The practicality of vertical shells as paleobathymetric markers

REX E. CRICK Department of Geology, University of Texas at Arlington, Arlington, Texas 76019

ABSTRACT the shell, total volume of the shell, density motion to describe the sinking behavior of of sea water, and shell geometry, the the shells of Nautilus by applying the phys- The depth to which an intact coiled observed sinking behavior of Nautilus can ics of the sinking of hollow, rigid bodies. cephalopod shell will sink with its plane of be duplicated experimentally using equa- Experiments using shells of Nautilus yielded symmetry vertical is related to shell geome- tions developed by Weaver and Chamber- sinking velocities in agreement with their try. Equations that relate shell geometry to lain (1976) and Chamberlain and Weaver calculated values and also showed that the physical constants of pressure, sea-water (1978). Given that the earliest coiled cepha- orientation of a sinking Nautilus shell varies density, and gravity yield the maximum lopods had shell construction similar to that as the phragmocone fills with water. With a depth of stable verticality of a shell. Water of Nautilus (Flower, 1964; Mutvei, 1972) small negative buoyancy, the shell sinks depths calculated from the geometries of and assuming that constants such as atmos- with its plane of symmetry upright (verti- vertical shells of Cymatoceras hilli (Shat- pheric pressure, acceleration of gravity, and cal), but as the phragmocone fills, the shell tuck), Drakeoceras drakei Young, and density of sea water have not changed sig- begins to rock from side to side until the Mortoniceras wintoni (Adkins) from the nificantly during the Phanerozoic, the phragmocone is about 55% full, at which Fort Worth Formation (Upper , necessary parameters (total volume of the point the shell leans over and sinks with its ) of north-central Texas are used to shell and shell geometry) can be measured plane of symmetry horizontal. Weaver and reconstruct a portion of the paleobathyme- or estimated with sufficient precision to Chamberlain were also able to refute the try of the East Texas Embayment during allow for the description of the sinking common argument that vertical shells may late Fort Worth time. The maximum water behavior of the coiled shells of fossil result from embedding upon impact with depth to which shells with these geometries . In their experimental work, the bottom. The observed and calculated would have sunk with the plane of symme- Weaver and Chamberlain (1976) and sinking velocity of a Nautilus shell was try vertical range from 1.6 m for the least Chamberlain and Weaver (1978) placed shown to be approximately 30 cm/sec, a stable shell geometry (£). drakei) to 2.6 m emphasis on the behavior of the shell during velocity too slow to cause embedding upon for the most stable shell geometry (C. hilli). actual sinking because it is during this por- impact. They were able to show empirically Water depths were deeper than 2.6 m at tion of the post-mortem history that shell that the maximum depth to which Nautilus localities where no vertical shells were ob- geometry determines the attitude of a shell sinks in a vertical position ranges from less served and shells with the plane of symmetry at the time of burial. This statement than 7 m for rapidly filling shells to as much horizontal showed no evidence of being assumes that other physical constants were as 600 m for slowly filling shells. In the lat- reworked from the vertical orientation. invariable or nearly so. Thus, a coiled shell ter case, however, the shell will quickly of a given geometry, mass, and volume will, assume a horizontal orientation because it if the shell maintains its integrity, pass will continue to fill after reaching bottom INTRODUCTION through a series of events that can be de- and the stability of the vertical shell will be scribed using equations of motion in sink- removed within a few hours or a few days, For most shell-bearing , death is ing. If, during its descent through the water depending on depth. Chamberlain and followed by a fairly mundane set of events, column, the shell reaches bottom in a verti- Weaver (1978) modified the equations in- but post-mortem history of the chambered cal position and remains in this position troduced in their 1976 paper to allow for cephalopod Nautilus is far more spectacular long enough to be preserved, reasonable variations in shell geometry, the mass of the than that of other important marine inver- estimates of maximum water depth can be shell, and the total volume of the shell (shell tebrates. After death, gases released during calculated. material plus camerae). By incorporating decay of the visceral mass (including the the effects of hydrodynamic stability and siphuncular cord) often increase the buoy- Weaver and Chamberlain (1976) tested loss of buoyancy during sinking, they were ancy of the shells (if not already of positive ideas put forth by Reyment (1958, 1970) able to calculate sinking velocity and pres- buoyancy) so that they rise to the surface of and Raup (1973) concerning the presinking sure across the shell wall as a function of the water, where they float until stranded and postsinking history of coiled shells and depth for shells of any size and shape. The near a shoreline or become waterlogged and did so by using shells of Nautilus to describe results of this analysis indicated that the sink. Due to the relationships between the sinking behavior of chambered shells. largest single source of variation in the acceleration of gravity, buoyancy, mass of They were able to derive equations for

Geological Society of America Bulletin, v. 94, p. 1109-1116, 7 figs., 1 table, September 1983.

