ELSEVIER Earth and Planetary Science Letters 160 (1998) 147–161 Orbital cyclicity in the Eocene of Angola: visual and image-time-series analysis compared B. D’Argenio a,c,L , A.G. Fischer b , G.M. Richter d , G. Longo e , N. Pelosi c , F. Molisso c,f , M.L. Duarte Morais g a Dipartimento di Scienze della Terra, Universita ` di Napoli, Largo San Marcellino, 10, 80138 Naples, Italy b Department of Earth Sciences, University of Southern California, Los Angeles, CA 90089-0740, USA c Istituto di Ricerca GEOMARE, CNR, via A. Vespucci, 9, 80142 Naples, Italy d Astrophysikalisches Institut Potsdam, ander Sternwarte, 16, 14482 Potsdam, Germany e Osservatorio Astronomico di Capodimonte, via Moiariello, 16, 80131 Naples, Italy f Institut und Museum fu ¨r Geologie und Pala ¨ontologie, Universita ¨t Tu ¨bingen, Tuebingen, Germany g Departamento de Geologia da Universita ` A. Neto, Luanda, Angola Received 21 August 1997; accepted 24 April 1998 Abstract Photographic coverage of hemipelagic Eocene marls of Angola (Africa), supplemented by limited sampling, shows rhythmic stratification patterns of two types: (a) hierarchically cyclic variation in calcium carbonate=clay ratios forming couplets grouped into bundles at ratios of ca. 5 : 1; these are coupled with (b) a redox cycle of bottom waters, expressed in darkness of sediment (organic carbon) and variations of the ichnofauna. These patterns resemble those previously observed in the pelagic Albian Scisti a Fucoidi of Italy. Visual study and time-series analysis based on image processing provide ratios compatible with those of Milankovitch theory. Whereas the chronostratigraphic control in Angola does not afford a basis for an independent chronology, the similarity to the Italian Albian supports attribution of these rhythmicities to orbital forcing. 1998 Elsevier Science B.V. All rights reserved. Keywords: periodicity; cyclic processes; image analysis; Eocene; Angola 1. Introduction The stratigraphy of many pelagic and hemipelagic sediments contains rhythmic oscillations in carbon- ate content, optically expressed in colour and resis- tance to weathering. In some cases this rhythmicity is simple, but commonly it takes a hierarchical form. In this, high-frequency oscillations (couplets of a more clayey bed followed by a more limy one) are L Corresponding author. Tel.: C39 (81) 597-9220; Fax: C39 (81) 597-9222; E-mail: [email protected]modulated by a longer-period oscillation in which progressively more clayey couplets are followed by progressively more limy ones, and back, so that the couplets become grouped into bundles. Such bun- dled sequences in turn may be similarly modulated on a yet longer scale, in which successive bun- dles become more calcareous and less calcareous, to divide the sequence into superbundles. Examples of such sequences are the Aptian–Albian of cen- tral Italy [1–4], the late Maastrichtian of northern Spain [5], and the Quaternary of the eastern Gulf of Mexico. 0012-821X/98/$19.00 1998 Elsevier Science B.V. All rights reserved. PII S0012-821X(98)00074-0
Transcript
ELSEVIER Earth and Planetary Science Letters 160 (1998) 147–161
Orbital cyclicity in the Eocene of Angola: visual and image-time-seriesanalysis compared
B. D’Argenio a,c,Ł, A.G. Fischer b, G.M. Richter d, G. Longo e, N. Pelosi c, F. Molisso c,f,M.L. Duarte Morais g
a Dipartimento di Scienze della Terra, Universita di Napoli, Largo San Marcellino, 10, 80138 Naples, Italyb Department of Earth Sciences, University of Southern California, Los Angeles, CA 90089-0740, USA
c Istituto di Ricerca GEOMARE, CNR, via A. Vespucci, 9, 80142 Naples, Italyd Astrophysikalisches Institut Potsdam, ander Sternwarte, 16, 14482 Potsdam, Germany
e Osservatorio Astronomico di Capodimonte, via Moiariello, 16, 80131 Naples, Italyf Institut und Museum fur Geologie und Palaontologie, Universitat Tubingen, Tuebingen, Germany
g Departamento de Geologia da Universita A. Neto, Luanda, Angola
Received 21 August 1997; accepted 24 April 1998
Abstract
Photographic coverage of hemipelagic Eocene marls of Angola (Africa), supplemented by limited sampling, showsrhythmic stratification patterns of two types: (a) hierarchically cyclic variation in calcium carbonate=clay ratios formingcouplets grouped into bundles at ratios of ca. 5 : 1; these are coupled with (b) a redox cycle of bottom waters, expressed indarkness of sediment (organic carbon) and variations of the ichnofauna. These patterns resemble those previously observedin the pelagic Albian Scisti a Fucoidi of Italy. Visual study and time-series analysis based on image processing provideratios compatible with those of Milankovitch theory. Whereas the chronostratigraphic control in Angola does not afford abasis for an independent chronology, the similarity to the Italian Albian supports attribution of these rhythmicities to orbitalforcing. 1998 Elsevier Science B.V. All rights reserved.
