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Sedimentary Geology 321 (2015) 49–69
Contents lists available at ScienceDirect
Sedimentary Geology
journal homepage: www.elsevier.com/locate/sedgeo
Morphometric patterns in Modern carbonate platforms can be applied to
the ancient rock record: Similarities between Modern Alacranes Reef and
Upper Palaeozoic platforms of the Barents Sea
Sam Purkis a,⁎, Giulio Casini b, Dave Hunt b, Arnout Colpaert b
a
b
National Coral Reef Institute, Nova Southeastern University, Dania Beach, FL, USA
Carbonate Plays and Reservoirs, Technology Projects and Drilling, Statoil, ASA, Norway
a r t i c l e
i n f o
Article history:
Received 12 December 2014
Received in revised form 3 March 2015
Accepted 4 March 2015
Available online 11 March 2015
Editor: B. Jones
Keywords:
Depositional facies
Comparative sedimentology
GIS
Barents Sea
Alacranes Reef
Biotic self-organisation
a b s t r a c t
In recent years, considerable research has been undertaken in order to gain a better quantitative understanding
of morphometric patterns within modern carbonate depositional systems. The industrial application of the scaling/juxtaposition relationships derived from the Modern to subsurface Cenozoic carbonate reservoirs appears
relatively straightforward, given that many key biota are common to both. However, the direct application of
Modern sedimentary insight further back into the geologic rock record is more controversial, given the enormous
changes in the biota, climate, sea level, water chemistry and so on, that have taken place. To justify such an approach, we contend that similar morphometric patterns should be observed in both the Modern and ancient
data. In the Norwegian Barents Sea, numerous seismic surveys have imaged Upper Palaeozoic carbonate buildups
arranged in polygonal networks, or reticular patterns. These patterns are observed in both warm water photozoan
and cool water heterozoan carbonate stratigraphies, and are developed atop platforms founded on stable shelves,
in tectonically active settings and platforms developed over basinal evaporites. GIS mapping of multiple seismic
horizons allows the Palaeozoic reticulated morphology to be numerically compared to that mapped in Alacranes
Reef from QuickBird satellite imagery. QuickBird's metre-scale resolution allows identification of subtle crossplatform trends, such as windward-leeward differences in the packing density of ridge-and-pond complexes,
which can be correlated with the kilometre-scale patterning extracted in the Barents subsurface. Despite different controls and architecture, the patterning of reticular networks is statistically inseparable between the two
systems, once the metre-scale Modern dataset is down-sampled to seismic resolution. Whilst other controls
cannot unequivocally be ruled out, these results suggest that biotic self-organisation is a fundamental driver of
sedimentary patterns on carbonate platforms. To our knowledge, this is the first quantitative comparison of
morphometric patterns from the Modern and Palaeozoic that clearly reveals similar patterns of self-organisation.
For the depositional environments considered, the findings suggest that juxtaposition rules, facies proportions
and scaling relationships extracted from the Modern can successfully be applied to the ancient.
© 2015 Elsevier B.V. All rights reserved.
1. Introduction
Modern oceans, the classical place to link process to product in
sedimentology, indicate that carbonate platforms develop the same
environments of deposition and adopt comparable ranges in size and
shape as their ancient counterparts (Harris, 1985; Purdy and Bertram,
1993; Harris and Vlaswinkel, 2008; Yose et al., 2010; Jung and Aigner,
2012; Schlager and Purkis, 2013; Menier et al., 2014). Although the biological producers of carbonate have changed through geological time,
their affinity for sunlight and well-oxygenated water has not and nor
have the dominant environmental controls that sculpt platforms:
tides, winds, waves, currents, storms, and so on. Modern carbonate
⁎ Corresponding author. Tel.: +1 954 262 3647.
E-mail address: purkis@nova.edu (S. Purkis).
http://dx.doi.org/10.1016/j.sedgeo.2015.03.001
0037-0738/© 2015 Elsevier B.V. All rights reserved.
platform-tops display abundant detail in the arrangement of facies
belts and through a seismic facies comparison from a subsurface dataset
captured with extraordinary fidelity beneath the Barents Sea, this paper
explores whether the intricate patterning observed in the Modern is
morphologically comparable to an example from the Upper Palaeozoic.
Our work therefore trials the concept of “comparative sedimentology”,
whereby facies patterns are compared within and between geologic
periods, but over a greater time-span than is typically considered. Likely
because of the abundance of hermatypic corals, most comparative
studies contrast Mesozoic or younger rocks with the Modern (Riegl
and Purkis, 2009; Jung and Aigner, 2012; Purkis and Vlaswinkel, 2012;
Purkis et al., 2012a,b). Such comparisons are of interest as it is now
well-established that size and shape, i.e. so called “morphometric”, analysis is a useful tool for facies prediction in newly explored areas and for
conditioning geologic and reservoir models (Harris and Vlaswinkel,
50
S. Purkis et al. / Sedimentary Geology 321 (2015) 49–69
2008; Ruf et al., 2008; Harris et al., 2011; Jung and Aigner, 2012; Purkis
et al., 2012b; Harris et al., 2014).
The facies patterns compared and contrasted through time in this
paper are reticular reef ridges. Regardless of the reef architect, this
buildup morphology is persistent in both Modern and ancient carbonate
depositional environments. The aims of the work are to: First, compare
and contrast the reticular reef buildups mapped in the Modern and
Upper Palaeozoic. Second, to seek to understand reticular reef buildups
in process-terms. And third, to gain insight into the degree to which
patterns in Modern carbonate platforms can be applied to the ancient
rock record.
1.1. Upper Palaeozoic buildups of the Finnmark Platform and Norsel High
The Bashkirian to Artinskian architects that built ornate structures
atop the Finnmark Platform and Norsel High considered in this study
are not scleractinia, but rather photozoan Palaeoaplysina-phylloid
algae and younger heterozoan bryozoan-Tubiphytes (Stemmerik and
Worsley, 2005). These organisms are very different carbonate mound
builders to Modern corals, though this study will show them to organise
similarly at large-scale.
Palaeoaplysina is a long extinct thalloid organism originally thought
to be a filter-feeder such as a sponge or hydrozoan (Chuvashov, 1973;
Davies and Nassichuk, 1973), but more recently reconsidered as a photosynthetic ancestral coralline algae (Vachard and Kabanov, 2007;
Anderson and Beauchamp, 2010). A combination of these two lines of
evidence may be suggestive of an animal living as a filter-feeding organism that was later encrusted by the red algae Archaeolithophyllum
(Mamet et al., 1987). This interpretation is controversial, though.
The similarity of the canal system in Palaeoaplysina is particularly
striking when compared with the plate-shaped segments in the green
algae Halimeda which led Watkins and Wilson (1989) to propose
Palaeoaplysina to be an enormous carbonate-secreting green algae with
plate lengths in the approximate range of 40 cm to 100 cm (Skaug et al.,
1982; Kano, 1992). The internal precipitation of calcium carbonate has
been a common-life strategy for marine organisms since the Proterozoic.
Regardless of its true nature, Palaeoaplysina flourished along the
northern low palaeo-latitude Pangean shelf under high-frequency,
high-amplitude glacioeustatic sea-level fluctuations during the Upper
Palaeozoic which periodically submerged and subaerially exposed
the Barents Sea (Davies and Nassichuk, 1986; Stemmerik, 2000;
Stemmerik and Worsley, 2005). The climate at the time was tropical
to arid, as favoured by today's warm-water photozoan reef-builders.
Inspection of seismic data and borings on the Finnmark Platform
and beyond (e.g. Bruce and Toomey, 1993; Bugge et al., 1995;
Ehrenberg et al., 1998; Colpaert et al., 2007; Brocheray, 2010) indicates
Palaeoaplysina to have initially built separate, upwardly aggrading,
domal bioherms. As the system matured and vertical growth became
hampered by decreasing accommodation, the isolated buildups developed flat-tops and prograded laterally such that adjacent minor mounds
amalgamated into reticular networks of tabular ridges and ponds
surrounding a lagoon. The thickness of the buildups and associated ridges
is modest, typically varying from metres to a few tens of metres. But their
lateral extent can be considerable, with Palaeoaplysina wackestone and
boundstone bodies being traced over an area of ~10 km.
The Palaeoaplysina buildups occur within a series of stratigraphic
cycles. Each cycle of sediment deposition is separated by an exposure
surface. The primary control of cyclic development is considered
to have been changes in sea level driven by glacio-eustasy due to
the Late Carboniferous and Early Permian glaciation in southern
Gondwanaland (Chen et al., 2013; Hanken and Nielsen, 2013). The
buildups developed over a time interval of 35 Ma, but, despite their
longevity, their locations were relatively static (Elvebakk et al., 2002).
The Palaeoaplysina buildups contain muddy carbonates with a clotted
fabric between the fossil matrix (Colpaert et al., 2007; Hanken and
Nielsen, 2013). Separate Palaeoaplysina plates are common within the
buildups and associated deposits, together with a micritic matrix
between the plates which has been interpreted by Hanken and
Nielsen (2013) to be an early marine, possibly autochthonous, cement.
This interpretation is consistent with theories that microbial carbonate
production was crucial for the stabilisation of Phanerozoic reefs and
mounds (e.g. Grotzinger and Knoll, 1995; Weidlich, 2002).
Outcrop studies report that the uppermost part of some
Palaeoaplysina buildups contains Microcodium, root calcification products of terrestrial plants, indicating intermittent subaerial exposure
and vegetation cover during lowstand, probably caused by eustatic
sea-level changes (which were on the order of 50 m amplitude) and/
or local tectonics (Hanken and Nielsen, 2013). It appears that the
Palaeoaplysina-encircled lagoons, characterised by a fine-grained bedded dolostone, became cut off from normal seawater outside the
buildups during the low stands and in dry climates, evaporation caused
hypersalinity. For this reason, the stratigraphy of the algal buildups often
alternates with restricted evaporites (gypsum) with low faunal diversity. The expression of such intervals is an evaporite-dolomitic mudstone
facies. Palaeoaplysina abruptly disappeared during the Late Sakmarian,
creating a huge change in the nature of buildups thereafter (Anderson
and Beauchamp, 2010).
