correspond to Biblical events, particularly the beginning and end of the Flood and Creation. The acceleration function can be determined directly through time series measurements of deposits which were repeatedly laid in succession from the same volcanic system during the Flood. Examples include mid-ocean ridge basalts, large igneous provinces, or multiple sill/dike intrusions for which the stratigraphic ordering can be independently determined. For such deposits, each individual deposit should be subject to approximately the same inheritance, and changes due to reservoir relaxation during the Flood should be generally low. The decay acceleration can then be determined by the difference in measured ages over the time interval to within two orders of magnitude, which can then be tightened by coupling with a kinematic model of deposition timelines. Once multiple values of Ξ( t) can be determined, new measurements can be fitted to times with the same regime, and inheritance and relaxation parameters can be determined. With a large number of determinations made at various localities of the Flood initial and terminal boundaries, radiometric boundaries can be determined. Analysis of multiple rocks laid down during the last portion of the Flood would then yield the overall total amount of post-Flood acceleration, since all would be subject to the same modern era decay product accumulation. This set would also yield typical inheritance regimes for Flood rocks. A similar statistical treatment of modern volcanoes, assumed to have substantially similar relaxation parameters per volcano type (i.e., subduction stratocone, basalt monogenetic, hotspot, etc.) would yield typical cryptic inheritance parameters, which can then be used to analyze specific systems for locale-dependent relaxation parameters and provide constraints on the post-Flood decay acceleration regime. Maximal inheritance could also be established, and with the measurements from the youngest Flood rocks, a radiometric post-Flood/Flood boundary could be determined along with any overlapping ambiguous range, if one exists. More detailed modeling of variable decay during the Flood can be made by adding additional fixed points to more chronological events, or by using kinematic models of the Flood to interpolate between events. Continued theoretical work on the mechanism of AND might constrain the total number of rate determinations that must be made. Relaxation and excess inheritance parameters for individual magmatic systems will be difficult to determine initially before a well-supported decay history model is in place to subtract out the effects of AND. This potentially presents a bootstrapping problem, since all real measurements will be subject to their magmatic system’s unknown equilibrium condition, which in general are unavailable to direct measurement in either time, space, or both. An initial recommendation for the ordering of the overall synthesis was given above. In the case of individual rocks in particular systems, there are a variety of potential observations which will help to separate and estimate the inheritance and relaxation parameters. In the case of historical eruptions of single volcanoes with sufficient eruptions and historical timing constraints, the value of the relaxation parameter can be directly fit. Using the data from Kilauea in table 1, yields a K-Ar relaxation parameter value between 0.2 · 10–2 –1.5 · 10–2/year, though this is likely to be unreliable due to the quality of some of the measurements. More recent, high-quality measurements from multiple radioisotope systems will be needed. Fumarole and spring data, along with tomographic measurements of magma chambers and seismic data can be used to estimate the relaxation parameters of currently active volcanic systems. For extinct volcanic systems, some elements of the total system are no longer available for observation, but there is in many cases good exposure of plutonic systems. Some exquisite geological sites offer the opportunity to study rocks from different levels in the magmatic system, and can provide information about the final partitioning between different minerals and magma constituents. Plutonic data is particularly important for the U-Pb system in zircon and other systems where the closure of the crystal system happens in the magma chamber. Many mining districts have detailed observations of plutonic complexes and their associated hydrothermal systems. An estimate of the total inventory of daughter products provides an estimate of the initial inheritance parameters and can be used as a starting point to determine the relaxation parameter. Radiometric dating is usually carried out a small number of times for a single rock, often once, with additional analysis resources mostly being devoted to dating other rocks to determine the age relationships among them. Recently, reduction in cost of doing multiple analyses has led to a more statistical use of zircons in detrital sediment studies. Uncertainty on published dates is primarily dominated by analytical uncertainty associated with the measurement apparatus. The isotopic inventory of the rocks themselves can vary, however, and this is poorly constrained in general. The general messiness of rapid geological change during the Flood, coupled with AND, would cause additional natural variability. Studies to examine this could help determine how much inheritance and relaxation impact a particular magmatic system, and provide minimum and maximum bounds for a fully defined decay history function at various points in time. When dealing with a radioisotope system which has multiple decays between the parent isotope and the final daughter isotope, such as the U/Pb system, dating is performed under the assumption that the sample has reached secular equilibrium. When this condition is reached, Figure 8. H( t) is an integral over the decay accelerations experienced since crystallization. This can be represented geometrically as the area under a curve. The two curves above have the same area and represent two possible acceleration histories that yield the same radiometric age at point t = 1. The areas are different for any other value of t. MOGK Disequilibrium Relaxation Following Accelerated Nuclear Decay 2023 ICC 338
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