The stratigraphy of many pelagic and hemipelagicsediments contains rhythmic oscillations in carbon-ate content, optically expressed in colour and resis-tance to weathering. In some cases this rhythmicityis simple, but commonly it takes a hierarchical form.In this, high-frequency oscillations (couplets of amore clayey bed followed by a more limy one) are
modulated by a longer-period oscillation in whichprogressively more clayey couplets are followed byprogressively more limy ones, and back, so that thecouplets become grouped into bundles. Such bun-dled sequences in turn may be similarly modulatedon a yet longer scale, in which successive bun-dles become more calcareous and less calcareous,to divide the sequence into superbundles. Examplesof such sequences are the Aptian–Albian of cen-tral Italy [1–4], the late Maastrichtian of northernSpain [5], and the Quaternary of the eastern Gulf ofMexico.
0012-821X/98/$19.00 1998 Elsevier Science B.V. All rights reserved.PII S 0 0 1 2 - 8 2 1 X ( 9 8 ) 0 0 0 7 4 - 0
148 B. D’Argenio et al. / Earth and Planetary Science Letters 160 (1998) 147–161
The periods of these oscillations approximate thehierarchy of the orbital variations that influence thedistribution of solar energy: the ca. 20 ka preces-sional cycles, and the two major eccentricity cyclesat ca. 100 and 400 ka. Fourier analyses reveal ad-ditional peaks for the obliquity cycle, and show thecharacteristic bifurcation of the 100 ka and 20 kapeaks. It is thus clear that orbital variations affectedthe Earth’s climates not only during ‘glacial’ times[6] but in the greenhouse state as well.
In the offshore Angola Basin, drilled by DSDPSite 364 [7], shoal-water carbonate sedimentationturned to marly pelagites in Aptian time, and contin-ued in this facies to the present. The Aptian–Albiancores reveal a strong rhythmic oscillation betweenlight chalky and dark shaly sediments, much likethose of the central Italian Aptian–Albian, with awave-length of 20–40 cm.
In 1991 D’Argenio observed and photographedstriking rhythmicity in the Eocene Cunga-GratidaoMarls exposed in the coastal cliffs north of Cabo SaoBraz on the coast of Angola (Figs. 1 and 2). Ad-
Fig. 1. Map of Cabo Sao Braz area; the inset shows its positionwith respect to Luanda. Sampling sites: A D cliff of Fig. 2; B Dlateral ravine where the middle upper part of the sequence hasbeen sampled.
ditional work by D’Argenio, Fischer, Duarte-Moraisand others was cut short by renewed warfare thatlimited further study to photographs.
2. The Cunga Marl at Cabo Sao Braz
The coastline at Cabo Sao Braz, about 160 kmsouth of Luanda (Fig. 1), consists of 50–70 m cliffs(Fig. 2) which, undercut by surf, are only accessibleby boat at low tide. Directly north of the Cape,however, in the Bahia de Sao Braz, a sand spit hasisolated a small lagoon, where the base of the cliffsmay be reached. Whereas the cliffs of Cabo Sao Brazare of Miocene clays and sandstones, the cliffs at thelagoon and extending northward expose the EoceneCunga-Gratidao Formation in a gentle arch or domecresting near the northern end of the lagoon. Bothlimbs of this structure are truncated by paleovalleysfilled with Miocene sediments.
2.1. Age
Samples from the basal and upper parts of the ex-posed sequence (white and black dots in Fig. 2) yielda microbiota of coccoliths (studied by D. Bukry ofthe U.S. Geological Survey and by S. Percival) andforaminifera studied by Molisso. The foraminiferaare poorly preserved and etched, and lack most ofthe age-specific keeled Tethyan species. The faunais not older than zone NP-10 and best fits NP-11,though a possible range into NP-12 (sensu Bolli etal. [8]) cannot be excluded. Dominance by claviger-inellids (normally rare) suggests cold water [9] andtherefore existence of a Benguela Current in Eocenetimes. The coccolith flora, examined by Bukry andby Percival, is diagnostic throughout zone CP-13b(Table 1).
2.2. Sedimentology
Our direct observations relate to the basal 14 m,and to the upper few meters. The chief constituentsare terrigenous clay and biogenic carbonate madeof coccoliths and foraminifera. Pyrite is common;dispersed quartz and feldspar grains in the range of30–100 µm are consistently present in the samplesexamined. No beds or laminae of silt or sand were
B. D’Argenio et al. / Earth and Planetary Science Letters 160 (1998) 147–161 149
Fig. 2. Cliff at Cabo Sao Braz. The black dots show the sampling site at the base of the cliff, while the white dots indicate the samplingin a lateral ravine, projected (see Fig. 1). The rectangle frames the sequence shown in Fig. 4.
seen, nor was grading observed. In places bedding isobscured by a superficial rind of epigenetic gypsum-cemented dust.
Black clays occur in the uppermost part of thesequence. With this exception, colors on fresh, moistcliff faces range from the dark chocolate brown anddark olive green of clays through intermediately col-ored marls to white limestones. Most of the cliffshave, however, been somewhat bleached, and darkclay samples bleached to shades of tan upon dry-ing and oxidation, suggesting that the dark shadesof fresh rock are partly caused by unstable ironmonosulfides.
2.3. Trace fauna and redox cycles
A black shaIe near the top of the sequence sug-gests an episode of carbon-enrichment due to anaer-obic conditions on the sea floor. We did not reachthis level but would assume absence of benthos, inwhat may have been a minor ‘oceanic anoxic event’.
In most of the strata trace fossils are abundant.The dark brown clays are crowded with Chondritesand contain some Zoophycos. As the clays lighten
the abundance of Chondrites decreases, and Zoophy-cos becomes more common. In still lighter, more cal-careous clays Chondrites and Zoophycos are joinedby thick, back-filled burrows of Planolites, and in thewhite limestones these are joined by Thalassinoidesand Ophiomorpha.