1109

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observed and calculated depth limits of tions derived from equations used by naval Filling of the Shell shells is the geometry of the shell. Although architects and others to describe motions in the mass and total volume of the shell may the sinking of hollow, rigid bodies. Only the If the integrity of a shell has not been lost vary from shell to shell and from taxon to equations necessary for the calculation of as it sinks (no breakage of the phragmo- taxon, these differences are so slight that depth estimates are discussed below. The cone), filling will occur in one of two ways: they do not noticeably affect the depth reader is directed to Weaver and Chamber- rapid or slow. During rapid filling, the gas limit. Thus, as Raup (1973) suggested, shell lain (1976) and Chamberlain and Weaver contained in the shell will be trapped and geometry as it describes the stability of the (1978) for the derivation of these equations. the influx of fluid into the camerae will be shell is the key to estimating water depth In their experiments, Chamberlain and proportional to the pressure difference from a vertical shell. Weaver (1978) considered an incompres- between the external fluid (sea water) and Aside from occasional published reports sible shell sinking from the surface of a the internal gas. If the siphuncular tube has prior to 1958 of coiled cephalopod shells stationary fluid (sea water) of constant den- deteriorated, leaving a conduit for the found preserved in a vertical position, sity. This was done for convenience, with entrance of sea water through the open sep- Reyment (1958) was the first to report on full knowledge that sea water is not motion- tal necks, the pressure difference will be the phenomenon as it relates to the distribu- less and that its density varies slightly as a small and the shell can be said to fill rapidly. tion and buoyancy of fossil cephalopods. function of salinity and temperature. The Sinking by rapid filling was probably a rare Although Reyment made no prediction of variation in these factors, however, did not event because well-preserved shells com- water depth, he did recognize that all occur- prove large enough to introduce a signifi- monly show that the siphuncle was intact at rences were in facies he believed to be cant error in their calculations. It was also the time of fossilization. Slow filling, shallow-water and which quite possibly assumed that the chambers of the shell con- whereby sea water moves slowly through represented strandline deposits. Reyment tained an ideal gas and an amount of exter- the wall of the siphuncular tube by diffu- (1970) later examined a number of cephalo- nal fluid (sea water) that had entered by sion, was probably the common mode of pod-bearing localities unrelated in space diffusion through the wall of the siphuncu- filling for most shells (Collins and Minton, and time for the presence of vertical shells. lar tube. 1967). Owing to the slow addition of weight At each locality, he was able to document as the shell sank, stability would have been that at least a few coiled ammonites or nau- prolonged to a much greater depth. How- ever, if a shell reached the bottom under tiloids were in a vertical orientation as a q«0 result of the shell coming to rest on the bot- conditions of slow filling in water deeper & than the lower limit of its vertical stability, tom under conditions whereby verticality was sustained either by rapid burial or pro- I filling would have continued and the verti- longed buoyancy plus a rate of sedimenta- cal stability of the shell would have been tion sufficient to anchor the shell in a 6 lost within hours or days (Chamberlain and vertical position. However, Reyment's hy- J Weaver, 1978). pothesis that "almost any ammonite locality Chamberlain and Weaver (1978) found it will sooner or later yield vertically im- q-0.07 convenient to describe the filling of a shell bedded ammonite shells, likewise for nauti- (9 as it sinks by a dimensionless parameter (q) loids" (Reyment, 1970, p. 110) must be that describes the fill fraction of the shell rejected in light of what is now known and is an index of the extent to which the about the post-mortem history of the coiled phragmocone is filled in excess of that shell. required to produce neutral buoyancy. The The purpose of this paper is to demon- parameter ranges from q = 0 for neutrally strate the degree to which the equations of q»0.37 CP buoyant shells to q = 1 for shells completely Chamberlain and Weaver (1978) combined filled with water (Chamberlain and Weaver, with the occurrence of coiled ammonoid 1978). and shells preserved with their plane of symmetry vertical can be used to Stability describe the paleobathymetry of entombing sediments. The cephalopod fauna of a por- As Raup (1973) suggested and Weaver tion of the Fort Worth Formation (Lower and Chamberlain (1976) demonstrated, the Cretaceous, Comanchean-Albian) of north- stability of the shell is the factor that plays central Texas is used to illustrate this point. the major role in controlling sinking behav- Figure 1. Sinking behavior of a Nautilus ior. As a shell of Nautilus fills with water CALCULATION OF shell due to the loss of stability from the during sinking, the accompanying loss of DEPTH ESTIMATES influx of water entering the shell through stability causes the shell to begin a rocking the siphuncular tube. At q = 0, the shell is sequence at q - 0.07 (^0.75 m) and to The physics necessary to describe the stable and the plane of symmetry is vertical. assume a horizontal position at q - 0.37 (^9 sinking behavior of a coiled and chambered The onset of rocking beings at q- 0.07, and m) (Fig. 1). The onset of rocking and horiz- shell has been elegantly related by Weaver at q - 0.37 the plane of symmetry is horizon- ontality results in significant, but predicta- and Chamberlain (1976) and Chamberlain tal. From Figure I of Chamberlain and ble, departures from a calculated sinking and Weaver (1978) through a series of equa- Weaver (1978). velocity because the general equation of

