Some comments on the problem of using vertical facies changes to infer accommodation and eustatic sea-level histories with examples from Utah and the southern Canadian Rockies

Some of the confusion in the literature on the history of eustatic sea level over time results from the incorrect assumption that the eustatic signal is given directly by vertical changes in water depths inferred from vertical facies patterns in stratigraphic sections. In particular, increases in water depth are often assumed to record an increase in eustatic sea level, and decreases in water depth are often assumed to record a decrease in eustatic sea level. Vertical changes in water depth, however, reflect only the local relative sea-level change, which is influenced by the balance between changes in the rate at which accommodation space forms (space available for sediments to fill) and changes in the rate at which sediment fills that space. Under certain conditions, which may not be uncommon in many areas, the balance may be such that no significant water depth change occurs, even during a relatively large third-order eustatic cycle, or such that shoaling occurs during a eustatic sea-level rise and deepening occurs during a eustatic sea-level fall. The key to sorting out the correct relation between eustatic sea level and vertical facies changes lies in first identifying the accommodation change, along with its timing and scale, and then determining whether that accommodation change (not the water depth change) occurred synchronously over a large region (continental or intercontinental). Using R2 analysis, a procedure we developed recently, we attempt to distinguish the local relative sea level from the regional or eustatic sea-level signal by recovering the accommodation history from detailed stratigraphic sections that can be correlated over large distances. We describe two examples from the late Middle Cambrian carbonate platform strata in the Cordillera of North America. In the first example, from the Pierson Cove and Trippe Formations in south-central Utah, the water depth changed little during a large (third-order?) accommodation cycle because the accumulation of sediment essentially kept pace with the change in accommodation. The form of the accommodation cycle in the Utah example is corroborated by the results of a Fischer plot of shoaling-upward meter-scale cycles in both formations. The Fischer plot is constrained by evidence, which we describe in another article (Bond et al., this volume) that the cycles are periodic (orbitally forced). In the second example, from the approximately correlative Arctomys and Waterfowl Formations in the southern Canadian Rockies, we have identified a similar-scale accommodation cycle in which the water depth decreased as accommodation increased and then increased as accommodation decreased. This complicated relation between the accommodation cycle and the water depth appears to be due to the effects of a large change in the sediment accumulation rate. The eustatic origin of the accommodation cycle observed in both examples is implied by the similarity in its timing and scale in several stratigraphic sections in the southern Canadian Rockies and in Utah. Demicco et al. (this volume) suggest a different relative sea-level history for the Arctomys and Waterfowl Formations in the southern Canadian Rockies. They suggest, mainly on the basis of water depth changes, that the Arctomys formed during a relative sea-level fall and that the Waterfowl formed during a relative sea-level rise. We do not disagree with their interpretation of the water depth change; our field data indicate the same water depth history in sections 40 km (25 mi) north of theirs. We also recognize in our R2 curves the same cycles that they describe within the Waterfowl Formation (one full cycle and part of another), but in our curves these cycles are strongly modulated by at least two lower orders of cyclicity with time scales of several millions of years to tens of millions of years. We suggest that their interpretation of the Arctomys-Waterfowl sea-level history applies only to the local relative sea-level change, probably mainly confined to the southern Canadian Rockies. Because of the effects of changing sediment accumulation rates, the local sea-level history for these strata is almost the reverse of the accommodation and, probably, the eustatic sea-level change. In addition, their field interpretations and modeling of the sea-level history for the Waterfowl Formation are limited by their emphasis on meter-scale cyclicity and the acquisition of data from a short stratigraphic section comprising only the Arctomys and Waterfowl Formations. Observations limited in this way tend to obscure the lower orders of cyclicity, which we argue from the results of our R2 analyses were important components of the eustatic signal in Middle and Late Cambrian time

Some comments on the problem of using vertical facies changes to infer accommodation and eustatic sea-level histories with examples from Utah and the southern Canadian Rockies

