Implications for the Santa Cruz Formation, Argentina
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Age modeling in deep time An improved approach to age-modeling in deep time: Implications for the Santa Cruz Formation, Argentina Robin B. Trayler1,2,†, Mark D. Schmitz1, José I. Cuitiño3, Matthew J. Kohn1, M. Susana Bargo4, Richard F. Kay5, Caroline A.E. Strömberg6, and Sergio F. Vizcaíno4 1Department of Geosciences, Boise State University, 1910 University Drive, Boise, Idaho 83725, USA 2Department of Life and Environmental Sciences, University of California Merced, 5200 Lake Road, Merced, California 95343, USA 3Instituto Patagónico de Geología y Paleontología, CENPAT-CONICET, Boulevard Almirante Brown 2915, Puerto Madryn, U9120ACD, Chubut, Argentina (CIC and CONICET) 4División Paleontología de Vertebrados, Museo de La Plata, Unidades de Investigación, Anexo Museo, Av. 60 y 122, 1900, La Plata, Argentina 5Department of Evolutionary Anthropology, Trinity College and Division of Earth and Ocean Sciences, Nicholas School of the Environment, Duke University, Durham, North Carolina 27708, USA 6Department of Biology and Burke Museum of Natural History and Culture, University of Washington, Seattle, Washington 98195, USA ABSTRACT ing a Monte Carlo technique. This approach through each measured age, instead they are fit allows us to estimate robust uncertainties on as closely as possible to each point, usually by a Accurate age-depth models for proxy re- isotope composition through time, impor- least squares approach (Blaauw and Heegaard, cords are crucial for inferring changes to tant for comparisons of terrestrial systems 2012). With the addition of Monte Carlo meth- the environment through space and time, to other proxy records. ods to simulate the underlying uncertainties in yet traditional methods of constructing age, probabilistic classical models may produce these models assume unrealistically small INTRODUCTION satisfactory chronologies. However, they have age uncertainties and do not account for several limitations. First, classical models do many geologic complexities. Here we modify Placing measurements of proxy records (e.g., not explicitly consider stratigraphic relation- an existing Bayesian age-depth model to fos- fossils, geochemical data, pollen or phytolith ships among samples and may produce chronol- ter its application for deep time U-Pb and abundances) in a broader geochronologic con- ogies that violate superposition and imply nega- 40Ar/39Ar geochronology. More flexible input text is crucial for inferring environmental and tive accumulation rates (See fig. 6 in Blaauw likelihood functions and use of an adaptive faunal variations in space and time. For proxy and Heegaard, 2012). Second, these methods proposal algorithm in the Markov Chain records where stratigraphic position is known, often underestimate the uncertainties associated Monte Carlo engine better account for the chronology construction relies on both accurate with undated positions (Blaauw et al., 2018; De age variability often observed in magmatic and precise age determinations and an age-depth Vleeschouwer and Parnell, 2014). crystal populations, whose dispersion can model that describes the relationship between Bayesian inference offers an alternative to reflect inheritance, crystal residence times stratigraphic position and time. This process is the classical approach by combining data (age and daughter isotope loss. We illustrate this complicated by the underlying uncertainties in determinations) and prior information (strati- approach by calculating an age-depth model both the age determinations and the complex graphic positions) to generate a satisfactory with a contiguous and realistic uncertainty nature of sediment accumulation. Furthermore, probabilistic posterior chronology. Originally envelope for the Miocene Santa Cruz For- datable materials are often intermittently distrib- developed for radiocarbon calibration and mation (early Miocene; Burdigalian), Ar- uted and are not necessarily co-located with the chronology construction (Blaauw and Chris- gentina. The model is calibrated using new, proxy record of interest, resulting in uncertainty ten, 2005; Bronk Ramsey, 2008; Haslett and high-precision isotope dilution U-Pb zircon in correlation and interpolation. Parnell, 2008), Bayesian age-depth modeling ages for stratigraphically located interbed- Considerable effort has been expended on has become increasingly applied to other types ded tuffs, whose weighted mean ages range how best to interpolate time from dated to un- of geochronologic data (De Vleeschouwer and from ca. 16.78 ± 0.03 Ma to 17.62 ± 0.03 Ma. dated stratigraphic positions, and a variety of Parnell, 2014; Sahy et al., 2015; Wotzlaw et We document how the Bayesian age-depth proposed statistical methods have