This spectrum of successive trace-fossil assem-blages in shale–limestone gradations is similar tothat found by Savrda and Bottjer [10] in the LateCretaceous Niobrara Formation of Colorado. Intheir interpretation the black shales accumulated onanoxic bottoms. The dark shales accumulated underdisaerobic conditions that limited the benthos topChondrites, and progressive availability of oxygenled to well oxygenated conditions recorded by theThalassinoides fauna. The trace-fossil assemblagesof the cyclic Italian Aptian–Albian [11] show thesame trends but lack the highly aerated Thalassi-noides ichnofauna.
2.4. Interpretation
The extremely planar stratification and the ab-sence of beds of sand, of wave ripples or of graded
150B
.D’A
rgenioet
al./Earth
andP
lanetaryScience
Letters
160(1998)
147–161
Table 1Biostratigraphy of foraminifera and coccoliths
Calcareous nannofossils. Chiasmolithus consuetus (Bramlette and Sullivan, 1961); Hay and Mohler (1967), C. gigas (Bramlette and Sullivan, 1961) Radomski (1968), C.grandis (Bramlette and Riedel, 1954) Radomski (1968), C. solitus (Bramlette and Sullivan, 1961) Locker, 1968, C. titus Gartner (1970), Coccolithus eopelagicus (Bramletteand Riedel, 1954) (Bramlette and Sullivan, 1961), C. pelagicus(Wallich, 1877) Schiller (1930), Cribrocentrum sp. Perch-Nielsen (1971d), Discoaster barbadiensis Tan(1927), D. binodosus Martini (1958), D. martinii Stradner (1959b), D. sublodoensis Bramlette and Sullivan (1961), Ericsonia formosa (Kamptner, 1963) Haq (1971),Helicosphaera lophota Bramlette and Sullivan (1961), H. seminulum Bramlette and Sullivan (1961), Lophodolithus nascens Bramlette and Sullivan (1961), L. mochloporusDeflandre inDeflandre and Fert (1954), Nannotetrina cristata (Martini, 1958) Perch-Nielsen (1971d), N. fulgens (Stradner, 1960) Achuthan and Stradner (1969), N. quadrata(Bramlette and Sullivan, 1961) Bukry (1973a), Reticulofenestra sp Hay, Mohler and Wade (1966), Sphenolithus radians Deflandre in Grasse (1952), S. spiniger Bukry(1971a), Zygrhablithus bijugatus Deflandre in Deflandre and Fert (1954); Deflandre (1959).
B. D’Argenio et al. / Earth and Planetary Science Letters 160 (1998) 147–161 151
beds point to deposition in quiet waters below stormwave base, by particle-by-particle setting from sus-pension. The bottoms generally lay above the calcitecompensation depth, but absence of aragonitic mat-ter and lack of molds of aragonitic shells such aspteropods suggest water depth on the order of 1–2km, i.e. deposition on the continental slope. The dis-persed fine sand suggests vigorous eolian transport.The trace fauna, the limited bioturbation, and thesulphide content point to deposition in a setting ofrestricted oxygen supply — the O2 minimum zone,i.e. the upper part of the mid-water mass. Cold-waterforaminifera suggest that the Benguela Current wasrunning as it is now, and the dispersed fine sandsuggests that the coast was arid and very windy —as seems likely in view of the region’s then moresoutherly position. There is every reason to thinkof this region as having been, throughout, one ofupwelling and high productivity. Whereas neither di-atomites nor chert were seen at Cabo Sao Braz, cherthas been reported from the Cunga Formation else-where [12]. In the absence of evidence for erosionor tractional transport by currents, the stratigraphywould appear to be the result of continuous depo-sition. Due to scarcity of biostratigraphic data therate of sediment accumulation remains poorly con-strained.
3. Visual cyclostratigraphy
Visual analysis of the photographs to identify themain oscillatory components cycle-by-cycle yieldsthe following results.
3.1. Cyclicity: couplets and bundles
The sediments throughout were muds, and themain pattern of variation was an oscillation in car-bonate=clay ratios. The fundamental stratigraphicpattern that has resulted (Figs. 3 and 4) is an al-ternation of relatively carbonate-poor layers, darkerand weathering recessively, and carbonate-enrichedlayers, lighter and more prominent. The boundariesbetween these units are not generally sharp but gra-dational. We speak of this visually distinct alterna-tion as a couplet structure, and define a couplet asconsisting of a lower carbonate-poorer and a higher
carbonate-enriched layer, in an arbitrary division ofwhat is generally a continuous sine-wave. Coupletstend to average about 20 cm thick. The successionof couplets is punctuated in a regular manner bya number of features. The most consistent of theseis the appearance of particularly clay-rich couplets(dark and recessive bands). Generally every 4th to5th couplet contains such a clay, and these layersserve to divide the sequence into segments (bundles)each consisting of 4–5 couplets.
In Fig. 3 these bundles have been numbered con-secutively, from 1 upward. Our discussion is di-rected at the better resolved part of the sequence(Fig. 3-right) comprising bundles 0–26. The regularrepetition of couplets and of bundles leads us tothe supposition that they are the results of rhyth-mic oscillations in deposition, with a characteristictime-constant. The bundle may contain one or morecouplets particularly enriched in carbonate. Thesemay be centrally located, forming a symmetricalbundle such as 2 or 16, or may be eccentric, skewingthe bundle.