Some of the confusion in the literature on the history of eustatic sea level over time results from the incorrect assumption that the eustatic signal is given directly by vertical changes in water depths inferred from vertical facies patterns in stratigraphic sections. In particular, increases in water depth are often assumed to record an increase in eustatic sea level, and decreases in water depth are often assumed to record a decrease in eustatic sea level. Vertical changes in water depth, however, reflect only the local relative sea-level change, which is influenced by the balance between changes in the rate at which accommodation space forms (space available for sediments to fill) and changes in the rate at which sediment fills that space. Under certain conditions, which may not be uncommon in many areas, the balance may be such that no significant water depth change occurs, even during a relatively large third-order eustatic cycle, or such that shoaling occurs during a eustatic sea-level rise and deepening occurs during a eustatic sea-level fall. The key to sorting out the correct relation between eustatic sea level and vertical facies changes lies in first identifying the accommodation change, along with its timing and scale, and then determining whether that accommodation change (not the water depth change) occurred synchronously over a large region (continental or intercontinental). Using R2 analysis, a procedure we developed recently, we attempt to distinguish the local relative sea level from the regional or eustatic sea-level signal by recovering the accommodation history from detailed stratigraphic sections that can be correlated over large distances. We describe two examples from the late Middle Cambrian carbonate platform strata in the Cordillera of North America. In the first example, from the Pierson Cove and Trippe Formations in south-central Utah, the water depth changed little during a large (third-order?) accommodation cycle because the accumulation of sediment essentially kept pace with the change in accommodation. The form of the accommodation cycle in the Utah example is corroborated by the results of a Fischer plot of shoaling-upward meter-scale cycles in both formations. The Fischer plot is constrained by evidence, which we describe in another article (Bond et al., this volume) that the cycles are periodic (orbitally forced). In the second example, from the approximately correlative Arctomys and Waterfowl Formations in the southern Canadian Rockies, we have identified a similar-scale accommodation cycle in which the water depth decreased as accommodation increased and then increased as accommodation decreased. This complicated relation between the accommodation cycle and the water depth appears to be due to the effects of a large change in the sediment accumulation rate. The eustatic origin of the accommodation cycle observed in both examples is implied by the similarity in its timing and scale in several stratigraphic sections in the southern Canadian Rockies and in Utah. Demicco et al. (this volume) suggest a different relative sea-level history for the Arctomys and Waterfowl Formations in the southern Canadian Rockies. They suggest, mainly on the basis of water depth changes, that the Arctomys formed during a relative sea-level fall and that the Waterfowl formed during a relative sea-level rise. We do not disagree with their interpretation of the water depth change; our field data indicate the same water depth history in sections 40 km (25 mi) north of theirs. We also recognize in our R2 curves the same cycles that they describe within the Waterfowl Formation (one full cycle and part of another), but in our curves these cycles are strongly modulated by at least two lower orders of cyclicity with time scales of several millions of years to tens of millions of years. We suggest that their interpretation of the Arctomys-Waterfowl sea-level history applies only to the local relative sea-level change, probably mainly confined to the southern Canadian Rockies. Because of the effects of changing sediment accumulation rates, the local sea-level history for these strata is almost the reverse of the accommodation and, probably, the eustatic sea-level change. In addition, their field interpretations and modeling of the sea-level history for the Waterfowl Formation are limited by their emphasis on meter-scale cyclicity and the acquisition of data from a short stratigraphic section comprising only the Arctomys and Waterfowl Formations. Observations limited in this way tend to obscure the lower orders of cyclicity, which we argue from the results of our R2 analyses were important components of the eustatic signal in Middle and Late Cambrian time

Evidence for orbital forcing of Middle Cambrian peritidal cycles: Wah Wah range, south-central Utah