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Figure 2. Stability diagram for coiled cephalopod shells 0 0.2 0.4 0.6 as where the stability coefficient (Ks) is expressed as the ratio between WandD. Filled circles,^ as a function of Wm&D.

Empty circles, Ks calculated using equation 1. W = 1/D defines a line that separates shells with overlapping whorls from shells with whorls that do not overlap. Modified from Figure 19 of Raup (1967).

the relative distance between the generating curve and the axis of coiling. See Raup (1967, p. 44) for discussion of the calcula- tion of these parameters. Thus, as D increases relative to W (increasing involute- ness), the centers of mass and buoyancy are brought closer together and the shell be- comes less stable (body-chamber length constant). This relationship is illustrated in Figure 2, where the isopleths record the change in stability with varying values of W motion (Chamberlain and Weaver, 1978, shells of equal shape will elicit the same and D. Again, stability is expressed as the p. 676) assumes no change in orientation sinking behavior regardless of the size of the ratio of the distance between the centers of during sinking. shell (Chamberlain and Weaver, 1978). mass and buoyancy and the total diameter It has been repeatedly demonstrated that The stability of Nautilus is known empir- of the shell. Also plotted in Figure 2 are the stability of a coiled shell, where stability ically (Weaver and Chamberlain, 1976; stability values computed from equation 1 is measured as the ability of a shell to main- Chamberlain and Weaver, 1978), and the (circles) and those from calculations of W tain a vertical orientation in a column of stability of any shell can be compared to and D (dots) for Nautilus and three Cre- water, is dependent primarily on the dis- Nautilus by the equation taceous cephalopods from north-central tance between the center of mass and the Texas. Differences between the results of = the two methods of determining stability are center of buoyancy (approximated by the C$ Ksn/Kstli (1) degree of evoluteness of the shell) and body slight and indicate that If and D are reason- able estimates of shell stability and that chamber length (Trueman, 1941; Raup, where Cs is the stability coefficient, Ksn is their use in this regard will provide accurate 1967; Raup and Chamberlain, 1967; Mutvei the stability constant for Nautilus, and Ksa and Reyment, 1973; Reyment, 1980). If the is the stability constant for another shell. As stability constants (Ksa).

length of the body chamber is constant (or Nautilus will be Cs times as stable as the nearly so) relative to shell diameter (the shell being compared, the drag force re- Depth Estimates usual case for related genera from the same quired to rock this shell will be C/1 times stratum), then the degree of evoluteness will the drag force necessary to cause rocking in Equations 2 and 3 are equations 27 and be the primary variable determining the rel- Nautilus, and so forth. The stability con- 28 of Chamberlain and Weaver (1978) and ative stability of various genera. That is, if stant Ksa for any shell can be obtained by define depths corresponding to the onset of the two centers are close together (an invo- first measuring the diameter of the shell and rocking (Zr) and horizontality (Z/,): lute shell) and the body chamber is at least then calculating the center of gravity and one whorl in length, stability is low. An evo- buoyancy using equations 8 and 9 of Raup Zr = grPo/[pg(Q-qr) ] (2) lute shell (centers more widely separated) and Chamberlain (1967). Ksa is then calcu- and with a body chamber of equal length (rela- lated by E/d, where E is the distance Zh =

of similar shape, sinking behavior is inde- coiled shell as a function of its linear dimen- At depths less than Zr, a shell is stable pendent of size. This is basic because it sions: W, which describes the whorl expan- and vertical. At depths greater than Z/,, a establishes that a given amount of filling in sion rate of a shell, and D, which describes shell is unstable and horizontal. In the