The Artinskian times of the considered stratigraphy are characterised
by cooler water heterozoan biota (Larsen et al., 2002). The succession is
dominated by bioclastic packstones and grainstones in the proximal
parts of the platform (Ehrenberg et al., 1998), whereas the more distal
parts of the slope to basin are characterised by deposition of large
bryozoan-Tubiphytes buildup complexes surrounded by fine-grained
carbonates and shale (Blendinger et al., 1997; Samuelsberg et al.,
2003; Colpaert et al., 2007; Rafaelsen et al., 2008). Beauchamp and
Olchowy (2003) describe the internal configuration of the build-up
based on outcrop work in the Canadian Arctic. Bryozoan, sponges and
Tubiphytes are found exclusively in the core and inner flanks of the
mound, where fusulinacians and phylloid algae dominate the outer
flanks. Intermound and basinal areas are dominated by more finegrained and thinly bedded limestones, together with carbonate breccias
that originated from collapse of the unstable flanks of the mounds.
1.2. Modern buildups of Alacranes Reef
The Modern facies distributions of Alacranes Reef have been well
studied. Folk (1967) reports the platform-margin reefs to be built from
the typical Atlantic scleractinian coral assemblage of Porites, Montastraea,
Diploria, Millepora and Acropora, which is in agreement with the more
recent surveys conducted by Macintyre et al. (1977) and Bello-Pineda
et al. (2005). The reticulated reefal buildups in the platform-interior
were described by Folk (1967) to be primarily composed of interlocking
Acropora branches heavily encrusted by coralline algae, as is typical
for this morphology (see, for example, Fig. 1A of Schlager and
Purkis, 2015). The shallow lagoon floor of Alacranes Reef is composed of
biogenic sands composed primarily of Halimeda segments admixed with
faecal pellets (Hoskin, 1963, 1966). In proximity to islands and reefs,
Kornicker et al. (1959) report that an increased proportion of coral rubble
serves to coarsen the sediment. The authors also observed meadows of
Sargassum, Thalassia and Halimeda to abound in the shallow lagoon
which serve to bind the seabed. As would be anticipated given their abundance, Halimeda segments are also the dominant contributor to the numerous sand cays on the platform-top (Kornicker and Boyd, 1962; Folk,
1967). As reported by Kornicker et al. (1959), deeper areas in the lagoon
consist of silt-sized calcium carbonate flour containing aragonite needles.
1.3. Recent coral reefs are imperfect analogues to Upper Palaeozoic
Palaeoaplysina and bryozoan-Tubiphytes buildups — but useful parallels
exist
Recognising Palaeoaplysina as both a carbonate platform- and islandforming organism strengthens the parallel to Cenozoic scleractinian reefs.
S. Purkis et al. / Sedimentary Geology 321 (2015) 49–69
How the Palaeozoic buildups grew to maximise their occupancy of the
platform-top once accommodation became limited is also strikingly
similar to that observed in Holocene lagoons. Like Modern coral reefs,
the Palaeoaplysina mounds capitalised on possessing multiple growth
centres that amalgamated into polygonal networks of interconnected
patch reefs at the point that the aggradation of individual buildups
became hampered by sea level.
Whilst their morphology and hyperbolic occupancy of space, in
particular, tempt comparisons between the ancient analogue and the
Holocene, there are important differences. For instance, outcrop studies,
such as those reviewed by Hanken and Nielsen (2013) in Spitsbergen,
reveal that the Palaeoaplysina buildups contain sparse fauna as
compared with Recent reefs. The authors note that beyond the large
plate-shaped Palaeoaplysina, the carbonate buildups from the Upper
Palaeozoic were constructed by relatively small organisms such as
calcareous algae, Tubiphytes, fusulinid foraminifera and bryozoans. By
contrast, Holocene reefs are not by any means made of corals alone
and many other calcareous organisms, both animal and plant, may
contribute more to the volume of a reef than do the corals. This said,
Holocene reefs constructed by mono-specific coral associations exist
(Keck et al., 2005), but rarely so. As evidenced by its colonial growth
into bioherms, the life strategy of the photozoan Palaeoaplysina “alga”
was, however, similar to scleractinia, as like stony corals, it required
abundant sunlight, access to clean ocean water into which to discard
its metabolites and if a filter feeder, to feed also. For these reasons,
Palaeoaplysina mounds could conceivably have “self-organised” into
patterns that optimise the organism's demands for light and clean
water, whilst adopting an arrangement that avoids overcrowding and
competition, whilst maximising resistance to erosion, in much the
same way as reported for Recent coral reefs (Blakeway, 2000; Schlager
and Purkis, 2013; Blakeway and Hamblin, 2014; Schlager and Purkis,
2015).
Unlike the photozoan Palaeoaplysina that proceeded them, because
the heterozoan bryozoan-Tubiphytes were situated in deeper water,
they did not depend on light for nourishment. However, stark similarities remain in the life-strategy of the bryozoan assemblage and that of
the photozoan Palaeoaplysina and stony corals. For instance, all three
organisms are colonial and share the same requirement of access to
clean ocean water for feeding and removal of harmful metabolites.
Furthermore, problems associated with overcrowding and smothering
are equally prominent for the heterozoan community as for the
photozoan. Such competing demands for resources and shelter generate
elaborate arrangements of organisms, the most widely reported of
which are reticular and labyrinthic patterns, such as documented for
the accumulation of filter-feeding bivalves (Rietkerk et al., 2004; Van de
Koppel et al., 2005; Liu et al., 2012) and tree cover in arid ecosystems
(Rietkerk et al., 2004). Carbonate shelves and platforms also commonly
exhibit networks of coral-sediment ridges, informally called “mesh
reefs” (Stoddart, 1969), “reticulate reefs” (Hopley, 1982; Guilcher, 1988;
Purkis et al., 2010; Schlager and Purkis, 2015), or “honeycomb ridges”
(Purdy and Bertram, 1993; Macintyre et al., 2000); a reef architecture
modelled in terms of its biological underpinning by Blakeway (2000)
and Blakeway and Hamblin (2014).
1.4. Reticular reefs in the Recent and rock record
Polygonal mesh-like topographies on the seabed of the Holocene
Arabian Gulf (Shinn, 1969), are generated by the expansion of rapidly
cementing seafloor grainstone. Here, the expansion of lithifying subsea
sediment produces bending, folding and overthrusting of hardground
layers, termed “tepees”, which, because they are topographically higher
than the seabed, attract the settlement of corals that in turn accentuate
the antecedent structures (Purkis and Riegl, 2005). Whilst this mechanism might plausibly generate reticular reefs in the Arabian Gulf, it is
not easily transferred to other settings lacking the high salinity and
summer temperatures that leads the seawaters of the Gulf to become
51
super-saturated with calcium carbonate (Purkis et al., 2010). It is the
process of CaCO3 enrichment that allows the accumulation of metastable minerals in the Gulf waters to drive the widespread and rapid
lithification of seabed grainstones through abiotic precipitation of
aragonite cements (Purkis et al., 2011).
The origin of polygonal patterns has more commonly been discussed
as part of the broader issue of the origin of atolls, where the antecedent
karst hypothesis has a long tradition (Hoffmeister and Ladd, 1945;
MacNeil, 1954; Purkis et al., 2010; Gischler et al., 2013). Indeed, it has
been demonstrated repeatedly on both regional and local scales that
Pleistocene karst relief provided antecedent topography for Holocene
reef formation (e.g., Purdy, 1974a,b; Halley et al., 1977; Shinn et al.,
1977; Shinn, 1980; Gischler and Hudson, 1998, 2004; Purdy and
Winterer, 2006). More recent treatment of the patterns of reticulate
ridges of reefs and sediment in Holocene lagoons has suggested biotic
self-organisation (Blakeway, 2000; Blakeway and Hamblin, 2014;
Schlager and Purkis, 2015), though they may develop also as emergent
patterns by interaction of air or water with loose sediment (Paola et al.,
2009). As reviewed by Schlager and Purkis (2015), in a number of cases,
karst can be excluded as controlling the pattern because drilling and
seismic traverses, or a combination of the two, reveal Holocene reticulated reefs to be founded on a flat Pleistocene abrasion surface (Fig. 1).
On Middleton Reef, for example, seismic surveys by Woodroffe et al.
(2004, 255–257 and their Fig. 7) indicate some relief of the Pleistocene
surface. However, the data also show that only few Holocene reefs grew
on Pleistocene topographic highs. Most Holocene patch reefs, particularly the younger ones, show no relationship with the Pleistocene relief.
Menier et al. (2014) extend the record of scleractinian reticular buildups
back to the Miocene and are the first group, to our knowledge, to recognise the pattern in seismic. Alacranes Reef, the focus of this study, is
an exemplary Modern example of platform-interior reticular buildups
(Fig. 2).
Whilst karst has been discussed as a possible mechanism to explain
the labyrinthic patterns of Palaeoaplysina buildups, outcrop examples,
in which the presence of in situ Microcodium evidence subaerial exposure, have only flat or slightly undulating surfaces. This lack of positive
karst forms indicates, according to Hanken and Nielsen (2013), selective
levelling of topographical highs due to rapid erosion in the tidal zone by
a combination of bioerosion and wave-induced erosion. Whilst rapid
erosion might preserve negative karst forms after the transgression,
their typical signatures, such as solution-enlarged fissures, cracks and
caves, have not been recorded in the Upper Palaeozoic outcrops.
Support for depositional control on the reticular patterning of the
Palaeoaplysina reefs therefore outweighs karst influence, as has been
proposed to be the case for Recent reticulated reefs (Blakeway, 2000;
Blakeway and Hamblin, 2014; Schlager and Purkis, 2015).
Artinskian bryozoan buildups sitting directly on the slope of the
antecedent warmer-water carbonate platform do not show any evidence for pre-existing karst and neither is their evidence of antecedent
topography serving as a preferred location for mound growth. Colpaert
et al. (2011) reveal from seismic that the growth pattern history of such
a reticulated network starts with individual mounds, progressively
amalgamating into ridges and eventually forming polygonal systems.
Given that convincing evidence exists to suggest that corals can
construct reticulated ridges by biological means alone, it is reasonable
to question whether both Palaeoaplysina and bryozoan-Tubiphytes,
which clearly occupied a similar ecological niche to modern scleractinia,
could do the same. This question forms the basis for this paper.