We have applied a new method (gamma method) for constructing high-resolution age models to peritidal cycles in the Middle Cambrian Pierson Cove Formation (13 cycles) and the Trippe Limestone (40 cycles) exposed in the Wah Wah range, south-central Utah. Spectral analyses of the time series for the gamma age model indicate the presence of significant spectral peaks (relative to a null model) in both data sets. After experimenting with different assumptions for the duration of the mean primary or measured cycle, we found that for the Trippe data set assigning the mean duration of precession to the mean primary cycle produced a reasonably good correlation between the spectrum and the early Paleozoic estimate of insolation forcing. In particular, the periods of the three significant spectral peaks in the Trippe record correspond to estimated line periods for eccentricity and precession and a combination tone of precession. A spectrum for the Trippe cycles based on the conventional assumption that time is proportional to thickness contained only one significant peak, and reasonable estimates of the duration of the mean primary cycle produced a poor fit to the insolation model. Spectral results from the Pierson Cove cycles were less compelling, possibly because of the short length of the record. The presence in the Trippe spectrum of significant peaks with periods corresponding to high-frequency orbital variations suggests that preservation of high-frequency Milankovitch signals is more common than implied by models of shallow marine cyclicity based on Pleistocene sea-level records. The results of these spectral analyses suggest that the gamma method can be used to construct age models for peritidal carbonate cycles that are accurate enough to test for periodicity and deterministic mechanisms, even in rocks as old as the Cambrian

Evidence for orbital forcing of Middle Cambrian peritidal cycles: Wah Wah range, south-central Utah

We have applied a new method (gamma method) for constructing high-resolution age models to peritidal cycles in the Middle Cambrian Pierson Cove Formation (13 cycles) and the Trippe Limestone (40 cycles) exposed in the Wah Wah range, south-central Utah. Spectral analyses of the time series for the gamma age model indicate the presence of significant spectral peaks (relative to a null model) in both data sets. After experimenting with different assumptions for the duration of the mean primary or measured cycle, we found that for the Trippe data set assigning the mean duration of precession to the mean primary cycle produced a reasonably good correlation between the spectrum and the early Paleozoic estimate of insolation forcing. In particular, the periods of the three significant spectral peaks in the Trippe record correspond to estimated line periods for eccentricity and precession and a combination tone of precession. A spectrum for the Trippe cycles based on the conventional assumption that time is proportional to thickness contained only one significant peak, and reasonable estimates of the duration of the mean primary cycle produced a poor fit to the insolation model. Spectral results from the Pierson Cove cycles were less compelling, possibly because of the short length of the record. The presence in the Trippe spectrum of significant peaks with periods corresponding to high-frequency orbital variations suggests that preservation of high-frequency Milankovitch signals is more common than implied by models of shallow marine cyclicity based on Pleistocene sea-level records. The results of these spectral analyses suggest that the gamma method can be used to construct age models for peritidal carbonate cycles that are accurate enough to test for periodicity and deterministic mechanisms, even in rocks as old as the Cambrian

Are cyclic sediments periodic? Gamma analysis and spectral analysis of Newark Supergroup lacustrine strata

Methodologies are suggested for the analysis of cyclic sediments. These include (1) linear analysis to determine whether cycles are of approximately constant duration and whether the relation between thickness and time is facies dependent and (2) multiple prolate-spheroidal windowing spectral analysis to determine whether time-series data indicate periodicities, either of the primary cycles or of higher or lower orders. The results of both methods are compared to a null hypothesis as a semiquantitative test of periodicity. Application of the methods to Newark Supergroup lacustrine cycles suggests that the primary cycles are approximately periodic and record a response to astronomical precession. The time represented by a given thickness of the different facies increases with the depositional water depth of that facies and with decreasing grain size. Precessional index cycles and long-period precessional index beats, or eccentricity, are strongly recorded in the spectra. Spectral results suggest but do not prove lengthening of the periodicities of orbital parameters since 200 Ma

Are cyclic sediments periodic? Gamma analysis and spectral analysis of Newark Supergroup lacustrine strata