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strictest sense, Zr is the maximum depth at THE FORT WORTH LIMESTONE: tion from the subsurface suggests that the which a shell would remain vertical on the A CASE FOR SHALLOW WATER embayment opened to the Gulf of Mexico sea floor. However, estimates of maximum southeasterly between the southern end of

water depth (Ze) presented here are one-half The Fort Worth limestone, a member of the Sabine Uplift and the Stuart City car- of the calculated depth for 2/, for the follow- the Washita Group (Lower Cretaceous, bonate complex (Cook and Bally, 1975; ing reasons. As a shell descends from Zr to Comanchean-Albian), crops out in a nar- Murray, 1961). Zh, its plane of symmetry passes through row belt that extends from the Red River The Fort Worth limestone varies little in 90° (from vertical to horizontal) and there- (Texas-Oklahoma boundary) south toward thickness along strike, commonly crops out fore the plane of symmetry could form any Waco, Texas (Fig. 3). The outcrop belt in planar exposures in stream beds, and angle between 90° and 0° with the sea floor, approximates the western margin of the contains abundant specimens of the ammo- depending on the depth at which a shell East Texas Embayment during late Co- nites Mortoniceras wintoni (Adkins) 1918 becomes anchored (if less than Zf,). At manchean-Albian time. This embayinent and Drakeoceras drakei Young 1957 and angles greater than 45°, possibilities for occupied a salient that had formed earlier as the nautiloid Cymatoceras hilli (Shattuck) reworking a shell to the vertical position by the Ouachita Fold System changed from an 1903, in addition to a varied bivalved- organic or physical processes are many. At east-west trend to a north-south trend. The gastropod-echinoid assemblage. angles less than 45°, the chances that a shell northern margin of the embayment was Working only planar exposures, 336 spec- would be anchored in such a way as to pre- defined by the remnants of the fold belt, the imens were observed and collected from 17 vent its assuming a horizontal orientation western margin was defined by the Central localities (see Fig. 7 below for the location once buoyancy was removed are considera- Texas Platform and the North Texas Shelf, of collecting sites). Of these, 51 specimens bly less. It may be difficult, if not impossi- the eastern margin was the Sabine Uplift, from 11 localities were vertical. All speci- ble, to differentiate between shells that were and in the south, the San Marcos Arch or mens were taken from the upper 10 to 15 cm anchored in a vertical orientation at depths Platform to the southwest and the Stuart of the Fort Worth limestone at the contact less than or equal to Zr and shells that may City carbonate complex to the southeast. with the overlying Denton marl. The orien- have come in contact with the sea floor at Circulation in the embayment (in some tation of each vertical shell relative to north depths greater than Zr but less than Ze and sense, a back-reef environment) alternated was recorded before the shell was removed reworked to a vertical orientation. It seems between an open and a restricted system, as from the outcrop with the aid of a portable prudent, therefore, to state estimates of evidenced by the succession of carbonate rock saw. Mortoniceras wintoni (moder- maximum water depth in terms of Ze. build-ups along the shelf margin. Informa- ately evolute form with a square to rectan-

Figure 3. Early Cre- taceous (Comanchean- Albian) geography of Texas. Outcrop pattern of Washita Group in north-central Texas shown as solid black. For a description of the major physiographic fea- tures, see Murray (1961). Modified from Figure 3 of Young (1972).