1.5. Self-organisation in patchy ecosystems
Self-organisation is a key tenet to this paper and therefore a brief
description is warranted. The commonly accepted description of a
self-organised process is one where some form of global order or coordination arises out of the local interactions between the components of
an initially disordered system. Beyond the Earth Sciences, the process
52
S. Purkis et al. / Sedimentary Geology 321 (2015) 49–69
Fig. 1. Reticular coral buildups in the interiors of Holocene carbonate platforms demonstrably founded on flat Pleistocene surfaces (after Schlager and Purkis, 2015; modified). (A) Mataiva
Atoll in the central Pacific where the stratigraphy is well known because mineable phosphorite underlies the Holocene buildups. The phosphorite in Mataiva caps a Pleistocene karst surface and provides a smooth substrate for the Holocene reticulate (Roe and Burnett, 1985; Rossfelder, 1990; Trichet and Fikri, 1997). (B) The “maze district” of the Houtman–Abrolhos group
(NW Australia) where drilling and seismic surveying have shown the foundation of the Holocene reticulate reefs to be a flat abrasion surface on Pleistocene limestone (Collins et al., 1993,
1996; Wyrwoll et al., 2006), as is also the case for Heron Island, Great Barrier Reef, Australia (Walbran, 1994; Smith et al., 1998) (C). Broken lines depict traverses where subsurface topography has been constrained by seismic or borings.
can be found in fields as diverse as economics, sociology, medicine and
technology. A visual hallmark of self-organised patchiness is coherent
striped, banded and labyrinthine patterns that spontaneously form in
both biotic and abiotic systems (Rodriguez-Iturbe and Rinaldo, 1997;
Snover and Commito, 1998; Klausmeier, 1999; Rietkerk et al., 2004;
van de Koppel et al., 2005; Fagherazzi, 2008; Paola et al., 2009; Tice
et al., 2011; to list but a few), including geochemical self-patterning in
rocks (Merino et al., 1983; Wang and Merino, 1992; Ortoleva, 1994;
Budd et al., 2006).
The trigger for self-organisation might be a random fluctuation
which is amplified and reinforced by positive feedbacks within the
system. In self-organised terrestrial ecosystems, Rietkerk et al. (2004)
identify sudden catastrophic changes in their structure and functioning
as a trigger which is reinforced by positive feedback between consumers (e.g. plants) and limited resources (e.g. water, nutrients). Whilst
terrestrial and marine ecosystems function differently, the salient point
here is that self-organised patchiness can arise spontaneously out of the
fine-scale interactions between consumers and resources. In the case of
self-organised reefs, the reef-builder is the consumer and the resource is
well-oxygenated ocean water. Self-organised complexity is autogenic in
its purest sense because it arises out of processes that are wholly internal to the system. Note, however, that in the course of this paper we will
pitch reduced accommodation as an initiator for self-organised reef
buildups and therefore the trigger might be allogenic. Because the
controls on the patterning of a self-organised system are wholly
decentralised or distributed over all the components of the system,
the resulting structures are typically very robust and able to self-repair
substantial damage or perturbations. The swift reestablishment of the
characteristic channelled tidal flat morphology in Andros after the
2001 passage of Hurricane Michelle, as reported by Rankey et al.
(2004), is a good example of the robustness of an autogenic system
with decentralised controls on sediment accumulation. The relevance of self-organisation in the rock record is that it can generate
persistent and predictable patterns within ranges of scale. This
paper will posit that similarly structured reticular reef buildups
atop carbonate platforms for the last 300 MY are another example
of the robustness and persistence of self-organisation. Even further
back in time, Archean microbial mat communities have also been
suggested to display the hallmarks of biotic self-organisation (Tice
et al., 2011).
2. Focus areas
The study considered two focus areas. The first, from the subsurface,
is Upper Palaeozoic in age and situated beneath the present-day Norwegian Barents Sea (Fig. 3A). Two seismic volumes are considered, the first,
the Norsel High (seismic survey ST0828), from which two time slices
were extracted for analysis. The second is the Finnmark Platform (seismic survey ST9802) and from this volume a third time slice was extracted from a flattened seismic volume to correct for the later tilting of the
strata imposed by regional tectonics. The three seismic slices were selected on the basis of the prominence of reticular patterning (Fig. 3B).
Neither of the three slices captures the full lateral extent of the reticular
patterning and all are either truncated by the spatial limits of the seismic acquisition (slices 2672 and 2868, Norsel High) or compromised
by the fidelity of the seismic data (as per slice 2028 extracted from the
S. Purkis et al. / Sedimentary Geology 321 (2015) 49–69
53
Fig. 2. Alacranes Reef as imaged by the QuickBird satellite (©DigitalGlobe, 2010). Deep water is black in this RGB colour composite, shoal-water carbonate sands are beige to bright white
and the reefal buildups are tan in colour. The platform-interior provides a textbook example of reticular coral buildups. (For interpretation of the references to colour in this figure legend,
the reader is referred to the web version of this article.)
Finnmark Platform). We therefore consider multiple horizons spread
between two volumes so as to capture the breadth in morphological
variation for the reticular Palaeozoic networks both for photozoan
Palaeoaplysina buildups (slice 2868 Norsel High) and heterozoan bryozoan buildups (slice 2672 Norsel High and slice 2028 Finnmark
Platform).
From the Recent we analyse Alacranes Reef, an isolated carbonate
platform situated atop the Campeche Bank, Mexico (Fig. 3C). The
Campeche Bank is a submerged extension of a low-lying carbonate
limestone plateau that forms the Yucatan Peninsula. Alacranes is the largest and easternmost reef complex on the Campeche Bank, rising above
the bank from depths of 50 m to form a shallow-water platform
(250 km2) that has been termed a “shelf atoll” (Kornicker and Boyd,
1962; Macintyre et al., 1977). Alacranes' sub-oval outline – approximately
22 km long and 11 km wide – encloses a shallow lagoon with a maximum
depth of 15 m (Liceaga-Correa and Euan-Avila, 2002). Detailed facies
work to refine understanding of this system is ongoing (Rankey and
Garza-Pérez, personal communication). Within the lagoon is an extensive
maze of reticular patch-reef buildups, as can be resolved by QuickBird
satellite imagery (Fig. 3D).
3. Methods
3.1. Seismic facies analysis of the Palaeozoic platforms
The Upper Palaeozoic carbonate buildups of the Norwegian
Barents Sea have been extensively examined with 3-D seismic data
(Samuelsberg and Pickard, 1999; Elvebakk et al., 2002; Samuelsberg
et al., 2003; Colpaert et al., 2007; Rafaelsen et al., 2008; Brocheray,
2010). Understanding of the stratigraphic evolution of these carbonate
successions is therefore relatively mature. Further, it is clear that the
best seismic expression of the low-relief Palaeoaplysina and high-relief
bryozoan buildup complexes is obtained when they are imaged with
RGB-blended colour schemes in spectral decomposition volumes (e.g.
Colpaert et al., 2007, 2011). Similar, elongated-to-polygonal, features
were distinguished in all three of the considered seismic slices, despite
the fact that they encompass buildups constructed by both photozoan
and heterozoan communities. Well-control on both the Norsel High
and Finnmark Platform allowed calibration of the geomorphic features
on the RGB blends with respective litho-facies. On the Norsel High,
the well is positioned in the lower section on the border between a
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S. Purkis et al. / Sedimentary Geology 321 (2015) 49–69
Fig. 3. (A) Location of the two seismic volumes considered. The first from the Norsel High (survey ST0828) and the second from the Finnmark Platform (ST9802), Norwegian Barents Sea.
From the two volumes, three seismic time slices were selected for analysis. (B) These slices are displayed with RGB blended colour schemes in flattened frequency decomposition cubes.
(C) Shows the location of the Recent analogue, Alacranes Reef, situated atop the Campeche Bank, offshore the Yucatan Peninsula, Mexico. (D) Is an enhanced RGB colour composite of
Alacranes Reef as imaged by the QuickBird satellite (©DigitalGlobe, 2010). The seismic horizons and satellite image are plotted to scale. All host reticular reefs. (For interpretation of
the references to colour in this figure legend, the reader is referred to the web version of this article.)
ridge and an inter-ridge pond. Penetrating the stratigraphy of both
features, this well reveals the succession to be composed of sulphate
evaporites and dolomitic mudstone which alternate with Tubiphytesalgal buildup facies (slice 2868) (Colpaert et al., 2011). In the younger
sequence, the well penetrates a 150 m stacked bryozoan buildup
(slice 2672). It is important to note that the reticular patterning is subtle
and could easily be overlooked in the absence of advanced seismic attribute analysis, such as employed for these volumes by Elvebakk et al.
(2002) and Colpaert et al. (2007). Recognise too that the lateral resolution of the seismic horizons is on the order of 50 m, which is insufficient
to capture reticular morphology at length-scales of less than 10 m, such
as observed on the platform-top of the Recent analogue. The seismic
data were acquired with an average frequency of 20 Hz and the
measured range in velocity for the carbonates was 4500–5000 m/s.
Vertical resolution of seismic is up to 1/4 of the wavelength, which
yields a vertical seismic resolution for the considered volumes of 56 m
to 62 m.
Seismic time slices in which the best resolved polygonal patterns
were observed were extracted as RGB slices from the decomposed volumes and exported as 11-bit GeoTIFFs into a Geographic Information
System (GIS). Following the protocol of Purkis et al. (2014a) and
Harris et al. (2014), the slices were analysed using eCognition (v. 8.9,
Trimble Inc.). By applying textural and edge-detection routines, refined
by manual-editing, the polygonal buildup “ridges” and intra-buildup
“ponds” were mapped and exported as GIS vector files for further
analysis (Fig. 4).
