
Fig. 11. Terraces generated by normal growth from an inclined rough surface with growth rates that depend on the surface slope and distance from the
upper boundary (at the right-hand-side in the figure).
E. Jettestuen et al. / Earth and Planetary Science Letters 249 (2006) 108–118
initial slope ranging from 25 ° to 65 ° (from |∇h| ≈ 0.47 to |
∇h| ≈ 2.14), keeping the initial random perturbation,
produced similar results.
The evolution of a horizontal cross section shown in
Fig. 12 illustrates how the initially rough surface
develops the smoothly curved shapes characteristic of
SNG. The model would also produce growth ‘microstructures’ similar to that shown in Figs. 8 and 9b, with
details depending on the frequency and location of new
nucleation events if height perturbations during growth
were added to the model. Growing travertine deposits
are continually perturbed by the deposition of debris,
damage by large animals and other events. Localized
decreases in surface height often result in increased
water depth and more turbulent flow, which increases
the local growth rate. Similarly, increases in surface
height often lead to reduced flow and reduced growth.
Consequently, small perturbations are rapidly healed
and have little impact on the large scale structure.
However, we have observed distinct erosion/dissolution
channels in freshly deposited travertine associated with
a very active hot spring at the Mammoth Hot Springs.
These channels appear to be a typical.
5. Summary
Simple surface normal growth of mineral aggregates
may produce surprisingly complex microstructures and
surface morphologies in systems with surface normal
growth, interrupted by roughening/nucleation events.
This is probably a very common situation during the
growth of layered mineral deposits close to the Earth's
surface where the growth velocity may fluctuate
strongly with time, for example as a response to
intermittent fluid flow. The SNG model provides an
accurate description of the complex morphology of the
Ca, Mg-carbonates precipitated on the walls of chimney-structures in the basaltic Sverrefjell volcano at
Svalbard, and it provides constrains of the temporal
distribution of nucleation events. We expect that the
same model will be able to reproduce a wide variety of
spheroidal and botryoidal growth morphologies.
Surface normal growth in systems with fluid flow may
produce step flow and terrace formation in situations where
the local mineral precipitation rate is strongly dependent on
the local slope. Thus the SNG model may also provide a
first order approximation to travertine terrace formation.
Acknowledgements
Discussion and suggestions by Jens Feder (PGP),
Øyvind Hammer (PGP) and Dag Dysthe (PGP) are grate-
117
fully acknowledged. Francois Renard (University of
Grenoble/PGP) carried out the initial analysis of the
scaling properties of the Ca,Mg-carbonate surface. We
thank the participants at the 2003 AMASE expedition to
Svalbard for their enthusiasm and company. Insightful
comments by an anonymous reviewer helped clarify the
paper. This study was funded by the Norwegian Research
Council through a Center of Excellence grant to PGP.
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