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gular whorl cross section) was the most the phragmocone of sea water required to sonal observation). This infilling is related abundant, whereas Drakeoceras drakei induce sinking. to holes that formed in the shell by solution (similar to M. wintoni except in aspects of Shells near neutral buoyancy coming to or by boring organisms and that help to ornamentation and by being more involute) rest on the bottom of a shallow body of create a small but effective draft. Under and Cymatoceras hilli (involute generally water might, at first, display a random conditions of draft filling, a shell would subglobular with a rounded whorl section) orientation with respect to the prevailing have remained vertical only if it was occurred in near-equal numbers. current directions. It would be expected, anchored by sediment within the body however, that the shells would have reor- chamber or by some other means. Evidence of Verticality iented their plane of symmetry normal to Of the 51 vertical shells (Mortoniceras the direction of the prevailing current wintoni, 26; Drakeoceras drakei, 11; Cy- There is abundant evidence at each sam- (greatest surface area exposed to the force matoceras hilli, 14), most were oriented with pling locality that the original sediment was of the strongest current). Unless there were the plane of symmetry aligned in a north- extensively bioturbated by the large echi- large differences in the coiling geometry of a northwest-south-southeast direction at noids Hemiaster elegans and Holaster sim- shell, the aperture would have an equal each locality, suggesting orientation by cur- plex. Judging from the size of these echi- opportunity of lying to the right or to the rents (Fig. 4). Forty-two shells were pre- noids and the density of burrows on the left of the force of the current. served with living chambers down and outcrop, it is quite possible that shells with Geopetal features within shells provide slightly rotated so that the apertural mar- an original orientation other than vertical the most conclusive evidence regarding the gins were located 5° to 15° from the could have been reworked into a vertical or original orientation of shells at the time of expected life position. Of the remaining nine near-vertical orientation. Fortunately, there primary burial. These features, which are shells, three were preserved with the living are several useful criteria that aid in deter- related to the sedimentary infilling of the chambers approximately 180° from life mining the original orientation of a cepha- chambers of shells as they sat vertical or lay position and six were preserved with living lopod shell at the time of its burial. These horizontal on the bottom, have been de- chambers at various positions other than are: (1) orientation of the aperture with scribed and discussed by Seilacher (1968, those described. There was no preferred respect to observed attitude of the shell, 1971). Of the nine expected series of events position of apertures with respect to the (2) a nonrandom orientation of vertical or routes that a shell can follow before final presumed direction of the current flow shells presumably reflecting the dominant burial (Seilacher, 1971, Fig. 1), routes 3, 5, (Fig. 4). This is the expected situation, direction of currents, and (3) geopetal 6, 7, and 8 are the easiest to detect and are because the geometries of the shells of these features preserved in the interior of the common in the Fort Worth cephalopods. three genera are such that the aperture shell. The type of geopetal features that are most would have had an equal opportunity of The body chamber and aperture should useful are laminae that form as sediment is lying to the right or to the left of current be near that of life position if the vertical pulled into camerae by draft filling (intra- direction. orientation is primary. In fact, Reyment cameral draft stream created by external Examination of the interior of the 51 ver- (1980) has shown the expected position of turbulence) through constricted siphuncular tical shells for evidence of original orienta- the aperture would be rotated a few degrees openings (route 3 of Seilacher, 1971). tion revealed that 42 shells (22 Morton- away (upward) from that of the living Although this would seem to be the most iceras wintoni, 1 Drakeoceras drakei, and due to a combination of body- uncommon means of infilling, it appears to 13 Cymatoceras hilli) had settled to the bot- chamber length and the distribution within be the most common (Seilacher, 1971; per- tom with the plane of symmetry normal to

Figure 4. An example of the preferred compass orien- tation of vertical shells. Denton- Fort Worth Alignment of the plane of contact symmetry of 11 of 14 shells in the same general direc- Fossil Creek tion on two bedding sur- faces at one locality sug- gests orientation by currents rather than organic activity. Arrows indicate the direc- tion of aperture orientation. C, Cymatoceras hilli; D, Drakeoceras drakei; M, Mor- toniceras wintoni. Locality, Cobb's Park, Fort Worth.

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TABLE 1. DEPTH ESTIMATES AND VALUES REQUIRED TO DESCRIBE SHELL GEOMETRY AND STABILITY

Genus W D Cs Zh ze

Drakeoceras drakei 1.71 0.491 0.100 1.50 0.49 3.25 1.63 Mortoniceras wintoni 2.13 0.38:: 0.125 1.20 0.61 4.42 2.21 Cymatoceras hilli 2.43 0.059 0.140 1.07 0.69 5.23 2.62 Nautilus pompilius 3.33 0.047 0.150 1.00 0.75 5.82 2.91

Note: W = whorl expansion rate; D- a measure of the distance separating generating curve and axis of coiling; Ks - stability constant; Cs = stability coefficient; Zr - depth for onset of rocking (in metres); Z^ = depth of horizontally (in metres); Zt - estimated maximum depth of verticality (in metres).

kei, contained laminae in the interior of the Of the 285 horizontal shells from the 17 shell. Alignment of these laminae parallel localities, 153 were suitable for sectioning. with the original bedding surface (see Fig. 5) When sectioned in the plane of symmetry, placed the shells in an orientation whereby 36 shells from 4 of the 11 localities having Figure 5. Geopetal features of the type the living chamber was down and the aper- vertical shells contained laminae that would used to determine primary orientation of ture was within 10° of presumed life posi- have had to have formed while the shell was shells. Diagram of a sectioned Mortoniceras tion. Before reorientation, the living cham- in the vertical position. The horizontal wintoni showing the attitude of laminae bers of the shells were 80° and 55° from life orientation of these 36 shells was, therefore, formed during the infilling of the body position. These secondary orientations pre- secondary (route 7 of Seilacher, 1971). The chamber and phragmocone of a vertical sumably were the result of reworking of the remaining 117 shells contained either geo- shell. Cessation of infilling resulted in the surrounding sediment by the bottom fauna. petal structures indicating that horizontally absence of laminae in some chambers and in When sectioned in a plane normal to the was primary (routes 5 and 6 of Seilacher, portions of others. plane of symmetry, the remaining seven 1971) or no discernible geopetal structures shells contained laminae that indicated that at all. This suggests that for the six localities bedding and had remained in this position the plane of symmetry was parallel to where vertical shells were not observed (no long enough to be buried and preserved bedding when infilling occurred (route 8 of sampling bias suspected) the water depth (route 3 of Seilacher, 1971). When sectioned Seilacher, 1971). Verticality of these shells for latest Fort Worth time was deeper than in the plane of symmetry, two of the remain- was, therefore, secondary and presumably the limit of verticality for the most stable ing nine shells, a M. wintoni and a D. dra- due to reworking of the sediment. shell geometry present at these localities.

