The Proceedings of the Eighth International Conference on Creationism (2018)

point as the trapezoidal rule is then perfectly adequate. 4. Spreading rate In the long time scale calculations we treat the spreading rate as a constant, a rough equivalent of the present-day half spreading rate for the Atlantic, i.e. 2.5 cm/year. Although uniformitarian authors use the accepted timings of magnetic field reversal markers to infer ocean basin spreading histories without the assumption of constant spreading rates, the above fixed rate is sufficient for the purpose of comparing our spreadsheet results with their published model predictions. Given our assumption that the present-day ocean floors have in reality formed during and since the Flood, they must have spread several thousand kilometres in no more than 4500 years, implying an average half spreading rate of order 0.5-1 km/year. Furthermore Baumgardner’s (2003) 3D model of CPT implies maximum plate speeds measured in metres per second. Thus there must have been a brief phase of rapid plate motion which is most naturally associated with the Flood and its immediate aftermath. Baumgardner’s simulations naturally suggest that the motion quickly accelerated to a maximum near the onset of the Flood and then subsided continuously down to present-day rates. However our simulations only seek to model the latter part of the Flood and the following 4400 years. Assuming that the Flood produced the rocks conventionally dated between 600 Ma and 65 Ma (Vardiman et al. 2005), and that today’s ocean floors date from 200 Ma, we are covering only (200-65)/(600-65) ≈ 0.25 of the Flood, together with the post-Flood period. The simplest way to model this is to assume a constant high spreading rate for 0.25 year, which then decays exponentially to present-day rates. Thus in the final form of our spreadsheet models we use a half spreading rate of the form where ʋ ρ is the present-day half spreading rate, ʋ 0 is a reference half spreading rate, τ ƒ is the Flood period covered in the simulation, and τ d is the characteristic decay time of the plate motion. The maximum half spreading rate is thus ʋ p + ʋ 0 . The values of ʋ 0 , τ ƒ and τ d are not independent because the total distance travelled since Flood onset, ≈ ʋ 0 (τ ƒ + τ d ) , must amount to a few thousand km. For values of ʋ 0 in the range expected (of order 0.1-1 ms -1 ) this constrains τ d to a value of order 1 year or less. We thus assume rapid post-Flood decay of plate motion and set τ d = 0.2 year. The ratio τ hs /τ ƒ (see equations 14 and 15) determines the shape of the heat flux and depth profiles against distance from the ridge axis, and hence their variation against equivalent uniformitarian time. RESULTS 1. Repeat of uniformitarian calculation The uniformitarian or long time scale calculation aimed at verifying that our spreadsheet is correctly set up is done on a mesh with 100 intervals along the vertical axis of Δ z = 950 metres each, the timestep being Δ t = 10,000 years. Given the input parameters in Table 1, these intervals correspond to a dimensionless timestep μ = 0.2841, well within the stability limit. The calculation is continued up to a simulated time of 200 Ma. Stein and Stein’s (1992) predictions for surface heat flux and ocean depth up to 160 Ma are reproduced in Fig. 1 here. Note that their model overpredicts heat fluxes close to spreading centres, as also do the half space and PSM models. This is generally attributed to the effect of heat transport by hydrothermal flows in young lithosphere with very little sediment cover (Stein and Stein 1992, Qiuming 2016). The data also show a decrease in depth in the 90-130 Ma range of uniformitarian ages, which is not predicted by these models; this has been attributed to mantle convection (Crosby et al. 2006). Our results for the equivalent case are shown in Figs. 2 and 3. It is clear that our spreadsheet-based predictions are extremely close to those of Stein and Stein’s (1992) GDH1 model; the visible difference in predicted depth at large times, notably for the half space model at 150 Ma, arises because the ridge depth in Stein and Stein’s (1992) Fig. 1 is 2.5 km [they have used Parsons and Sclater’s (1977) value for comparison]; here we have used their preferred value of 2.6 km. Our figures for final values of heat flux and depth match theirs as closely as can be judged. Plots of the temperature profile at various times in our calculation are shown in Fig. 4; by 200 Ma simulated time conditions have almost reached steady state. Exactly as in Stein and Stein’s (1992) GDH1 model, our model overpredicts heat fluxes close to spreading centres and does not predict the shallowing observed in older ocean Worraker and Ward ◀ Ocean floor cooling ▶ 2018 ICC 677 Figure 1. Fig. 1 from Stein and Stein (1992), showing the comparison of the half space model (HS), Parsons and Sclater’s (1977) plate model (PSM) and their own GDH1 plate model against global average data. The assumed ridge depth here is 2.5 km. The data (shown by dots) are averaged in 2 Ma bins and the envelopes (wavy/spiky lines) delineate one standard deviation about the mean.