3.2. Remote sensing Alacranes Reef
Whilst the fidelity of the seismic gathered for this study was excellent, a great deal more detail could be captured from the QuickBird
satellite imagery of Alacranes Reef which was acquired 17th August,
2010 (DigitalGlobe Inc.). With a spatial resolution of 2.4 m in the multispectral (colour) channels, QuickBird equals the highest resolution of
any commercially available Earth-observation imagery. The sensor
also carries a panchromatic (grayscale) channel with a spatial resolution
of 1 m. Through a process termed “pan-sharpening” (Laben and Brower,
1998), the spectral resolution of the colour channels can be resampled
to the 1 m spatial resolution of the panchromatic to yield a colour
dataset with 1 m pixels, as was conducted for this study. This enhanced
spatial resolution was sufficient to capture the fine-scale ornamentations of even the narrowest reticulate reef-ridges, such as the transition
between the coralgal frameworks and their associated debris aprons
(Fig. 5A). For consistency, the satellite data were mapped using the
same workflow as applied to the seismic horizons with the exception
that emergent islands and cays (which are small and rare) were first
masked out of the image using the infrared channel of the satellite
that is fully absorbed by water, but reflected strongly by terrestrial
targets. As per the treatment of the seismic horizons, facies mapping
then proceeded using eCognition and manual editing (Fig. 5B). The
platform was partitioned into the platform-exterior and interior, for
which eight facies classes were used to characterise the former and
five for the latter. Table 1 provides a detailed biotic and sedimentological description of each facies class. The evolving map was crosschecked against the seabed observations of Kornicker et al. (1959),
Kornicker and Boyd (1962), Hoskin (1963, 1966), Folk (1967), and
Macintyre et al. (1977) and in particular, the exhaustive platformtop audit provided by Bello-Pineda et al. (2005). Since the reticular
coral reef ridges have a pronounced topographic signature, a digital
elevation model (DEM) was extracted from the QuickBird imagery
following the ratio–algorithm method of Stumpf et al. (2003). This
empirical approach for extracting depth from satellite data capitalises on the differential attenuation of blue and green light by water.
Calibration for the spectrally-derived bathymetry was provided by
S. Purkis et al. / Sedimentary Geology 321 (2015) 49–69
55
Fig. 4. Interpreted seismic slices from the Norsel High (A and B) and Finnmark Platform (C), Norwegian Barents Sea. Horizons cast as RGB blended colour schemes in spectral decomposition volumes to emphasise reticular patterning of ridges and ponds. These maps form the basis for morphometric analysis. (For interpretation of the references to colour in this figure
legend, the reader is referred to the web version of this article.)
the extensive set of depth soundings for the platform-top published
by Liceaga-Correa and Euan-Avila (2002). The extracted DEM, which
captures seabed morphology down to a water depth of 20 m, was
used to verify the interpretation of the reticular ridges and associated inter-ridge ponds that had been delineated on the basis of the
spectral data (Fig. 5C).
The subsurface data, deemed to have an effective spatial resolution
of ~ 50 m, are an order of magnitude coarser than the 1 m QuickBird
image of Alacranes Reef. This mismatch in fidelity complicates a direct
comparison between the buildups mapped from the Palaeozoic horizons versus the Recent analogue. Whilst the full-resolution QuickBird
data are valuable in that they reveal the intricacies of the polygonal
reef morphology across all length-scales that it inhabits, we also strived
to produce a satellite realisation of the Alacranes Reef platform-top as is
might be resolved in seismic. To this end, in the same vein as Benson and
Bachtel (2006), the QuickBird imagery and associated DEM were downsampled from their 1 m native resolution to 50 m pixels to equal the resolution of the subsurface horizons (Fig. 5D). The mapping and validation
exercise was then repeated in its entirety to yield a second satellite map,
but tendered at “seismic” resolution (Fig. 5E). An alternative means to
this end would have been to simply down-sample the original 1 m
map product to 50 m, but this action would assume a linear relationship
between the two resolutions. An assumption for which we have no
support and neither is one suggested in the literature. By re-mapping
without consideration of the high-resolution interpretation of the
QuickBird data, we believe that we have generated a fairer representation of the Alacranes Reef ridge-and-pond morphology as it would be
resolved in the lithosphere from seismic. As for the subsurface facies
interpretations, the Alacranes Reef map was exported as GIS vector
files for further analysis.
3.3. Morphometric analysis of the Palaeozoic buildups and the modern
analogue
The motivation behind this paper is to expand on the work of
Colpaert et al. (2011) who conducted a geomorphic analysis of the
development of the reticular Palaeozoic Palaeoaplysina and bryozoanTubiphytes buildups through time. Although very different biota are
identified, recticular patterns were revealed for both photozoan carbonate growth of Bashkirian to Sakmarian age and heterozoan buildup
growth during Artinskian age.
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S. Purkis et al. / Sedimentary Geology 321 (2015) 49–69
Fig. 5. Facies and depth prediction of the Holocene Alacranes Reef platform-top. (A) Full resolution true-colour QuickBird satellite imagery (©DigitalGlobe, 2010). Pixel size is 1 m × 1 m.
(B) Interpretation of facies for the full resolution imagery called upon a scheme of 13 classes distributed between the platform interior and exterior (Table 1). A digital elevation model was
derived from the satellite imagery to aid facies delineation (C). (D) Is the same dataset as (A), but down-sampled to the effective resolution of the Barents Sea seismic horizons
(50 m pixels). The seismic resolution image was re-mapped to capture two classes only: ridges and ponds (E). Different resolutions of these products derived from the QuickBird imagery
highlighted in the five magnifications whose positions are denoted by red rectangles. (For interpretation of the references to colour in this figure legend, the reader is referred to the web
version of this article.)
The morphometric analysis conducted by Colpaert et al. (2011)
revealed subtle variations in the geomorphic growth of buildups dependent on palaeoenvironment which could be broadly related to the
availability of accommodation. For instance, the authors report the
form of the polygonal patterning to vary dependent on position on the
platform-top, slope, or proximity to active fault blocks (faulting seems
to have exerted principal control on the palaeo-relief of the platformtop). The authors also suggest that isolated Palaeoaplysina patch reefs
develop preferentially in shallow-water environments whereas areas
with higher accommodation favour the formation of more continuous ridges. The complexity of the buildup networks was shown to
increase through time. As presented by Colpaert et al. (2011), understanding of the two considered volumes has increased recently because of new well-control which allows for a better calibrated
seismic facies analysis.
The GIS facies maps of the Palaeozoic and Modern buildups were
analysed in two ways. The polygons describing the ridges and ponds
of the polygonal buildup complexes were considered first. The area of
the ridges and ponds were tallied to yield size–frequency distributions
(Figs. 6 and 7). Next, the map vectors for the platform-top buildups
were gridded into binary raster images with zero values used to signify
inter-ridge ponds and a value of “1” to code the ridges. The binary
images were produced at the resolution of the underlying data (i.e.
1 m for the QuickBird faces maps, 50 m for the QB facies maps at seismic
resolution and 50 m for the subsurface horizons). The binary rasters
were used as the basis for quantification of the width of the components
of the ridge-and-pond complexes, lacunarity assessment, and analysed
for the spatial periodicity of ridges and ponds using a Fast Fourier
Transform (FFT). All analyses were implemented using code written in
Matlab (MathWorks, v. 2013a).
3.3.1. Ridge width maps
For each interpreted image scene, “width maps” were generated
(e.g. Edmonds et al., 2011; Purkis et al., 2012a, 2014b). These plots use
colour to describe the minimum distance from any point atop each
buildup to the periphery of the nearest inter-ridge pond. This step was
accomplished via a Euclidean distance transform computed on the binary images which assigns a number to each pixel that is the distance
between that pixel and the nearest nonzero pixel. This number is equivalent to the minimum distance to most proximal inter-ridge pond. The
purpose of generating the width maps is to highlight gradients in the
plan-form extents of the buildups across the Modern (Fig. 8A) and
Palaeozoic platform-tops (Fig. 9). Alacranes, for which contemporary
wind and current data could be assembled, was used to develop an understanding of the variation in the development of reticular ridges along
a hydrodynamic gradient. To this end, a map of long-term (2006
S. Purkis et al. / Sedimentary Geology 321 (2015) 49–69
57
Table 1
Description of the environments of deposition mapped atop Alacranes Reef.
Platform exterior
Platform-top
Coral framework
Class description
Coral frameworks, mostly of low relief, interspersed
with rubble and detritus
Platform interior
Ponds
Shallow ponds
Reef flat
A flat expanse of dead reef rock which is partly
or entirely dry at low tide; shallow pools, potholes,
gullies. Colonised by sparse stunted stony corals,
calcareous and turfing algae
Deep ponds
Sand
Unconsolidated sand sheets, elongate perpendicular
to hydrodynamic gradient in high-energy areas.
Situated platform-ward of the reef flat and likely
colonised by sparse macro-algae and seagrass
Well-sorted skeletal sand shoals with defined
crests. Likely unvegetated
Confined to the western margin of the platform.
Planation terraces of carbonate hardbottom, likely
colonised by sparse stony corals and a dense
gorgonians-sponge assemblage. Occasional macro-algae
An assemblage of mixed seagrass (Thalassia testudinum,
Syringodium filiforme, etc) and macro-algae colonising
unconsolidated sand sheets
Characteristic of the eastern (windward) platform
margin. Supratidal near-shore ramparts as well as
back-reef, reef-flat, and shallow fore-reef rubble
accumulations. Composed mainly of massive corals
ripped from the fore-reef during storm events,
transported across the reef-flat
Sand cay islands, all located on the northwest-trending
bank-barrier reef leeward of the main reef complex.
Average elevation of islands is 1.5 m above mean sea
level. Composition is uncemented sand and gravel
Debris aprons
Sand shoals
Hardground
Seagrass
Storm deposits
Terrestrial
through 2010) monthly mean circulation in the southern Gulf of Mexico
was modified from Sanvicente-Añorve et al. (2014) (Fig. 8B) and wind
data for Alacranes Reef were compiled from QuikSCAT satellite observations for the period Jan. 2013 through Jan. 2014 and assembled as a
wind rose (Fig. 8C).
3.3.2. Lacunarity analysis
The same binary images which formed the basis for the width maps
were used for lacunarity analysis. This technique was first proposed by
Mandelbrot (1983) and since has been used to quantify geologic structures and to recognise cyclic patterns in the sedimentary record
(Plotnick et al., 1996; Rankey, 2002; Perlmutter and Plotnick, 2003).
