signature would manifest as a constant vertical offset on the primordial reservoir line. Sampling from a reservoir can be seen as a vertical drop in the measured age. The derived reservoirs are subject to relaxation, but only in the case of the rapid relaxation of reservoir B is it easily visible at this time scale. Samples which do not relax are taken from the derived reservoirs at their differentiation to show the effect of relaxation back to equilibrium on the reservoirs. Figure 4 shows the same reservoirs as figure 3, but the domain is expanded to include all of history. At this time scale, the effects of relaxation on the reservoirs are more readily apparent. Two samples are taken of reservoir B at its original differentiation as well as at the end of the Flood when the smaller relaxation regime takes effect. The difference between the two sample lines shows the total effect of the high relaxation rate during the Flood. Figure 5 shows the hypothetical measured radiometric ages of the decay history function, reservoirs A and B, as well as samples taken from the reservoirs. In contrast to figures 3 and 4, the measurements in figure 5 are taken at the present time, having accumulated their full contingent of radiogenic daughter products since the “sampling” time listed on the domain. The domain of the left panel covers the modern era, and the right panel covers the Flood. The samples taken in this example in the modern era have realistically low inheritance from the parent reservoirs, so even though the reservoirs retain a significant fraction of their original decay product inventories, the samples have plausibly low dates. The parameters chosen for the two reservoirs illustrate how the relaxation mechanism can cause relative dating to be inaccurate between different magmatic systems, even when they are subject to the same decay history and inheritance regime. The two series of samples also demonstrate one magmatic system which exhibits elevated radiometric dates from modern eruptions (Res A samples), and one which measures correctly at zero. Both systems exhibit dates in the immediate post-Flood period which are greatly inflated, and which decrease with decreasing stratigraphic position, as is observed with real volcanic systems. For the samples taken during the Flood, inheritance for samples taken from res B are much greater than those taken from res A. This illustrates that having high inheritance causes sample behavior to couple more strongly to the parent reservoir conditions, whereas low inheritance causes samples to be more strongly coupled to the underlying decay history function, as expected. Figure 6 shows how the samples would be converted to absolute dates if inheritance and reservoir relaxation are not taken into account. Under these assumptions, the corrected sample dates can only be interpreted as maximum closure ages. In all cases, the time of Figure 3. An example system of reservoirs displaying a variety of relationships and behaviors that are possible to model with the equations derived in this paper. The network shown begins as the primordial reservoir with no initial radiometric age. At the beginning of the Flood, it is sampled with 10% inheritance. Later, this reservoir is partitioned into two sister reservoirs, each containing a fraction of the accumulated daughter product at a 30-70 split. Both differentiated reservoirs are undergoing relaxation, but the yellow reservoir has a relaxation parameter 100x greater than the blue one. A sample which does not have any relaxation behavior associated with it of reservoir A is taken at the time of differentiation. During the accelerated nuclear decay epoch, the relaxation behavior is too small to observe at this scale (cyan line). The y-axis is the total radiometric response less the value of the decay history function. This is equivalent to a chilled sample being taken and radiometrically dated at each point in history. Figure 4. This is the same system described in figure 2 and shown in figure 3, but with the domain expanded to all of history including the modern era. The dates on the vertical axis shown are the dates that would be obtained if measured at each point in history on the horizontal axis. Modern dates are indicated by the intercept of each line with the vertical axis. The rapidity of events during the Flood prevents seeing any detail, but the evolution of the systems over time can clearly be seen. The relaxation behavior of both reservoirs A and B can clearly be seen with reservoir B having a faster relaxation time. Because of this, these two systems violate relative dating conditions 1 and 2, so their radiometric dates cannot be meaningfully compared in a relative sense without knowing the total radiometric response of both systems. Reservoir B undergoes two different relaxation regimes during the Flood. Samples (non-relaxing) are taken at the beginning of both the fast regime (red line) and the slower regime (green line) to show the effect that relaxation had during the Flood. The cyan line is a sample taken from reservoir A which also reveals the effect of relaxation. MOGK Disequilibrium Relaxation Following Accelerated Nuclear Decay 2023 ICC 335
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