Some bundles are more clayey throughout, othersare more calcareous. In some bundles the coupletstend to be well defined, in others they are fuzzy,and in some the couplet structure has been partly orwholly destroyed. As pointed out above, the mostcalcareous bundles (limestones) such as 1–3, 11–12,14, 21–22, 25 have lost most of their internal strati-fication due to burrow-mixing by Thalassinoides andOphiomorpha.
Couplet structure is best preserved in ‘marly’bundles of intermediate carbonate content, such asbundles 0, 13, 23. The most clay-rich units, darkerand recessive, such as bundles 6, 7 and 14–16 alsoshow little or no couplet structure. The reason forthis remains unclear: it may be that at these times theepisodes of plankton productivity were suppressed,or that these were episodes of carbonate dissolution.These clay units lacking a couplet structure wereassigned ‘bundle’ status because their thickness anddark recessive boundaries made them fit the generalpattern.
Also, units that are clearly bundled in one areamay lose their structure laterally. Thus a thin andonly vaguely bi-divided limestone in Fig. 3-right(21–22) is seen in Fig. 3-left to consist of two unitsof which the upper is divided into five couplets, and
152 B. D’Argenio et al. / Earth and Planetary Science Letters 160 (1998) 147–161
Fig. 3. Details of couplet=bundle syndrome. Quoted as 3-left and 3-right in the text.
has therefore been assigned to two bundles in ourcount. The rather similar limestone 25–26 appears toconsist of two bundles as well. Bundles 11 and 12appear as a single bundle, but its extraordinary thick-ness leads us to believe that here too bioturbation ofthe limestones has amalgamated a larger number oforiginal couplets.
The 26 bundles shown in Fig. 3-right have acombined thickness of 27.2 m for a mean bundlethickness of 104 cm.
The roughly 5 : 1 ratio of couplets to bundles,expressed in both carbonate content and redox con-ditions, suggests that the 20-cm cycle is that ofthe precession and the bundle cycle is that of theca. 100 ka eccentricity. In the Albian of Italy thislink is supported by the calculated mean sedimen-tation rates, but in the Angolan Eocene the lack ofbiostratigraphic data leaves such an interpretationunconfirmed.
4. Image processing
In order to improve over visual inspection whichmay be biased by the need for subjective choices andother factors such as parallactic distortion, we madeuse of a version of the Potsdam Advanced FilteringFacility (PAFF) specifically tailored to discriminatebedding patterns. A summary of these correctiveapproaches follows.
Images are characterised by a strong dilution ofthe information and by a noise component whichneeds to be removed to perform an optimal extrac-tion of the information. This is usually achieved bymeans of stationary filters (see [13] for a review) theuse of which is undermined by the fact that in mostimages the information is highly inhomogeneous andanisotropic. In the general case, let g and a be, re-spectively, the input and the output images, K isthe so called transfer function which is assumed to
B. D’Argenio et al. / Earth and Planetary Science Letters 160 (1998) 147–161 153
Fig. 4. (A) The digitized image after adaptive filtering. (B) Gray-level curve (from the filtered image (A)). (C) Gray-level column. (D)Correlation of the gray-level column with real (photographic) image.
154 B. D’Argenio et al. / Earth and Planetary Science Letters 160 (1998) 147–161
be deterministic (i.e. identical input images produceidentical output images) and n is the noise whichis characterised by stochastic disturbances (i.e. iden-tical inputs provide different outputs). The detailedmathematical form of K depends on the specific ap-plication and comprises all the factors which enterinto the acquisition chain; n depends instead mainlyon the characteristics of the detector and of the digi-tisation device. In what follows we will assume forconvenience a, g and n to be vectors of N 2 elements.This hypothesis, however, does not affect the generalvalidity of the results. In order to make such a fil-ter useful in practice, we must restrict it to a linearsystem (K being an N 2 ð N 2 matrix):
a D Kg C n (1)
i.e., the output is a linear combination of the inputvalues disturbed by additive noise. Real systems maydepart from this behaviour and various tricks areused to approximate them by linear systems.
Most tasks in image processing belong to oneof the following three categories: smoothing, imagerestoration and pattern enhancement and recognition.
Smoothing: i.e. removal of the noise n. It is usu-ally performed by means of stationary filters, i.e. lin-ear systems with impulse response (hereafter PointSpread Function D PSF) invariant all over the im-age. They have low pass characteristics and workproperly only if the spectrum of noise reaches higherfrequencies than the highest resolution features inthe image g, otherwise the higher resolution detailsin g are degraded and smeared. Most geological im-ages require resolution down to a few pixels and thisrenders stationary filters almost useless.
Restoration: i.e. removal of the blur K introducedby the acquisition chain. The most direct way toachieve this result is the inversion of Eq. 1 (inversefiltering):
g0 D K�1a D g CK�1n (2)
As it is clear from Eq. 2, the restored image g0 isnot identical to g but is degraded by the additiveterm K�1n because it is usually not orthogonal (andnot even regular). K�1 can therefore have terms solarge to render g0 practically useless. There are manyapproaches to overcome these problems (e.g. by in-troducing extra information or restricting conditionssuch as positiveness of the results, etc.) but, in any
case, it greatly helps to eliminate the noise beforerestoration.