As described by Tolle et al. (2008), lacunarity is a measure of how data
fills space. It complements fractal dimension, which measures how
much space is filled. In simple terms, lacunarity can be thought as a
measure of ‘gappiness’ or ‘hole-iness’ of a ‘set’. For our purposes, the
set is a binary image from one of the study sites and the gaps are the
ponds separating the buildup ridges. In the binary image, the ponds
are designated by zero-valued pixels and the ridges by ones. Lacunarity
was used to reveal the extent to which the pattern of ridges and ponds
resolved in satellite imagery and seismic is regular, random, clustered or
fractal, and how the patterning varies between and within sites. Two
synthetic sets, one random, the other a mathematical fractal, were
used as end-members to the real-world data.
Fractal patterns are self-similar, meaning that the pattern exactly (in
the strict mathematical sense), or approximately, repeats across scale
(Halley et al., 2004). The pattern adopted by the reticulated pattern of
ridges and ponds is a good candidate for a self-similar fractal. In particular, inspection of the satellite imagery reveals a hierarchical arrangement of ridges and ponds whereby individual patch reefs coalesce to
ridges of only a few metres breadth, which in turn fuse to larger
complexes of ponds and ridges that themselves form the building components for the largest arrangements of the polygonal morphology.
Class description
Ponded depressions rimmed by coral ridges
within reticular reef complex. Sufficiently
shallow for seabed to be visible in the satellite
imagery. Likely coral-dominated
Ponded depressions rimmed by ridges within reticular
reef complex. Defined as ‘deep’ once seafloor cannot be
resolved in the satellite imagery. Likely dominated by
unconsolidated sand colonised by macro-algae and sparse
seagrass, occasional corals
Flanks of ridges sloping into ponds. Likely
dominated by unconsolidated sands, rubble,
stabilised by macro-algae. Occasional corals
Sills
Ridges — coral
Shallow ridges separating ponds within the
reticular reef complex. Likely dominated by
dead coral framework with occasional live colonies
Ridges — sediment
Shallow ridges separating ponds within the reticular
reef complex. Composed of unconsolidated sand, likely
stabilised by macro-algae, coral rubble and detritus
Schlager and Purkis (2013) similarly frame the propensity for reefs to
adopt a “bucket” structure — stiff reef rims holding a pile of loose
sediment — a pattern that repeats from the scale of patch reefs of tens
of metres to archipelagos of hundreds of kilometres in diameter. For
the analysis we use a gliding-box lacunarity algorithm based on the
ideas presented in Tolle et al. (2008) which is in the same vein, but an
evolution over, that described by Plotnick et al. (1993) and employed
by Rankey (2002). The premise of this strategy is similar to that of
box-counting, another means of calculating fractal dimension, which
has been used to identify self-similarity in ancient (Schlager, 2004)
and Modern carbonate systems (Purkis et al., 2005, 2007; Purkis and
Kohler, 2008). Lacunarity data are displayed as plots of lacunarity vs.
area, both on a log scale. Fractals should have a significant portion of linear slope in such plots. Random sets, by contrast, show upward-concave
trend lines that slowly approach the coordinate axis (Fig. 10).
3.3.3. Fast Fourier Transform
The spacing between buildup ridges in the Palaeozoic and Recent
landscapes was analysed by FFT along strike-orientated profiles
(Fig. 11). This technique is useful in identifying whether dominant
periodicities exist in the alternation of ridges and ponds, as would be
expected if the morphology is constructed as a self-similar hierarchy,
or whether the reticular structure is random. In this respect, the use of
FFT compliments the lacunarity analysis. Under the same guise, Harris
et al. (2011) employed FFT to compare and contrast rhythms in the
spacing of high-energy sand bodies on the margins of the Great Bahama
Bank. For this study, the analysis was based upon the binary representations of the ridge-and-pond landscapes and so as to ensure representative sampling, periodicities were extracted from ten replicate transects
for each site cast on a strike orientation across the platform-top. The
FFT results were presented as semi-log plots of length-scale versus
power. Dominant periodicities identify as pronounced peaks in the
plots.
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S. Purkis et al. / Sedimentary Geology 321 (2015) 49–69
Fig. 6. (A) Cumulative distribution function for the components of the ridge-and-pond morphology for the platform-interior of Alacranes Reef interpreted from full-resolution QuickBird
satellite imagery. X-axis — log area of the distinct components of the morphology (ridges constructed of coral frameworks, the debris aprons that onlap the ridges, and the ponds); y-axis —
log probability of encounter P(X ≥ x). Straight-line trend for ridge sizes (frameworks and debris aprons) 102.3–105.5 m2 indicates power-law relationships, upheld by the statistical test of
Clauset et al. (2009). For power laws, abundance can always be obtained from area by a constant factor α (quoted for each trend) and for this reason, the distributions are termed to be scale
invariant. As for the ridges, ponds are power law for sizes of 104.0–107.7 m2, with the exception of a handful of examples with areas in the range of 106 m2 (highlighted in red). (B) This
departure from the power-law trend at a scale of 106 m2 (1 km2) corresponds to ponds associated with conspicuously wide ridges that cross-cut the platform-top and could be interpreted
as lineaments (broken lines). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
4. Results
Inspection and interpretation of the three seismic horizons show the
distribution of ridges and ponds to vary along dip and strike within each
study site, but also to vary between the three sites (Fig. 4). For instance,
seismic slice 2672 from the Norsel High taken through heterozoan carbonates, shows the most laterally extensive example of the reticular
patterning, has smaller ponds and thinner ridges than reported by
slice 2868 extracted through a photozoan carbonate level. Slice 2028
from the Finnmark Platform is similar in morphology to Norsel slice
2672 and taken through a similar bryozoan buildup system, but the
shapes of the ponds are more convoluted which, in turn, translates to
high complexity for the inter-pond ridges. These differences, and others,
will be explored using width maps in an upcoming section.
Supported by substantial on-ground knowledge from the literature
for Alacranes Reef and because of the high spatial resolution of
QuickBird, the mapping of the platform-top for the Recent analogue
could be conducted at higher fidelity than was feasible in the
subsurface. This advantage offers the opportunity to explore the reticular ridge-and-pond morphology across the full span of length scales that
it expresses itself at in Holocene lagoons. The facies map (Fig. 5B) shows
the reticular ridges to consist of a constructional coralgal rim with
sediment-filled interiors. The longest ridges are either composed of continuous coralgal rims enclosing a sediment-filler interior, or, chains of
smaller ridges with the same structure. The outer margin of each ridge
is onlapped by a debris apron of loose sediment that spans the transition
from the topographic high of the ridge to the adjacent depression — the
pond. The DEM shows the tops of the ridges to rise to within one metre
of sea level and the ponds to attain depths down to −15 m (Fig. 5C). The
water depth of the ridge-tops increases in-step with their setbackdistance from the eastern margin of the platform. As such, the most
easterly examples are fully aggraded and reach sea level (coloured red
in the DEM), those offset 5–10 km lagoonward of the margin are submerged by 2–3 m of water (yellow), and the tops of those ridges at
greater setback distances, which inhabit the platform-centre, reach to
within only 5 m of the sea level (green in the DEM). Downgrading the
QuickBird image to 50 m resolution to mimic the level of detail that
might be resolved using seismic serves to obfuscate all but the most pronounced ridges and ponds (Fig. 5D), which, as would be expected, leads
to a very different and coarser interpretation of the morphology when it
is remapped (Fig. 5E).
4.1. Size–frequency distribution of ponds is the same for the Recent and
Palaeozoic platforms
Fig. 7. Cumulative distribution functions for the ponds mapped from Alacranes Reef at
seismic resolution (satellite imagery down-sampled to 50 m pixels) and from the three
Palaeozoic seismic horizons (two extracted from the Norsel High and one from the
Finnmark Platform). X-axis — pond area, y-axis — probability of encounter. Constantly
curved trends in log–log plot indicate exponential distributions. This classification of the
trends is upheld by the three-step statistical test of Clauset et al. (2009) adapted to test
for the presence of exponential distributions (Schlager and Purkis, 2013). Broken lines
chart ideal exponential distributions for the two populations. The size–frequency distribution of the ponds mapped in the three Palaeozoic landscapes and those in the Modern
analogue are statistically inseparable.
When mapped at the native QuickBird resolution of 1 m, the ponds
in the platform-interior of Alacranes Reef, the ridges constructed from
coral frameworks, and the debris aprons associated with those ridges,
all follow power law size–frequency distributions, as indicated by a
linear trend over a significant portion of the set in a log–log cumulative
frequency plot of area versus probability of encounter P(X ≥ x) (Fig. 6).
Following the three-step procedure provided by Clauset et al. (2009),
power-law scaling was statistically confirmed for the span of scales
between 102.3 and 105.5 m2 for the coral framework portion of the ridges
and their associated debris aprons, and between 104.0 and 107.7 m2 for
the ponds.
Power law behaviour facilitates prediction across scale because an
exponential decrease in probability of encounter for each object in the
S. Purkis et al. / Sedimentary Geology 321 (2015) 49–69
59
Fig. 8. Gradients in the width of reticular ridges in the Alacranes Reef platform-interior (A). Hot colours demark wide ridges whilst cool colours emphasise narrow buildups. The width map
highlights how ridges are best developed on the eastern platform-margin, which faces prevailing currents (B) and winds (C). Current data depict mean surface circulation in the southern
Gulf of Mexico for the period 2006–2010, modified from Sanvicente-Añorve et al. (2014). Box with red dot signifies the location of Alacranes Reef in the Gulf of Mexico. Wind rose shows
wind speed and direction data for Alacranes Reef extracted from QuikSCAT satellite observations for the period Jan. 2013 through Jan. 2014. (For interpretation of the references to colour in
this figure legend, the reader is referred to the web version of this article.)
population is coupled to an exponential decrease in unit area. For
instance, knowledge of the number of ponds on the platform-top with
areas N10 km2 would allow the number of ponds in the system with
an area of 1000 m2 to be estimated, and so on. Such “scale invariance”
is helpful for sedimentologists and stratigraphers working with ancient
strata in outcrop, core, or even seismic as the occurrence of small facies
bodies, which are typically challenging to detect, can be indirectly
inferred from the frequency of large ones (Purkis et al., 2007; Harris
et al., 2011; Purkis et al., 2012a, 2014a).
The cumulative distribution function for the ponds is offset to the
right of that for the ridges and their aprons, emphasising the area of
the ponds to be an order greater than that of the ridges. This difference
is supported by the observation that the ponds inhabit an area of
122 km2 in the platform-interior of Alacranes Reef, whereas the framework portion of the ridges covers 62 km2 and their associated debris
aprons, only 23 km2.