Sinking Velocities cm/sec

Figure 6. Sinking velocities as a function of depth for shells with geometries of Nautilus pompilius, Cymatoceras hilli, Mortoniceras wintoni, and Drakeoceras drakeL Solid line, stable

vertical sinking at depths less than Zr. Dashed line, unstable sinking with rocking. Sinking curves terminate when all vertical stability is lost and plane of symmetry of shell is horizontal (Zfi). Ze marks the maximum depth at which a shell would assume a vertical or near-vertical orientation if

it contacted the bottom during sinking and maintained that buoyancy. Ze is used as the estimate of the maximum depth of verticality for a given shell geometry. Although slow filling is probably the common mode of filling {see Nautilus) for reasons discussed in the text, rapid filling is used for calculative and illustrative purposes. Data for A', pompilius taken from Chamberlain and Weaver 1000 (1978).

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OKLAHOMA Estimates of Depth - ' n • - ^ r The stability constants (Ks) and coeffi- -DMC (1.6 m) cients of stability (Cs) for the Fort Worth cephalopods and Nautilus pompilius are •DMC (1.6 m) listed in Table 1. Based on measurements taken from the shells, Drakeoceras drakei is the least stable (higher D, lower W) (see Fig. -dmc (> 2.6 m) 2 and Table 1), whereas Mortoniceras win- toni and Cymatoceras hilli are similar, -dmc (> 2.6 m) although their respective D values are con- siderably different. This emphasizes the •dMC (2.2 m) importance of If as a better measure of sta- •DMC (1.6m) bility because it describes the whorl expan-> dmc (>2.6 m) sion rate, which is the measure of the separation of the centers of mass and -dMC (2.2 m) buoyancy. Although C. hilli and N. pom- pilius have similar D values, they differ appreciably in values of W. -DMC (1.6 m) The maximum depths at which each of the Fort Worth cephalopod genera would Fort -DMC (1.6m) have been capable of sustaining a vertical or Worth- near-vertical orientation were calculated -dMC (2.2 m) using equations 1, 3, and Z/,/2. These depths are listed in Table 1 and compared in Figure 6. The solid portion of each curve in Figure -dmc (>2.6mï 6 describes the range of velocity and depth over which each shell would remain vertical •DmC (1.6 m) without rocking. The dashed portion of •mc (> 2.6m) each curve describes the range of velocity and depth corresponding to the onset of dmc (>2.6m) rocking (Zr) and horizontally (Z/,). Using these data, it is possible to state -mC (2.6 m) that the depth of water covering the carbon- ate sediment in which these cephalopods -dMC (2.2m) were buried was no deeper than approxi- mately 1.6 m if shells of Drakeoceras drakei were preserved in a vertical orientation, 2.2 m if shells of Mortoniceras wintoni were preserved in a vertical orientation, and 2.6 A. m if shells of Cymatoceras hilli were pre-

served in this position. That is, the Ze for vertical shells with the least stable shell

geometry (low Ks) becomes the estimate of A Fort Worth A1 I I Sea the maximum water depth for a given local- Level ity. This reasoning assumes that the pres- ence of horizontal shells with Ks values C. smaller than those of vertical shells was due to a water depth greater than the Ze of the Figure 7. Paleobathymetry along a portion of the western margin of the East Texas horizontal shells. These conditions were Embayment during late Comanchean-Albian time. A. Estimated water depths for 17 found to exist in the Fort Worth limestone sampling localities at the top of the Fort Worth limestone in north-central Texas. Values in at the localities indicated in Figure 7. parentheses are estimates of water depth (Ze) for the least stable shell geometry of shells Localities can be used as reference points found with the plane of symmetry vertical or nearly vertical. At localities where no vertical for contouring estimated water depths at shells were found, water depth is given as greater than the estimated depth for the most particular horizons, because it is possible to stable shell geometry present at these localities. B. Resulting paleobathymetric contours. assign an estimated maximum depth of C. Cross section along strike illustrating the relationship of submarine topography to sea water to a sampling locality if it contains level. C, c = Cymatoceras hilli (vertical, horizontal); D, d = Drakeoceras drakei (vertical, vertical shells and minimum water depth if horizontal); M, m = Mortoniceras wintoni (vertical, horizontal). it does not. Reference points and paleo-