Pattern enhancement and recognition: i.e. en-hancement of structures (such as lines, edges, etc.) inorder to make them recognisable by automatic meth-ods. Simple problems can be resolved by means ofsimple tricks (such as thresholding), but more com-plex ones require the use of high-pass filters whichenhance the high-resolution structures and suppressthe long-wave fluctuations. Almost all filters usuallyquoted in the literature (Sobel operators, Robertsgradients, etc.) have the following shortcomings: (1)they are stationary filters which means that they aresensitive only to a specific scale length of the signal;(2) they are high pass filters which enhance the high-est frequencies present in the images even if theydo not carry any useful information. However, thehighest frequencies are also those which are mostdegraded by the presence of noise. The best wayto avoid these problems is to build a space-variablefilter which smooths extensively in the lower-resolu-tion regions of the image and not at all in the high-est-resolution parts, i.e. a filter which recognises thelocal resolution and adapts itself to it. Such a filterwas first built for astronomical applications [14,15]and is shortly summarised in the following section.
5. The adaptive filter
Any image matrix can be represented by twosymmetric matrices: C1 D G GT and C2 D GT Gwhere C1 and C2 are the covariance matrices whichmeasure the covariance of lines and columns, re-spectively, of the image G. These matrices can bediagonalized by their eigenvectors:
C1 D UΛΛΛ UT and C2 D VΛΛΛ VT (3)
and G D UΛΛΛ � VT, where U and V are orthogonalmatrices, the columns of which are the eigenvectorsui and vi , respectively.
The transformed matrix will be a diagonal matrixhaving as elements the eigenvalues of G, whichcan be calculated as the roots of the characteristicequation of the Nth order in ½ with N real roots:
det.½I� C1/ D 0 (4)
The eigenvectors are therefore obtained from the
B. D’Argenio et al. / Earth and Planetary Science Letters 160 (1998) 147–161 155
2N linear equation systems:
.½i � C1/ui D 0 and .½i I�C2/vi D 0 (5)
The eigenvalue transform has an important prop-erty. If the ½i are ordered to form a decreasingfunction of i, the sequence defines the lower bound-ary of the respective functions of all possible trans-forms. This implies that if the smallest ½i are avoidedbecause they are assumed to be representative ofthe noise only, then the smallest possible deviationbetween the original image and the retransformedone is obtained, compared to all transforms cut tothe same number of coefficients (a property whichcomes out naturally from the mutual non-correla-tion of the ½i produced by the diagonalization). Dueto the fact that any correlation decreases the infor-mation content this also implies that each has thelargest possible information content ½i. The eigen-value transform therefore provides the filter whichoptimally concentrates the information. It requireshowever extremely large computation time (Eqs. 4and 5) and is of no use in practical applications.This problem can be circumvented by estimating theaverage or expected eigenvectors of a whole classof images and then transforming the images in thetraditional way. The transform matrix used in thiscase would not be exactly a diagonal matrix (as in-stead it is the case for ΛΛΛ), but a matrix where allthe elements which are not diagonal are negligiblysmall and the elements of the diagonal are not ex-actly decorrelated but almost so. This approach iscalled the Karhunen–Loeve transform. It needs to bestressed, however, that this transform is only as goodas the estimates of the expected eigenvectors, andthat usually these are derived from statistical models(e.g. a Gauss–Markov process) which can have verylittle to do with the properties of real images.
We introduce now another way to define an imagemodel for the Karhunen–Loeve transform. Insteadof transforming a whole image, we can divide itin blocks and transform these blocks separately. Inorder to be clearer, let us take the case of blocks oftwo pixels only (which are neighbours in x) and letg1 and g2 be the values registered in these two pixels.Now we make the following three assumptions:
(1) Neighbouring pixels are correlated: i.e. if wedraw every block as a point in the g1=g2 diagram,then they are strongly concentrated along the diag-
onal. Data can then be decorrelated by rotating thecoordinate system g1, g2 to the a1, a2 system bycomputing:
a1 D .g1 C g2/=p
2 and a2 D .g1 � g2/=p
2 (6)
where a1 and a2 are decorrelated and the variance ofa1 is much larger than that of a2.
(2) The correlation is isotropic in x and in y. Nowwe take into account square blocks of 2 ð 2 pixels inthe form:
1 2
3 4
where i D 1; :::; 4 are the indices of gi. Then theequivalent of the g1=g2 diagram would be a 4-dimen-sional diagram with again only the diagonal beingpopulated and the decorrelation transform would be:
h0 D 1=2.g1 C g2 C g3 C g4/
hx D 1=2.g1 � g2 C g3 � g4/
hy D 1=2.g1 C g2 � g3 � g4/
hc D 1=2.g1 � g2 � g3 C g4/ (7)
where h0 is the mean, hx and hy are the gradientcomponents, and hc is the curvature term.
(3) The correlation extends to larger pixel dis-tances with decreasing magnitudes. The above pro-cedure can be iterated but this would quickly lead touncomfortably high dimension g spaces. This, how-ever, can be avoided by taking into account that the2ð2 blocks are already decorrelated by the transformin Eq. 7, which can be treated as a first order of thetransform. We can therefore put the h0 values of fourneighbouring 2 ð 2 blocks into Eq. 7 instead of thegi and repeat the process until neighbouring higherorder blocks turn out to be no longer correlated.