A feature worthy of comment in the cumulative distribution
function of the Alacranes ponds is evident between areas of
105.5 km2 and 106.1 km2 (Fig. 6A). These ponds, with areas in the
range of 1 km2, plot above the linear trend adopted by the ponds
through the rest of the set, indicating that they are anomalously
large, as compared to how they would be predicted by power-law
scaling. Highlighting the handful of ponds in this size range in the
GIS (Fig. 6B) reveals them to be associated with conspicuously continuous and expansive ridges. Though it cannot be verified, the departure from the morphology observed on the rest of the platform
conceivably could be related to lineaments that can be visually
interpreted from satellite imagery (Fig. 6B, broken lines). These
lineaments might be interpreted as faults, but the interpretation is
equivocal in the absence of further data.
In contrast to the power law reported for the size–frequency distribution of the Alacranes ponds, those interpreted from the Palaeozoic
seismic horizons are characterised by an exponential distribution
(Fig. 7). Verified by the test offered by Clauset et al. (2009), this distribution is robustly exponential across the full span of sizes of the ponds,
indicating that an exponential decrease in probability of encounter for
each pond in the population is coupled to a linear decrease in unit
area — both terms, by contrast, are exponential for power law. Whilst
a power law cumulative function describes the size–frequency distribution of the Alacranes ponds and an exponential function describes the
same aspect of the morphology for the Palaeozoic, the difference between the two systems is absent when the ridge-and-pond patterning
is remapped for Alacranes Reef using imagery downsampled to 50 m
pixels. Because the smallest aspects of the morphology are lost through
resampling, considered at “seismic” resolution, the size–frequency
distribution of the Alacranes ponds reverts from power law to an exponential and is statistically inseparable from the distribution reported by
the Palaeozoic landscapes (Fig. 7). This change in behaviour is important
for two reasons.
First, the switch in distribution emphasises how power laws truncated at the small end (i.e. where it is troublesome to sample at small
values of x) may masquerade as exponential or lognormal distributions.
This artefact has previously been reported by Perline (2005) and
discussed by Schlager and Purkis (2013) from the perspective of scales
of accumulation of Holocene carbonate. Drummond and Wilkinson
(1996) consider the same behaviour in the context of the problems
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S. Purkis et al. / Sedimentary Geology 321 (2015) 49–69
Fig. 9. Width maps emphasise site differences in the plan-form extent of ridges interpreted from seismic horizons from the Norsel High (A and B), Finnmark Platform (C) and QuickBird
imagery of Alacranes Reef down-sampled to 50 m pixels to equal the resolution of the subsurface data (D). Hot colours demark wide ridges whilst cool colours highlight narrower ones.
(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
sampling very thin layers in stratigraphy. This dichotomy is important
since it allows for the possibility that the Palaeozoic ridge-and-pond
patterning might also be power law and it is only the crude resolution
of the seismic that prevents the small-scale features from being
recognised. That is, the Palaeozoic platform-tops might host the same
abundance of reticular detail as resolved by QuickBird atop Alacranes
Reef.
Second, the statistical inseparability of the size–frequency distribution of the Palaeozoic ponds and those from the Recent highlights a
fundamental similarity in the ridge-and-pond morphology which
might suggest that similar controls are responsible for it, despite the
different reef architects (i.e. Palaeoaplysina versus bryozoan-Tubiphytes
versus stony corals). A premise that will be explored later.
4.2. Ridge width maps
Whilst size–frequency plots were useful to understand and characterise the configuration of the pond morphology between and within
sites, we employ width maps to highlight systematic patterns in the
plan-form extent of the ridges. Width maps for Alacranes Reef reveal
the best developed ridges, which are preferentially located on the eastern margin of the platform, to attain widths exceeding 500 m (Fig. 8A).
The widest ridges are also those which have most successfully aggraded
to sea level (Fig. 5C). The eastern margin of Alacranes Reef faces the
direction of dominant surface current, as reconstructed by SanvicenteAñorve et al. (2014) for this sector of the Gulf of Mexico (Fig. 8B).
Averaged QuikSCAT satellite observations show that prevailing winds
are also overwhelmingly from the east (Fig. 8C) which serves to confirm
that the best developed ridges have formed along the windward margin
of the Alacranes Reef platform. As was the case for their water depth, the
width of the ridges also declines in-step with distance along the
windward-leeward hydrodynamic gradient.
Since the platform-interior ridge-widths of Alacranes Reef were
neatly explained by prevailing hydrodynamics, it was hoped that
the learnings from the Modern could be applied to the patternings
interpreted from the Palaeozoic seismic horizons. Slice 2672 from the
Norsel High shows the majority of the ridges to have widths in the
range of 300–400 m (Fig. 9A), which, save for the particularly well
aggraded example that fringes the windward-margin of the platform,
corresponds to the widest examples from the Recent analogue
(Fig. 9D). In several areas, however, ridges display widths exceeding
1000 m. The wide ridges occur preferentially along the primary axis of
the interpreted horizon, as is the case for Finnmark slice 2028
(Fig. 9C). The distribution of ridge widths is the same for the remaining
slice, Norsel 2868, but in this case, as for Alacranes Reef, the best developed ridges appear along the periphery of the horizon (Fig. 9B), perhaps
suggesting that this slice approaches the Palaeozoic platform-margin of
the Norsel High.
4.3. Lacunarity analysis suggests that reticular patterning is hierarchical,
self-similar and scale-independent
As noted by Allain and Cloitre (1991) and Plotnick et al. (1993), and
demonstrated using the Sierpinski carpet (Fig. 10A, left image), the
S. Purkis et al. / Sedimentary Geology 321 (2015) 49–69
61
Fig. 10. Lacunarity plots for synthetic and real-world patterns. Lacunarity is a measure of the ‘gappiness’ of a geometric structure and a power-law trend between the scale of observation
and lacunarity indicates a self-similar pattern, as is the case for a mathematical fractal such as the Sierpinski carpet. Sets that are not self-similar, such as random patterns, show upwardconcave trend lines that slowly approach the coordinate axis (A). The ridge-and-pond patterns from the platform-interiors of both Alacranes Reef and the three Palaeozoic seismic horizons
display linear, power-law, trends in plots of lacunarity versus scale of observation (B). Broken lines are ideal power-laws for each set. The analysis confirms the ridge-and-pond patterns
atop the Palaeozoic platforms and the Modern analogue to be self-similar over 2.5 orders of magnitude.
lacunarity curve for a self-similar fractal is a straight line, indicating a
power law relationship between lacunarity and scale of observation.
The lacunarity curve for a random pattern, by contrast, is an upwardconcave trend that slowly approaches the coordinate axis (Fig. 10A,
right image). Random patterns are not self-similar. These fractal and
random end-members provided useful comparisons to the lacunarity
curves generated from our real-world data. Lacunarity curves for both
the Palaeozoic landscapes and the Recent analogue are robustly power
law across the span of considered length scales, suggesting that the
ridge-and-pond patterning, in both cases, is a self-similar fractal. The
distribution of ridges and ponds is statistically self-similar and scale independent across three orders of magnitude of linear size. Whilst there
is a broad overlap between the two datasets, the self-similar patterning
mapped in Alacranes Reef extends one order smaller than that of the
Palaeozoic. This difference should not be interpreted as a divergence
in the morphology, though, but rather arises because the QuickBird
imagery has an order finer spatial resolution than the subsurface data.
Because the seismic horizons are considerably larger than the satellite
image, the lacunarity assessment of the Palaeozoic landscapes extends
to a longer length-scale than achievable for the Modern data. This
said, beyond the penultimate audit of lacunarity for the seismic, the
curve rolls off of the linear trend, indicating the upper limit of selfsimilarity for the pattern to be in the range of 3000 m for the Palaeozoic
sections. The lower trend of self-similarity for Alacranes Reef is in the
range of 10–50 m. It should be noted that the roll-off on the small-end
of the Alacranes lacunarity curve, which occurs at a length-scale of
20 m, might be an artefact as the resolution of the set is approached
and cannot unequivocally be interpreted as the lower limit to the selfsimilarity of the ridge-and-pond pattern. With scale-invariance over
several orders confirmed by power law size–frequency relationships
for the morphology and self-similarity verified by lacunarity analysis,
over the same orders of scale, the necessary criteria are met to conclude
the ridge-and-pond patterning to be fractal.
4.4. Fast Fourier Transform highlights common periodicities for polygonal
reefs through time
Whilst size–frequency and lacunarity analysis have confirmed the
ridge-and-pond patterning of the Palaeozoic and Recent buildups to
be fractal over scales of tens of metres to thousands of metres of linear
length, we employ FFT to investigate whether there are certain scales
that are particularly relevant for the characterisation of the reticular
morphology. The motivation to identify these scales lies in the fact
that they might aid the understanding of the morphology in processterms. Such insight is also imperative for the creation of realistic
depositional facies models. Separate FFTs were run on the four sites
(three Palaeozoic, one Modern) and to ensure representative sampling,
each FFT graph is constructed from ten replicate strike-orientated
transects. Significant peaks in plots of power versus length-scale reveal
the ridge-and-pond morphology for Alacranes Reef to have dominant
periodicities at 0.4 km, 2 km, and 4 km (Fig. 11A). Alike in their hierarchical morphology, the three Palaeozoic landscapes share the 2 km and
4 km periodicities with Alacranes Reef, and have one additional at
20 km, but lack the 0.4 km periodicity (Fig. 11B, C and D). We do not
believe that either of the different peaks returned by the seismic
horizons represents a fundamental difference to the results from
Alacranes Reef. It is logical that the 0.4 km frequency would be absent
from the subsurface data as it is finer than the effective spatial resolution of the seismic. For this reason, it should certainly not be assumed
that the Palaeozoic buildups lack the fine-scale ornamentation of the
Alacranes Reef morphology and, indeed, as earlier noted, the exchangeability of exponential distributions with power law might be taken to
suggest that the seismic is indeed failing to capture the fine detail reported by the QuickBird imagery. The absence of the 20 km dominant
periodicity in Alacranes Reef is similarly easy to explain: the platform
is too small to harbour morphologies that bundle over such a long
length-scale.