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bathymetric contours for the top of the depths for sedimentary environments be- Brooklyn College of the City University of Fort Worth limestone are shown in Figures ginning with the Early (Areni- New York and New York City Aquarium, 7 A and 7B. The contours indicate that the gian) tarphycerids and extending through and Peter D. Ward of the University of water deepened to the east with a general the early Tertiary (Paleocene-Miocene) California at Davis for helpful discussions increase in depth from the Red River locali- aturids because it is reasonable to assume at various stages of this study. This work ties southward. Reversals in the general that the physical constants of atmospheric was funded by a grant from the Organized trend along strike exist and are to be pressure, acceleration of gravity, and den- Research Fund administered by the Univer- expected, as undoubtedly there were irregu- sity of sea water have not changed signifi- sity of Texas at Arlington. larities in the sea floor, as suggested by the cantly during the Phanerozoic. The limited

cross section of Figure 7C. distribution and low diversity of post- REFERENCES CITED

The paleobathymetry of Figure 7B agrees Miocene reduces the possibilities Chamberlain, J. A., Jr., and Weaver, J. S., 1978, Equations of motion of using these shells as paleobathymetric for post-mortem sinking of ccphalopod shells: Mathematical with the accepted regional geology of north- Geology, v. 10, p. 673-689. central Texas for Albian time (Cook and markers. Collins, D. H., and Minton, P., 1967, Siphuncular tube of Nautilus: Nature, v. 216, p. 916-917. Bally, 1975; Hendricks, 1967; Murray, 1961; The use of geopetal features to determine Cook, T. D., and Bally, A. W., eds., 1975, Stratigraphic atlas of North America: Princeton, New Jersey, Princeton University Young, 1972), although it significantly re- the orientation of shells at the time of" in- Press, 272 p. duces estimates of water depth. From the filling (their primary position) greatly facili- Flower, R. H., 1964, Nautiloid shell morphology: New Mexico Bureau of Mines and Mineral Resources Memoir 13, 79 p. limited sampling control presented here, it tates the use of coiled shells for determining Hendricks, L., 1967, Comanchean stratigraphy of the Cretaceous of north Texas, in Hendricks, L., ed„ Comanchean (Lower Cre- can be said only that along a portion of the water depth, because shells with the plane of taceous) stratigraphy and paleontology of Texas: Society of Eco- western margin of the embayment during symmetry either vertical or horizontal to nomic Paleontologists and Mineralogists, Basin Sec- tion, Pub. no. 67-8, p. 51-63. latest Fort Worth time the water depth was bedding can be used for this purpose. This Murray, G. E., 1961, Geology of the Atlantic and Gulf Coastal Province generally less than 2.6 m. This strongly sug- of North America: New York, Harper and Brothers, 692 p. eliminates potential biases in the estimates Mutvei, H., 1972, Ultrastructural studies on cephalopod shells—Part I, gests that waters covering the north Texas for depth that might result from observa- The septa and siphonal tube in Nautilus: Bulletin of the Geological Institutions of the University of Uppsala, new ser., Shelf and parts of the central platform tions of reworked shells. v. 3, p. 237-261. (Fig. 3) were exceedingly shallow at this Mutvei, H., and Reyment, R. A., 1973, Buoyancy control and siphuncle The 17 planar exposures located at the function in ammonoids: Palaeontology, v. 16, p. 623-436. time. Aside from occasional references to Raup, D. M., 1967, Geometric analysis of shell coiling: Coiling in top of the Fort Worth limestone (Lower ammonoids: Journal of Paleontology, v. 41, p. 43-65. the water depth of the Fort Worth sedimen- Cretaceous, Comanchean-Albian) of north- 1973, Depth inferences from vertically imbedded cephalopods: tary environment as being "shallow" or Lethaia, v. 6, p. 217-226. central Texas provide a fair coverage of the Raup, D. M., and Chamberlain, J. A., Jr., 1967, Equations for volume "deep," G. Scott (1940) gave a depth range and center of gravity in ammonoid shells: Journal of Paleontol- carbonate sedimentary environment that ogy, v. 41, p. 566-574. of 15 to 40 m based on what he considered existed at the end of Fort Worth time along Reyment, R. A., 1958, Some factors in the distribution of fossil cepha- to be the optimum depth of water for the lopods: Stockholm Contributions in Geology, v. I, p. 97-/84. the western