The above steps define a complete orthogonaltransform which we called H-transform to honourHaar, due to the fact that it is the direct analogueof the 1-D Haar transform. However, it needs to beemphasised that our transform is different from the2-D Haar transform which is usually found in theliterature. This H-transforms allows to produce anadaptive filter. The first problem to solve is how toteach the filter how to disentangle noise and signal inthe input image. Let sit be the standard deviation ofthe coefficients of order i and type t .t D x , y or c)
156 B. D’Argenio et al. / Earth and Planetary Science Letters 160 (1998) 147–161
and k be a parameter (to be chosen by the user) whichfixes the ‘strength’ (or the signal-to-noise ratio) ofthe filter. We can define a threshold t, as:
t D sit Ð k (8)
and apply it to the transformed image: i.e. all gradi-ents and curvatures with absolute values smaller thatt are interpreted as noise and set to zero. Otherwisethey are taken as significant and left unchanged. Ifwe back-transform the product of this operation, weobtain an image which is smoothed in the regionsof low gradient (i.e. where there is no signal allgradients and curvatures are zero) and untouched inthose with high gradients (i.e. where there is a signalall gradients are significant). Intermediate cases aresmoothed accordingly. Up to now, we have alwaysassumed additive noise. Different noise statistics canbe dealt with by properly transforming the image in-tensities before filtering. For instance, the Anscombetransform for the Poisson noise, the logarithm formultiplicative noise, etc. The performances of the fil-ter can be tailored to the specific needs (for instancemorphological knowledge) by using more sophisti-cated ‘test’ conditions than the one introduced bymeans of Eq. 8. Before obtaining the final, restoredimage one more step is needed. The filtered imagehas a block-like appearance due to the adopted pro-cedure. In order to obtain cosmetically acceptableimages (even though it needs to be stressed thatthere is no variation in the information content ofthe image) the image needs to be smoothed. Weuse once more a recursive Kalman-like variable filtercontrolled by the H-filter.
So far, in this paper, the H-filter has been de-veloped as a transform-filter. Like stationary filterswhich usually are designed in the Fourier transformdomain, the H-filter can also be used as a localoperator and as a pattern enhancement tool.
6. Image analysis data
A portion of the exposed sequence was subjectedto time-series analyses via image analysis. Whereasthe visual study was largely confined to the lowerand middle parts of the sequence (Fig. 3-right) thetime-series study covered the middle and upper parts(Fig. 3-left, Fig. 4D).
Images on normal Kodak film were digitised byscanning with a Perkin and Elmer microdensitome-ter. The entire stratigraphic sequence was coveredwith several partially overlapping exposures whichwere then combined into a single digitised image.The first two steps of the data reduction involved (1)rectification of the image to correct for geometricalvignetting and (2) rotation of the image in order toalign the bedding with the image pixels.
In order to reduce noise, both intrinsic to the im-age (small interruptions in the strata, bushes, etc.)and introduced by the acquisition procedure, the im-ages were adaptively filtered. The resulting imagewas then filtered again with a linear adaptive filterworking in the X-direction only. This procedure al-lowed us to enhance the morphological informationcontained in the strata (Fig. 4A). From the result-ing image we extracted a 100 pixel vertical sectionhaving the highest signal=noise ratio and binned it toproduce a one-dimensional set of data (Fig. 4B,C).
6.1. The periodogram
The stratigraphic signal extracted was analyzedwith a spectral analysis package based on analyticaltechniques originally designed for astronomical ap-plications. This package includes pre-processing andspectral analysis based on the Scargle [16] algorithmwith the following characteristics.
(1) It deals with unevenly spaced data [16]; thischaracteristic is important because the rebinning ofunevenly sampled data, like the stratigraphic signals,into equally spaced bins and the following compu-tation of a conventional periodogram may alter thespectrum and the significance of a periodic signal.
(2) It discriminates between meaningful frequen-cies and spurious ones on a physical basis, by eval-uating the false alarm probability, i.e. an estimateof the significance of the height of a peak in thepower spectrum. This is possible only if the peri-odogram has an exponential probability distributionfunction, achieved by normalizing the periodogramwith respect to ¦ 2, i.e. the variance of the data [16].
(3) It reduces the effects of aliasing bias in thedata.
To be more detailed, let X .ti ), with i D1; 2; : : :; N0, be the time series data, sampled at dis-crete intervals, and PX .!/ the corresponding power
B. D’Argenio et al. / Earth and Planetary Science Letters 160 (1998) 147–161 157
spectrum at frequency !. The equation to calculatePX .!/ is:
PX .!/ D 1
2
8>>>><>>>>:
�Xj
X j cos!.t j � −/½2
Xj
cos2 !.t j � −/
C
�Xj
X j sin!.t j � −/½2
Xj
sin2 !.t j � −/2
9>>>>=>>>>;where − is defined as follows:
tan.2!t/ D
�Xj
sin 2!t j
��X
j
cos 2!t j
�and represents a term that makes the periodograminvariant to a shift in the zero point of the time scale.
7. Periodicities: comparison of approaches
The resulting power spectrum of stratigraphic pe-riodicities, expressed in centimeter-spacing of bed-ding signals derived from image analysis, is shownin Fig. 5. This clearly shows several peaks: a firstpeak at 320.3 cm is followed by a group of peaks(138.3, 112.7, 101.4, and 89.5 cm). A second sethas peaks of 79, 69.9 and 60.2 cm. Beyond this, sixpeaks ranging from 49.1 to 25.7 cm rise to slightlyabove noise level (values derived by using refer-ence marks in the original images which lead to aconversion factor of 50 mm per pixel).
In time-series studies carried on by electrical en-gineers or seismologists, the time element is known,and a given frequency will produce a single peak. Instratigraphical time series, the stratigraphic distancebetween beds is taken as a proxy for time, but thisproxy deviates markedly from the mean value as ac-cumulation rates oscillate. According to the strengthof such oscillation the final result on the periodogrammight be either the broadening of the spectral peaksor their splitting into two or more aliased frequen-cies. Individual peaks may therefore be attributable
to real signals, to combination tones, or to splittingcaused by variable accumulation rates.