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S. Purkis et al. / Sedimentary Geology 321 (2015) 49–69
of the imagery, these features of the morphology are not independent,
but rather a manifestation of hierarchy of the reticular buildups whereby thin ridges and sub-ponds fuse to major ponds ringed by thicker
ridges, which in turn coalesce to the thickest ridges and composite
ponds — the hallmark of a self-similar pattern. The 20 km lengthscale, reported only in the subsurface, appears unrelated to the ridgeand-pond morphology, but rather linked to the tectonic grain of the
Norsel High and Finnmark Platform. Extensive faulting has been reported for both (Elvebakk et al., 2002; Colpaert et al., 2007).
5. Discussion
5.1. The reticular ridge-and-pond pattern is fractal
Fig. 11. Fast Fourier Transform (FFT) analysis of the ridge-and-pond patterns mapped
from Alacranes Reef (A), the Finnmark Platform (B) and the Norsel High (C and D). For
each site, solid red lines represent the position of strike-orientated transects across the reticular morphology (ridges are white, ponds black). Graphs of FFT power versus lengthscale plot the average FFT result obtained from the transect depicted by the red line and
a further nine, each rotated by a random angle between 0° and 5° around the centrepoint of that line. In this way, the morphology encountered by a total of ten transects is interrogated to ensure representative sampling for each site. Red dots in the graphs highlight the most pronounced periodicities, which are expressed at an approximate lengthscale of 0.4 km, 2 km and 4 km in Alacranes Reef, and 2 km, 4 km and 20 km for the
Palaeozoic landscapes. Coloured stripes highlight these four characteristic harmonies of
the morphology and relate to the coloured scale bars in Fig. 12. The 2 km and 4 km periodicity is common to both the Palaeozoic and Recent analogue. (For interpretation of
the references to colour in this figure legend, the reader is referred to the web version of
this article.)
Inspection of the satellite imagery and seismic allows the periodicities identified by FFT to be reconciled with the reticular morphology.
Atop Alacranes Reef, the 0.4 km FFT peak corresponds to the breadth
of the smallest “sub” ponds (Fig. 12A). These features are below seismic
resolution. The peaks at 2 km and 4 km, present in Alacranes Reef and all
three seismic horizons, relate to the breadth of “major” (Fig. 12B and
C) and “composite” ponds (Fig. 12D and E). As is clear upon inspection
Fractals have two intrinsic properties, self-similarity and scale
invariance. Self-similarity means that any part of the system, appropriately enlarged, looks like the whole; scale invariance necessitates that
an object looks the same on all scales. Fractals generated mathematically, such as the Sierpinski carpet (Fig. 10A), are infinite, a property that
cannot occur in nature (Halley et al., 2004). Real-world carbonate
depositional systems, though, can display both self-similarity and
scale invariance within certain thresholds and therefore are akin to a
mathematical fractal over a limited range of scales (Rankey, 2002;
Purkis et al., 2005; Purkis and Kohler, 2008; Correa et al., 2012;
Schlager and Purkis, 2013).
Self-similarity, the first prerequisite for a fractal, is confirmed for the
ridge-and-pond patterning through the calculation of lacunarity curves
(Fig. 10B). The second prerequisite, scale invariance, is upheld by size–
frequency plots which show power-law scaling over three orders of
linear size for Alacranes Reef. Though there is no hard and fast rule,
the literature suggests a span of three orders to be sufficient to declare
scale invariance (Lovejoy, 1982; Schroeder, 1991; Avnir et al., 1998;
Hergarten, 2002). Power-law distributed populations are scale invariant
across their entire distribution because the abundance (y) of an object
scales as an inverse power of the size of the object (x). Under these
conditions, y can always be obtained by scaling x by a constant factor
α, such that y = x−α. Given the property of scale invariance, in a strategy
termed “scale-linking” (Purkis et al., 2007), information from an observable spatial scale can be used to train a function with which to solve for a
property at an unobservable scale. This property of the distribution is an
exciting prospect for seismic interpretation because knowledge of α, the
slope of the power law distribution, for seismic-scale objects, provides
insight via extrapolation into the size–frequency distribution of the
ridge-and-pond morphology at scales finer than can be accessed with
seismic. The results from Alacranes Reef are in accordance with the
numerous examples of scale invariant accumulation of sediments
highlighted in the literature over similar length-scales for siliciclastic deposits (Posamentier et al., 1992; Van Wagoner et al., 2003; Edmonds
et al., 2011) and for carbonates (Thorne, 1995; Schlager, 2004;
Schlager and Purkis, 2013). It should be noted that the length-scale of
the power law size–frequency scaling for Alacranes Reef overlaps and
shares the same span as for the geometric self-similarity identified
through lacunarity analysis (Fig. 6).
On the basis of the analysis conducted, the ridge-and-pond
morphology resolved in the platform-interior of Alacranes Reef is
fractal. Lacunarity analysis shows the three Palaeozoic landscapes to
unequivocally possess one of the two requisite properties for a fractal,
self-similarity, with the second, scale invariance, unconfirmed. However, given the well-documented ease with which scaling artefacts
convert power law distributions to negative exponents and also considering the fact that the size frequency distribution for Alacranes Reef,
when reinterpreted at seismic resolution, is inseparable from that of
the Palaeozoic morphologies, scale invariant patterning in the subsurface is implied. The evidence is therefore strong that the reticular
morphology from the Modern and Ancient platforms alike, are fractal
patterns.
S. Purkis et al. / Sedimentary Geology 321 (2015) 49–69
63
Fig. 12. The hierarchies of scale of the ridge-and-pond morphology identified by Fast Fourier Transform analysis (Fig. 11). The periodicity of 0.4 km expressed on Alacranes Reef
corresponds to the breadth of the smallest “sub” ponds (A). This length-scale is absent in the seismic horizons because it occurs below the resolution of the seismic data. Periodicities
of 2 km and 4 km are detected in both the Palaeozoic landscapes and the Modern analogue and correspond to the breadth of “major” and “composite” ponds, respectively (B, C, D and
E). The final 20 km periodicity (F) is identified in the seismic data only (Alacranes Reef is too small to harbour morphology at this length-scale) and appears to be unrelated to the
ridge-and-pond morphology, but rather the scale of the tectonic grain of the Norsel High and Finnmark Platform. Coloured scale bars are of the lengths noted (i.e. white 0.4 km, blue
2 km, green 4 km and orange 20 km). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
5.2. Reticular reefs in process-terms
As pointed out by Wright and Burgess (2005), fractals remain poorly
understood in terms of their process significance and so mere identification of fractal geometry for the ridge-and-pond morphology in this
study offers little insight as to why the Palaeozoic and Modern reef
buildups should adopt this patterning. Recent studies, though, provide
a conceptual framework in process-terms as to why reef builders
might construct fractal morphologies in certain environmental settings.
To explain this, it is first necessary to recognise the relationship between
a reef building organism and the water mass in which it is immersed,
to understand the role of turbulence and to accept that sediment is
nothing but bad news for reef builders.
Schlager and Purkis (2013), in a study of Holocene reef morphology
from the central Indian Ocean, proposed that ring reefs with bucket structure (i.e. those with stiff reef rims holding a pile of loose sediment) are a
signature of biotic self-organisation. The authors judged that the bucket
morphology of bucket-reefs in the size range of 0.7–38,000 km2 satisfied
the criteria to be classified as a statistical fractal. Beyond the large span of
length-scales across which self-organised reef building is observed in the
Indian Ocean, Schlager and Purkis (2013) presented further evidence
from seismic data and boreholes in the Maldives that indicate the bucket
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S. Purkis et al. / Sedimentary Geology 321 (2015) 49–69
structure to have been a dominant depositional motif since the Oligocene.
These observations are relevant in the context of the present study. First,
they indicate the consistent influence of biotic self-organisation on the
accumulation of Maldivian carbonates across five order of magnitude of
linear scale. And second, pertinently, the observations emphasise the
longevity of the self-organised fractal reef pattern that persisted, uninterrupted, on the Maldives platform for 30 Ma. This study pitches the biotic
self-organisation of reef builders to extend back through 300 Ma of
geological time.
Schlager and Purkis (2015) extended the bucket principle of reef
growth to explain the development of reticulate coral ridges in
Holocene lagoons. Their hypothesis is easily applied to the reticular
patterning of Alacranes Reef and also bears relevance to the seismic
morphologies interpreted for the Norsel High and Finnmark Platform.
Applying the observations of Schlager and Purkis (2015) from Maupiti
Atoll to the fine-scale reef ornamentations of the platform-interior of
Alacranes Reef, incipient ridges can clearly be seen to develop from
the coalescence of discrete patch reefs (Fig. 13A). Further, like the
patch reefs that proceeded them, the coral ridges consist of a constructional coralgal rim and sediment-filled interior (Fig. 13B). This implies
that they have bucket structure in the sense of Ladd and Tracey
(1949) and Schlager and Purkis (2013). Also as observed for Maupiti,
the longer ridges in Alacranes Reef consist either of chains of buckets
(Fig. 13C) or continuous coralgal rims enclosing a sediment filled interior
(Fig. 13D).
Schlager and Purkis (2013) explained the fractal nature of the bucket
structure of reefs to arise for the following reasons.
First, ecological and hydrodynamic studies on modern reefs suggest
that the edge position in a reef is favoured over the centre position because bottom shear is higher and the diffusive boundary layer between
reef and water is thinner (e.g. Atkinson et al., 2001; Hearn et al., 2001).
Thus, the reef edge has easier access to nutrients, is better poised to discard harmful metabolites and is less likely to be buried by sediment.
Note here that even though the platform-interiors of rimmed reefs are
tranquil on human length-scales, there still exist pronounced gradients
in turbulence on the centimetre-to-millimetre scale that are relevant to
the metabolic functioning of a reef-builder (Andréfouët et al., 2001;
Monismith, 2007, 2014).