margin of the East Texas 1970, Vertically imbedded cephalopod shells: Some factors in the development of what R. W. Scott (1972) distribution of fossil cephalopods, 2: Palaeogeography, Palaeo- Embayment. The three species of coiled climatology, Palaeoecology, v. 7, p. 103-111. considered to be shelly, lime-mud substrate cephalopods present in the Fort Worth 1980, Floating orientations of cephalopod shell models: Palaeon- that was part of a level-bottom community. tology, v. 23, p. 931-936. Formation at these exposures have shell Scott, G., 1940, Paleoecological factors controlling the distribution and Although R. W. Scott (1970a, 1970b, 1971, mode of life of Cretaceous ammonoids in the Texas area: Journal geometries sufficiently different to provide a of Paleontology, v. 14, p. 299-323. 1972) has dealt extensively with the Washita range of water depths and to allow the Scott, R. W., 1970a, Paleoecology and paleontology of the Lower Cre- units and their lateral equivalents both from taceous Kiowa Formation, Kansas: University of Kansas Paleon- assignment of a water depth to localities tological Contributions, Article 52 (Cretaceous 1), 94 p. a sedimentological and paleoecological 1970b, Stratigraphy and sedimentary environments of Lower where shells of at least one of these genera Cretaceous rocks, southern western interior: American Associa- viewpoint, he has been unable to establish occur with the plane of symmetry vertical or tion of Petroleum Geologists Bulletin, v. 54, p. 1225-1244. satisfactory estimate of water depth. The 1971, benthic communities in Washita rocks, horizontal to bedding. Estimates of water northeastern Texas: Geological Society of America Abstracts same can be said of other studies of similar with Programs, p. 244-245. depth based on shells with a plane of sym- 1972, Preliminary ecological classification of ancient benthic facies. The vertical cephalopod shell is the metry that was originally vertical at 11 of 17 communities: International Geological Congress, 24th, Toronto, only means available at present by which Canada, Section 7, no. 24. p. 103-110. localities show a gradual increase in water Seilacher, A., 1968, Sedimentations prozessc in Ammonitengehaiisen: estimates of maximum water depth can be Akademie der Wissenschaften und der Literatur, Abhandlungen depth from west to east across the width of der Mathematisch-Naturwissenschaftlichen Klasse Mainz, No. 9, stated with reasonable confidence. The only the Fort Worth outcrop (toward the center p. 191-203. prerequisites are that the unit contain coiled 1971, Preservational history of ceratite shells: Palaeontology, of the embayment) and from north to south v. 14, p. 16-21. cephalopod shells and that the depth of Trueman, A. E., 1941, The ammonite body-chamber, with special along the length of the outcrop (the western reference to the buoyancy and mode of life of the living water during the time interval being investi- margin of the embayment). Although the ammonite: Quarterly Journal of the Geological Society of gated did not exceed the maximum depth London, v. 96, p. 339-383. general trend of the paleobathymetry pre- Weaver, J. S., and Chamberlain, J. A., Jr., 1976, Equations of motion range of verticality of the most stable shell for post-mortem sinking of cephalopod shells and the sinking of sented is in agreement with the Early Nautilus: Paleobiology, v. 2, p. 8-18. geometry present in the unit. Cretaceous geology and geography of Young, K-, 1972, Cretaceous paleogeography: Implications of endemic ammonite faunas: University of Texas at Austin Bureau of Eco- north-central Texas, southern Oklahoma, nomic Geology Geological Circular 72-2, 13 p. SUMMARY and eastern Louisiana, the estimates of water depth are at least an order of magni- Coiled cephalopod shells that sank to the tude shallower than previous estimates bottom of a body of water in depths less based on what might be less reliable criteria.

than or equal to the Ze for the geometry of these shells will, if preserved, provide a ACKNOWLEDGMENTS reasonable estimate of the depth of the water at the location at which they became I would like to thank Bob F. Perkins and anchored, infilled, and buried. Coiled shells C. I. Smith of the University of Texas at MANUSCRIPT RECEIVED BY THE SOCIETY MARCH 31, 1982 REVISED MANUSCRIPT RECEIVED SEPTEMBER 10, 1982 can be used to calculate estimates of water Arlington, John A, Chamberlain, Jr., of the MANUSCRIPT ACCEPTED SEPTEMBER 10, 1982 Printed in U.S.A.

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