7.1. Approach by image processing
In order to match the spatial values of the powerspectrum to the temporal units of astronomic fre-quencies [17,18], we compared the ratios of expectedorbital periodicities to the observed positions of thepeaks, following the procedure described in [19,20].In short, this is obtained by computing two tables ofadimensional ratios: one formed by the relative ratiosof each peak with respect to all the others, and thesecond one consisting of the relative ratios of eachexpected frequency with respect to the others. Thesetwo tables are then cross-correlated searching for thehighest correlation factor.
Present-day periodicities (Table 4) yield the bestmatch (correlation factor 0.998) to the dimensionalfrequency ratios observed in the power spectrum inthe column that sets the 100,000-year period as 1.This set of ratios ties to the spectral peak at 113cm. It closely approximates the 104-cm bundle ofthe visual analysis and identifies the 101-cm peakwith the 95,800 year eccentricity, the 60.2-cm peakwith the long obliquity, the 41.1-cm peak with theshort eccentricity, and the long component of theprecession with the peak at 25.7 cm, approximatingthe 20-cm couplet figure of the visual analysis. Inthis match the short precessional mode has left nosignificant signal in the power spectrum.
We assume that the highest energy peaks in thespatial domain are induced by time frequencies inthe 100 ka range (95.8 to 128.2 ka) then we cross-correlate each of the relative ratio sets in Tables 3and 4 with the relative ratios in Table 2, finding thematch which gives the highest correlation factor (re-ported in the last column of the Tables 3 and 4). Thethicker lines and light shaded areas mark the 100 karange of periodicities. The best matches are markedas solid boxes in Table 2 vs. Table 3 and as darkshaded boxes in Tables 2 and 4.
7.2. Comparison
Comparison of the visual approach data (coupletsand bundles) to the power spectrum (Fig. 5) yieldsstraightforward interpretations. As in the case of the
158 B. D’Argenio et al. / Earth and Planetary Science Letters 160 (1998) 147–161Ta
ble
2R
elat
ive
ratio
sets
for
the
obse
rved
spat
ial
freq
uenc
ies
(in
cm)
B. D’Argenio et al. / Earth and Planetary Science Letters 160 (1998) 147–161 159
Fig. 5. The power spectrum obtained from the curve shown in Fig. 4C.
Table 3Relative ratio sets for the estimated orbital frequencies (in yr) in the Eocene (values from Berger et al. [17,18])
403800 128200 100000 95800 48750 38200 22200 18350 corr. fac
Italian Albian the highest peaks in the spectrum cor-respond to the ca. 100 ka eccentricity; the visualapproach finds only one frequency, at 104 cm, but
time-series analysis splits the peak into its two maincomponents, at 101 and 114 cm. The visual ap-proach failed to identify obliquity signals, whereas
160 B. D’Argenio et al. / Earth and Planetary Science Letters 160 (1998) 147–161
frequencies in this intermediate range are apparentin the power spectrum. As in the case of the ItalianAlbian, the precessional periodicities, so apparent inthe visual approach, are only weakly represented inthe spectrum, and only by one (26 cm) peak insteadof the two frequencies to be expected. The visualpeak at ca. <0.20 cm is presumably a compromisebetween both. This lack of resolution in the powerspectrum is attributable to the sensitivity of the ma-chine approach to the distortion of the time axis, byvariations in sedimentation rate.
8. Conclusions
8.1. Timing and setting
The sedimentary sequence exposed at Cabo SaoBraz is of Middle Eocene (Lutetian) age, belongingto nannofossil zone cp13b. The cyclostratigraphyyields a duration of 46 bundles D 46 eccentricitycycles or 4.6 million years. The foraminiferal faunaindicates cold upwelling water, and suggests that theBenguela Current and upwelling already existed inEocene time.
8.2. Cyclicity
Bedding cyclicity in the Eocene Cunga-GratidaoMarls reflects oscillations in the carbonate=detritalratio, coupled to a seafloor redox cycle reflectedin the trace fossil assemblage. The couplet=bundlestructure is much like that in the Aptian–AlbianScisti a Fucoidi of central Italy [1–4,21], wherethe couples represent the precessional cycle and thebundles correspond to the 100-ka eccentricity cy-cle. Cunga-Gratidao couplets and bundles are abouttwice as thick as are the pelagic ones. The supplyrates of carbonate and of terrigenous matter appearto have fluctuated independently.
Visual interpretation of the photographs was am-plified and tested by an image processing programinvolving adaptive filtering, and the extraction of apower spectrum. Comparison of the visual interpre-tation with the power spectrum and the ratio calcu-lations yields a good match to the orbital periods.The image analysis program improves on the visualapproach by splitting the ca. ³100-ka eccentricity
peak into its two major components, and revealswhat appears to be an obliquity peak. As in the caseof the Italian Albian, the visual approach yields abetter appreciation of the precessional (couplet) cy-cle: the machine is far more sensitive than the eye tothe distortions introduced into the time axis by thedeviations introduced by variations in sedimentationrate. Like the power spectra of the Italian Albian, im-age analysis fails to record the 400-ka eccentricity,resolves the double peak of the 100-ka eccentricitycycle, and records the short obliquity cycle.
We conclude that the Mid-Eocene sediments atCabo Sao Braz responded to orbital forcing in sev-eral ways, involving the contribution rates of eoliandetritus and of pelagic carbonate as well as variationsin the intensity of the oxygen minimum, possibly re-lated to variations in upwelling.