Second, in addition to the fundamental effect of the diffusive boundary layer, more subtle positive effects of higher flow rates on corals have
been attributed to reduce competition from other reef biota (Schutter
et al., 2010) and to improved capture of zooplankton and other particulate food (Sebens et al., 1998; Pomar and Hallock, 2008). The same
ecological advantages enjoyed by corals can logically be extended to
all skeletal metazoan reef builders. For instance, Yose et al. (2010)
show syndepositional ridge-and-pond complexes with equivalent
morphology to those described in this study in the platform interior of
the Lower Cretaceous (Aptian) Shu'aiba Formation (their Figs. 4c, 12
and 22). Rudist bivalves are the architects in this case. The authors
also use Alacranes Reef as a scleractinian analogue to the rudist-built
reefal mounds interspersed with lagoonal ponds resolved from seismic
(Yose et al., 2010, their Fig. 15). In the same vein and considering the
same seismic volume of the Shu'aiba Formation, Yose et al. (2006)
pitch ridge-and-pond morphology from the Modern Great Barrier Reef
as an architectural analogue to the rudist complexes (their Fig. 6).
Third, the edge position offers the best vantage point for sexual
spawning as gametes can be effectively broadcast into the water and
are less likely to be entrained in the diffusive boundary layer. Regardless
of whether considering coral propagules, bivalve spat, or marine algal
spores, long-distance dispersal of gametes is important to assuage
local resource competition and inbreeding. We do not claim to understand the means by which Palaeoaplysina reproduced, though fossil
evidence hints that, like many Modern scleractinian corals, the organism might have an asexual phase evolving budding (Anderson and
Beauchamp, 2010). For the same reasons that sexual spawners strive
for a wide release of propagules, the same advantages remain for
those pursuing asexual mechanisms of reproduction involving budding
or fragmentation. Here, the edge position still favours effective dispersal
(Tunnicliffe, 1981; Highsmith, 1982).
All of these ecological factors conspire to make the edge position the
most favourable locus for reef growth and the same advantages hold
throughout the Phanerozoic, regardless of whether the architect is a
Fig. 13. Enhanced QuickBird satellite image of the platform-interior of Alacranes Reef (©DigitalGlobe, 2010) showing the fine-scale configuration of the photozoan ridge-and-pond morphology. Incipient ridges can clearly be seen to develop from the coalescence of discrete patch reefs (A). Minor ridges consist of a constructional coralgal rim and sediment-filled interior
(B). Longer ridges are either of chains of minor ones (C), or elongate structures built by a continuous coralgal rim enclosing a sediment filled interior (D). Coralgal rims, in this true-colour
image, are reddish in colour. Sediment filled interiors are beige to white. At all scales, the morphology therefore adheres to the bucket principle of reef growth which is a signature of biotic
self-organisation. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
S. Purkis et al. / Sedimentary Geology 321 (2015) 49–69
Palaeozoic Palaeoaplysina calcareous algae, a Palaeozoic bryozoanTubiphytes, a Mesozoic reef-building bivalve, or a Cenozoic coral.
Because of its fundamental metabolic underpinning, we propose that
the advantages afforded by the edge position over the core position
for reef growth is why the same bucket morphology and facies successions are recognised in outcrop studies of Palaeoaplysina buildups
(Fig. 14A) and the Modern (Fig. 14B), alike. Examination of seismic
slice 2868 from the Norsel High, which has particularly good fidelity,
reveals a speckled character to the RGB blend within the barren core
of the bucket (Fig. 14C). This seismic texture conceivably could be
caused by the presence of individual Palaeoaplysina mounds. If present,
these lower-order buildups would be analogous to the individual
coralgal patches that grow within the barren centres of the Alacranes
Reef buckets (labelled in Fig. 14B), strengthening the premise of a common biological control on depositional morphology.
The same suite of ecological factors that sculpt Phanerozoic reefs
likely operated in the Proterozoic. It is clear, for instance, that skeletal
metazoan reef builders are not a prerequisite for bucket structures;
Precambrian platforms (microbial carbonate) commonly show raised,
wave-resistant rims, often consisting of tall mounds (Hoffman, 1974;
65
Grotzinger, 1986, 1989). Framed by strong evidence that reticular reef
pattern is another manifestation of the bucket principle of reef growth,
this morphology can be toted as a signature of biotic self-organisation.
5.3. Reduced accommodation triggers reef reticulation
Inspection of the Alacranes Reef QuickBird satellite image and the
associated DEM reveals a change in the degree of reef reticulation instep with water depth. For instance, in the subset of the image
(Fig. 13) (though the relationship equally holds for the entire platform)
the buildups grade from circular patch reefs in the west of the platforminterior, where water depth exceeds 10 m, to a contorted tight-knit
mesh of ridges in the east (depth b 2 m). As highlighted in Fig. 2, this
gradient is particularly evident in the northwest of the lagoon, the
deepest precinct of the platform. Rising out of water depths of at least
15 m, a series of discrete and relatively high-relief circular patch
reefs exist here which are in contrast to the interconnected reticular
buildups that characterise the remaining (shallower) lagoon. Since we
have an accompanying DEM, the relationship between depth and
reef reticulation can be explored quantitatively for Alacranes Reef.
Fig. 14. Palaeozoic and Modern buckets. (A) Outcrop-interpretation of a ring-shaped Palaeoaplysina complex from central Svalbard (after Hanken and Nielsen, 2013, modified). The
Palaeoaplysina buildup forms an oval structure surrounding an inner area lacking buildups — a bucket structure. (B) Whilst the size of this Alacranes Reef coralgal bucket is an order smaller
than the Palaeoaplysina complex, examination of QuickBird satellite imagery shows the lateral facies successions to be the same. This buildup, a representative example from platforminterior of Alacranes Reef, is composed of a coralgal rim that rings a barren core where reef growth is stifled by sediment and restricted access to clean, well-ventilated, ocean water.
(C) Shows a sample of seismic slice 2868 from the Norsel High which captures a photozoan Palaeoaplysina complex. As for the outcrop interpretation, bucket structure is clearly evident.
Furthermore, the speckled character of the RGB seismic blend in the barren area could be interpreted as smaller-scale Palaeoaplysina mounds, a growth morphology which is readily
apparent in the cores of the coralgal Alacranes Reef buildups (B).
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S. Purkis et al. / Sedimentary Geology 321 (2015) 49–69
Cross-plotting the area of the ponds versus their average water depth
reveals an inverse relationship between the two. As accommodation
(i.e. water depth) decreases, the ponds become both more numerous
and smaller (Fig. 15). The same relationship to depth is visually apparent for other Holocene platforms (see Figs. 1AB, 3 and 6 in Schlager
and Purkis, 2015).
The association between water depth and the density of the reticulation suggests that the pattern is triggered by reduced accommodation.
This notion also fits with the biological underpinning of the morphology
as proposed by Blakeway and Hamblin (2014) and Schlager and Purkis
(2015), and is also in accordance with the observations made by
Colpaert et al. (2011) in the Barents Sea subsurface. Whilst unconstrained by water depth, platform-interior reefs grow as circular patch
reefs. This pinnacle-form maximises the surface area of the growing
reef-face in contact with turbulent waters (e.g. Adams and Hasler,
2010). Reducing accommodation curtails aggradation of the circular
patch reefs, and as on the scale of entire carbonate platforms, the
growth axis of the reef switches from aggradation to progradation, leading to the coalescence of patches, which in turn, yield ridges. As detailed
in Fig. 13, recently-formed ridges retain the original bucket structure of
the patches from which they were formed, but given time, coral growth
on the internal septa of the ridges is stifled by sediment and switches
solely to the edge position of the ridge (which remains bathed by turbulent flow) to yield elongate buckets. Further reducing accommodation
forces the secondary coalescence of reef ridges and just as for the coalescence of patches before, internal loci of reef growth become smothered,
whilst those that retain access to well-ventilated turbulent waters continue to prograde into the remaining accommodation space. Driven by
an aversion to sediment, it is this process of the actively growing face
of the reef ridge seeking-out remaining accommodation that delivers
the tightest mesh and widest ridges in the easternmost Alacranes Reef
lagoon (Fig. 8A). The reticular morphology is a transient form, however.
Unless new accommodation is created by subsidence of the platform
and/or sea level rise, the mesh becomes a victim of its own detritus.
As the platform-margin is approached, the ponds separating the ridges
become stuffed to sea level with debris, extinguishing the edge position
necessary for reef growth, and the morphology reaches a senile phase,
condemned to burial beneath the debris apron prograding lagoonwards
from the platform-margin. In time, the reticulated ridge-and-pond
mesh is therefore subsumed by the reef flat, a process that continues
until the entire platform is fully aggraded. An understanding of this
process is important to explain the complex vertical and lateral
interfingering of frame- and grain-stones in the interior of Modern
and Ancient carbonate platforms, alike. A good example of such heterogeneity is provided by Menier et al. (2014) for a Miocene platform in the
South China Sea (their Fig. 6).
6. Conclusions
This paper highlights the numeric similarity between the reticular
patterning of reefal buildups in a Modern and Upper Palaeozoic setting.
Biotic self-organisation is proposed to be the mechanism controlling the
development of the reticular morphology and a process common to
both the Modern and Ancient reefscapes. Despite the enormous changes in biota, climate, sea level, water chemistry and so on, that have taken
place since the Palaeozoic, the fundamental metabolic requirements of
reef architects remain constant through geological time. For this reason,
and because of hydrodynamic effects, reef builders routinely strive to
inhabit the edge position of topographic highs and it is this preference
that yields reticular reef patterns, created through the conjoining of
reef patches, at the point that accommodation becomes limited. We
hope that this work stimulates others to consider the relevance of
self-organisation as a driver of heterogeneity in the carbonate rock record as we believe that an understanding of these processes will allow
for better reconstructions of sedimentary patterns that can only be understood incompletely through inspection of seismic and outcrop. This
powerful mathematical comparison between modern and ancient reticular systems could allow us ultimately to better characterise the buildup
facies distribution below seismic resolution and create more realistic
facies distribution models in the subsurface based on self-organisation
relationships.
Acknowledgements
We thank Charlotte Purkis for assistance with eCognition, Neil
Pickard for guiding our seismic interpretations and Klaas Verwer, Jeroen
Kenter and Wolfgang Schlager for their mentorship. We also thank
Aart-Jan van Wijngaarden for supporting the project and Javier Bello
Pineda for his kind guidance on the topography and habitats of
Alacranes Reef. We are grateful to Steve Bachtel and an anonymous
reviewer who provided constructive comments for revision. This is
NCRI publication #161.
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