Methodologies are suggested for the analysis of cyclic sediments. These include (1) linear analysis to determine whether cycles are of approximately constant duration and whether the relation between thickness and time is facies dependent and (2) multiple prolate-spheroidal windowing spectral analysis to determine whether time-series data indicate periodicities, either of the primary cycles or of higher or lower orders. The results of both methods are compared to a null hypothesis as a semiquantitative test of periodicity. Application of the methods to Newark Supergroup lacustrine cycles suggests that the primary cycles are approximately periodic and record a response to astronomical precession. The time represented by a given thickness of the different facies increases with the depositional water depth of that facies and with decreasing grain size. Precessional index cycles and long-period precessional index beats, or eccentricity, are strongly recorded in the spectra. Spectral results suggest but do not prove lengthening of the periodicities of orbital parameters since 200 Ma

An Early Cambrian Rift to Post-Rift Transition in the Cordillera of Western North America

The upper Proterozoic and lower Palaeozoic wedge of miogeoclinal strata in the North American Cordillera is widely regarded as evidence for a proto-Pacific passive margin. The rifting history of this margin appears to have been protracted, possibly spanning more than 200 Myr in a tectonic setting that is not well understood. Quantitative subsidence analyses of lower Palaeozoic strata between British Columbia and Utah, however, provide indirect evidence that the transition from rifting to post-rift cooling occurred within a relatively short interval of time, although probably not synchronously, between 600 and 555 Myr. This age is significantly younger than that implied in previous studies. We describe here new field data, which, together with published geological data, provide direct evidence of a latest Proterozoic or early Cambrian age for the rift to post-rift transition. The data support recent arguments for widespread initiation of passive margins around the edge of the North American craton close to the Cambrian-Precambrian boundary

Hubble Space Telescope Imaging of Lyman Alpha Emission at z=4.4

We present the highest redshift detections of resolved Lyman alpha emission, using Hubble Space Telescope/ACS F658N narrowband-imaging data taken in parallel with the Wide Field Camera 3 Early Release Science program in the GOODS CDF-S. We detect Lyman alpha emission from three spectroscopically confirmed z = 4.4 Lyman alpha emitting galaxies (LAEs), more than doubling the sample of LAEs with resolved Lyman alpha emission. Comparing the light distribution between the rest-frame ultraviolet continuum and narrowband images, we investigate the escape of Lyman alpha photons at high redshift. While our data do not support a positional offset between the Lyman alpha and rest-frame ultraviolet (UV) continuum emission, the half-light radii in two out of the three galaxies are significantly larger in Lyman alpha than in the rest-frame UV continuum. This result is confirmed when comparing object sizes in a stack of all objects in both bands. Additionally, the narrowband flux detected with HST is significantly less than observed in similar filters from the ground. These results together imply that the Lyman alpha emission is not strictly confined to its indigenous star-forming regions. Rather, the Lyman alpha emission is more extended, with the missing HST flux likely existing in a diffuse outer halo. This suggests that the radiative transfer of Lyman alpha photons in high-redshift LAEs is complicated, with the interstellar-medium geometry and/or outflows playing a significant role in galaxies at these redshifts.Comment: Submitted to the Astrophysical Journal. 11 pages, 10 figure

Weighing the Universe with the Cosmic Microwave Background

Variations in $\Omega$, the total density of the Universe, leave a clear and distinctive imprint on the power spectrum of temperature fluctuations in the cosmic microwave background (CMB). This signature is virtually independent of other cosmological parameters or details of particular cosmological models. We evaluate the precision with which $\Omega$ can be determined by a CMB map as a function of sky coverage, pixel noise, and beam size. For example, assuming only that the primordial density perturbations were adiabatic and with no prior information on the values of any other cosmological parameters, a full-sky CMB map at $0.5^\circ$ angular resolution and a noise level of $15\,\mu{\rm K}$ per pixel can determine $\Omega$ with a variance of 5\%. If all other cosmological parameters are fixed, $\Omega$ can be measured to better than 1\%.Comment: 7 pages RevTex. Two uuencoded postscript figures. For postscript or hard copies, send mail to [email protected]