Acknowledgements
We wish to thank Edoardo Morais and the Depart-ment of Geology of the University A. Neto, Angola,for the help during field work at Cabo Sao Brazand for warm hospitality. We gratefully acknowledgethe coccolith determinations provided by Drs. DavidBukry and Steve Percival. B. D’Argenio thanks theCooperazione Italiana (Ministero Affari Esteri) forsupport of his teaching and research in Angola in theyears 1991–1993. Last but not least we are gratefulto our reviewers, A. Berger and L.J. Lourens, fortheir helpful comments. [RV]
References
[1] A.G. Fischer, T.D. Herbert, G. Napoleone, I. Premoli Silva,R. Ripepe, Albian pelagic rhythms (Piobbico core), J. Sedi-ment. Petrol. 62 (1991) 1146–1172.
[2] P.L. de Boer, Cyclicity and storage of organic matter inMiddle Cretaceous sediments, in: G. Einsele, G. Seilacher(Eds.), Cyclic and Event Stratification, Springer, Heidel-berg, 1982, pp. 456–475.
[3] T.D. Herbert, A.G. Fischer, Milankovitch climatic origin ofmid-Cretaceous black shale rhythms in central Italy, Nature321 (1986) 739–743.
[4] M.E. Tornaghi, I. Premoli Silva, M. Ripepe, Lithostratig-raphy and planktonic foraminiferal biostratigraphy of theAptian–Albian ‘Scisti a Fucoidi’, Piobbico core, Marche,Italy: background for cyclostratigraphy, Riv. Ital. Paleontol.Stratigr. 95 (1989) 223–264.
B. D’Argenio et al. / Earth and Planetary Science Letters 160 (1998) 147–161 161
[5] W.G.H. ten Kate, A. Sprenger, Orbital cyclicities above andbelow the Cretaceous=Paleogene boundary at Zumaya (NSpain), Sediment. Geol. 87 (1993) 69–101.
[6] L.J. Lourens, F.J. Hilgen, Long-periodic variations in theEarth’s obliquity and their relation to third-order eustaticcycles and Late Neogene glaciations, Quat. Int. 40 (1997)43–52.
[7] H.M. Bolli, W.B.F. Ryan, B.K. McKnight, H. Kagami, M.Melguen, W.G. Siesser, J. Natland, J. Longoria, F. ProtoDecima, J. Foresman, W. Hottman, (Eds.), Initial Reportsof the Deep Sea Drilling Project 40, 1975.
[8] H.M. Bolli, Saunders, K. Perch-Nielsen, Plankton Stratigra-phy, vol. 1, Cambridge University Press, Cambridge, 1985.
[9] R.M. Steinforth, Applied micropaleontology in coastalEcuador, J. Paleontol. 22 (1948) 113–151.
[10] C.E. Savrda, D.J. Bottjer, Trace fossil model for recon-structing oxygenation histories of ancient marine bottomwaters: application to Upper Cretaceous Niobrara Forma-tion, Colorado, Palaeogr. Palaeoclimatol. Palaeoecol. 74(1987) 49–74.
[11] I. Premoli Silva, E. Erba, APTICORE–ALBICORE; Aworkshop on Global Events and Rhythms of the Mid-Cre-taceous, Perugia, 4–9 October, 1992 (abstr.).
[12] O. Amore, P. De Capoa, M.L. Duarte-Morais, I. Sgrosso, D.Staiti, Preliminary Biostratigraphical notes and reworkingevidence on the Mesozoic and Tertiary sediments, IAS 15thRegional Meeting, Ischia, 13–15 April, 1994 (abstr.).
[13] T.S. Huang (Ed.), Picture Processing and Digital Filtering,Springer, Berlin, 1979.
[14] G.M. Richter, Zur Auswertung astronomischer Aufnahmenmit dem automatischen Flachenphotometer, Astron. Nachr.299 (1978) 283.
[15] G.M. Richter, P. Bohm, H. Lorenz, A. Priebe, M. Capac-cioli, Adaptive filtering in astronomical image processing,Astron. Nachr. 312 (1991) 24.
[16] J.D. Scargle, Studies in astronomical time series analysis II,Statistical aspects of spectral analysis of unevenly spaceddata, Astrophys. J. 263 (1982) 835–853.
[17] A. Berger, M.F. Loutre, V. Dehant, Astronomical frequen-cies for pre-Quaternary paleoclimate studies, Terra Nova 1(1989) 474–479.
[18] A.F. Berger, M.F. Loutre, J. Laskar, Stability of the astro-nomical frequencies over the earth’s history for paleocli-mate studies, Science 255 (1992) 560–566.
[19] G. Longo, B. D’Argenio, V. Ferreri, M. Iorio, Fourier ev-idence for high frequency astronomical cycles recorded inLower Cretaceous carbonate platform strata. Monte Mag-giore Southern Apennines, Italy, IAS Spec. Publ. 19 (1994)77–85.
[20] M. Brescia, B. D’Argenio, V. Ferreri, G. Longo, N. Pelosi,S. Rampone, R. Tagliaferri, Neural net aided detection ofastronomical periodicities in geologic records, Earth Planet.Sci. Lett. 139 (1995) 33–45.
[21] P.L. de Boer, A.A.H. Wonders, Astronomically inducedrhythmic bedding in Cretaceous pelagic sediments nearMoria (Italy), in: Berger et al. (Eds), Milankovitch andClimate, Reidel, Dordrecht, 1984,
