is a one-to-one correspondence between historical dates and radiometric dates. If different isotope systems have experienced different acceleration histories, then the same would apply to each system, though they may be different from each other. Two important aspects of the relations derived in this paper are locale dependent. The first is the sampling relation, which depends on time, temperature, chemistry, and source history of the magma (Karpinskiy et al., 1966). Successive sampling events geometrically reduce the influence of earlier ones, so for the low inheritance expected for workable radioisotope dating systems, prior sampling can likely be safely ignored. Conditions where anomalously high incorporation of extraneous daughter products occur are, however, more likely during and following an AND episode. Significantly different sampling (inheritance) behavior between two different localities can prevent dates from being strictly equivalent to each other and thereby violate the conditions for relative dating. The other locale-dependent factor is the relaxation parameter, β, which is certainly dependent on location and may also be dependent on time as a magma system is reconfigured and takes on new connection characteristics with respect to the environment (Byrne et al., 2021; Geist et al., 2021; Day and Hilton, 2020). For ( 21 ) (where T is a timescale of interest) reservoir relaxation is an insignificant contributor to the variability of measured radiometric ages over closure time. This changes, however, post-acceleration epoch as decay acceleration decreases to 1 and timescales increase. This introduces a pitfall for measuring corrected ages near or after the end of the Flood. The exact behavior of the system will depend on the relative rate of change between H( t) and the size of β. During the accelerated nuclear decay epoch, reservoir relaxation is likely to be very small compared to the accumulation of decay products and is likely insignificant. After the epoch, however, when a large excess of radiogenic daughter products is present, and with sufficient time for relaxation back to equilibrium to occur, the secular change in cryptic inheritance of measured ages will increase. Because the rate of change in inheritance caused by reservoir relaxation depends on the geological configuration, it cannot be guaranteed that radiometric dates from different magmatic systems are equivalent. As a consequence, late Flood and post-Flood may not be practically radiometrically distinguishable. Within the same system, the relaxation perturbation causes a decrease in the measured ages in the same direction as the decay history function over time, so their sum remains a bijection, and relative dating will still work, but only for samples sourced from systems which share reservoir ages and relaxation parameters. To determine absolute ages or to reliably determine relative ages across two different systems would require knowledge of the relaxation history of each system involved. Rocks which formed pre-epoch would not be subject to the secondary processes of reservoir relaxation and inheritance which redistribute radioisotope products, and so should date very consistently with each other. Another case with practicable application is plutons and associated volcanic rocks which underwent rapid cooling, fast enough to prevent relaxation back to equilibrium from changing the isotopic inventory of the reservoir. In this case, inheritance is likely to be a dominant effect, but if the degree of inheritance can be determined, or localized and excluded, then such plutons would provide useful fixed points. A. Developing and calibrating radiometric histories The promise of corrected absolute dating depends on the establishment of reliable decay history functions, with time indexed constraints on Ξ( t) for specific radioisotope systems. Several lines of evidence are important to defining and constraining these models through time. These include radiometric tie points that can be determined from other lines of evidence, time series radiometric gradients, determination of natural variability of isotopes in rocks, measurements of departure from secular equilibrium, discordances between radioisotope systems and alternate chronometric systems. Literature reviews or measurement campaigns should be carried out to identify the implied constraints on the mechanism and history of decay acceleration. Because the processes described in this paper produce variable and sometimes contrary effects on the measured ages of datable materials subjected to AND, full calibration of a comprehensive decay history model is a difficult and synthesis-level effort. It is far from intractable, however, by taking an iterative approach to constraining the globally applicable decay history function versus the locality-specific parameters. Datable geologic materials are subject to the total radiogenic accumulation of daughter products from the time of their crystallization going forward, so working backwards in time is necessary to completely account for a radiometric age. However, following from the definition in equation 1 the acceleration function may be determined independently for any subset of time without reference to later events. This is useful, since volcanoes in the postFlood period are most susceptible to the complications arising from the relaxation mechanism. The RATE authors developed four potential methods for constraining the acceleration function by the Po production requirements for the presence of Po radiohalos (Snelling, 2005), 14C in geological materials (Baumgardner, 2005), induced fission, and Po radiohalo energies (Chaffin, 2005). With continuous measurements of H( t), the acceleration factor function can be uniquely determined, but some ambiguity arises in the case of having only discrete measurements available. An example of this is shown in figure 8. For a single radiometric measurement from a particular time, t , there are multiple acceleration histories which could plausibly result in the same H( t ), and we do not know a priori which one we should choose. In general, at a different value of t= t , different acceleration histories will produce different values of H( t ). Therefore, to constrain the particular acceleration function, radiometric measurements from multiple different crystallization times must be analyzed. There will still remain some ambiguity where there are gaps in sampled times, but the uncertainty decreases as spacing between measurements decreases. Between sample times, the interpolated acceleration function represents the average value over the interval, which in most cases is likely to be a reasonable approximation. The most fundamental step in constructing a reliable decay history is to establish fixed points in the stratigraphic record which reliably MOGK Disequilibrium Relaxation Following Accelerated Nuclear Decay 2023 ICC 337
RkJQdWJsaXNoZXIy MTM4ODY=