been pro- al., 2018). model objectively reallocates probability posed for this purpose (see reviews of: Blaauw In this paper we introduce a modified version across the posterior ages of dated horizons, and Heegaard, 2012; Parnell et al., 2011). of an existing Bayesian age-depth model, Bchron and thus produces better estimates of rela- Broadly, these methods can be split into two (Haslett and Parnell, 2008), for use with U-Pb, tive ages among strata and variations in categories: classical and Bayesian models. Clas- 40Ar/39Ar, and other deep time geochronologic sedimentation rate. We also present a simple sical age-depth modeling encompasses a variety data. We then illustrate our approach for the method to propagate age-depth model un- of deterministic linear, spline, and polynomial Miocene (Burdigalian) Santa Cruz Formation certainties onto stratigraphic proxy data us- interpolation methods that aim to fit a smooth of southern Argentina (Fig. 1). We use our new curve that relates stratigraphic position to age. dates, cast within a Bayesian framework, as a test †[email protected] The resulting models do not necessarily pass case to address two broad questions. First, how GSA Bulletin; Month/Month 2019; v. 131; no. X/X; p. 1–12; https://doi.org/10.1130/B35203.1; 7 figures; 3 tables; Data Repository item 2019241. ; published online XX Month 2016. For permission to copy, contact [email protected] Geological Society of America Bulletin, v. 1XX, no. XX/XX 1 © 2019 Geological Society of America Downloaded from https://pubs.geoscienceworld.org/gsa/gsabulletin/article-pdf/doi/10.1130/B35203.1/4708190/b35203.pdf by University of California Merced Library Director, Robin B. Trayler on 23 May 2019 Trayler et al. does the inclusion of prior information affect the a 69° 200 CO3 interpretation of the non-symmetric uncertainties Río Sant N Cruz that arise from the analysis of several individual a CV-10 Toba Blanca mineral grains (e.g., zircon, sanidine)? Second, KARG-15-01 how can the significant uncertainties associated ArgentinSanta Cruz (masl) KARG-15-09 Province with age-depth models be considered in the inter- 150 pretations of proxy records? Study Area Cañadónde las Vacas Cerro Observatorio Position BAYESIAN MODELING Tuff Locality Towns Rincón del Buque Rivers Bayesian models attempt to estimate the 100 Major Roads Stratigraphic probable values of unknown parameters based 0 25 km CO on prior information about these parameters, 51° which can be conditioned by observed data, Puesto or likelihoods. The relationship between these CV-13 Estancia 50 terms is formalized in Bayes’ theorem: La Costa 17.6 17.2 16.8 16.4 Río Coyle Age(Ma) Px| Px| P . (1) Figure 2. Ten example chronologies, Px Killik Aike Norte Cabo Buen Santa Cruz Formation, Argentina. Tiempo Note that a wide variety of chronolo- The first term on the right-hand side of Equa- s Río Gallegos Río Gallego gies are possible in the lower section, tion 1 is the conditional probability of the data 69° while the upper section where ash beds given the proposed parameters, i.e., how prob- Figure 1. Map of tuff localities, Santa Cruz Forma- are more closely spaced requires tightly able are our data (x; age determinations) given a tion, Argentina. bunched model paths. CO—Cerro Ob- proposed parameter (θ; model age). The second servatorio; CV—Cañadón de las Va- term is the probability associated with any prior cas; masl—meters above sea level. knowledge of the parameters (θ), i.e., for our example, how constraints such as stratigraphic amount, where the number of accumulation superposition and/or assumptions of sedimenta- events is drawn from a Poisson distribution and tion rate and its variability affect the probability the amount of accumulation is drawn from a (Haslett and Parnell, 2008). Confidence inter- of the proposed age parameters (θ). The left- gamma distribution. These two processes are vals of chronologies based on classical methods hand term is the posterior conditional probabil- related using a compound Poisson-gamma dis- often exhibit a waist or hourglass effect where ity of the proposed parameters, i.e., what is the tribution to describe the prior probability of model uncertainties counterintuitively decrease most probable age (θ) given how our data (i.e., the sedimentation events (Haslett and Parnell, as distance from dated positions increases, un- the radiometric age determinations) and our 2008). In addition to the parameters associated derestimating uncertainty at these positions (De prior knowledge (stratigraphic position, sedi- with age determinations, Bchron uses two hy- Vleeschouwer and Parnell, 2014; Telford et al., mentation rate variability) interact. perparameters (µ, ψ) to control the mean and 2004). Conversely, by allowing the number of In most cases Bayes’ theorem cannot be dispersion of the compound