Weibull Analysis of Arch Collapses

Arches are one of the wonders of nature. Their seemingly physics-defying appearance has made them a popular attraction all over the world. Though these enigmatic structures are made of rock, they are fragile and are likely to collapse at some point due to several environmental factors associated with physical and chemical erosion, or even arson. Arch collapse is specifically interesting to the creation model as an indicator of youth, since they collapse regularly but are not presently forming at great rates. Arches have been discussed by Faulkner (2024) and others, but there is not a comprehensive explanation of the mechanism, age, and evolution of arches in the young earth creation model. This could give us insight into post-Flood processes. We are left with a quandary. Statistically, we are dealing with the population of arches, rather than a single arch. This distinguishes this study from the few conventional studies that examine the degradation of a single arch. The question remains: how should we aim to understand the lifespan of the population of arches? Weibull analysis is a statistical engineering technique used to understand failure characteristics in populations which experience aging processes. This paper applies Weibull analysis to arch collapses to constrain the total lifetime of a population of arches under the assumption that they formed around the same time. This is expected to better reflect the physical changes that arches undergo than the constant failure rate model assumed by Faulkner (2024). An unsuccessful attempt to validate the total count of arch collapses in Morton (2020) was made, including scholarly articles, two online arch databases, and inquiries to Arches National Park. Therefore, four synthetic arch collapse datasets were created to validate the Weibull analysis methodology. The datasets consist of collapse dates of arches, which are used to derive total lifetimes. The failure analysis yields two parameters, the shape (β, determines how the failure rate changes over time) and scale (η, represents characteristic lifetime), which define the distribution of failure ages (in this case an arch collapse). One of the things to determine is how much collapse data is necessary to be able to separate different failure models. We also created a failure probability calculator, which can provide forward-looking predictions of failure rates based on model parameters and applied it to a scenario like the arches at Arches NP. Predictions of the next likely arch collapse, and the total lifespan of remaining arches were made for each synthetic model. Weibull analysis was successful in finding the statistical parameters of the synthetic datasets. It was able to distinguish between distinct populations with only 50 years of arch collapse observations, so can potentially be used with real-world collapse observations. The precision of the estimated parameters is dependent on the number of collapses observed during the timeframe. If the real formation date is unidentifiable, then potentially geological context and collapse comparisons can be used to find it. An estimate of the number of prior collapses improved accuracy and might be needed for real-world analyses. Analyzed lifespan error in real arch populations may be governed by differing formation dates, and the number of unknown prior collapses. Weibull analysis is useful for understanding the history of arches. By determining arch population lifetime parameters, it can constrain “backwards” the number of arches that have existed and can help constrain the time of formation. A Weibull model can be used to integrate observations of multiple parameters, e.g. comparing measured and modeled modern day collapse rates. This model can be tested on real arch populations through predictions of the rate of future arch collapses. The analysis could be improved by estimating the Weibull shape parameter by the method of moments. Future studies of arch collapse will focus on finding more verifiable arch collapses and integrating seismic and weather data to parameterize arch collapse rates. This model works and can be applied to real datasets to estimate formation dates, collapse dates, and future lifespan of arches. REFERENCES Faulkner, D. R. 2024. How long have arches been around? Answers In Depth 19. https://answersingenesis.org/geology/how-long-have-arches-been-around/. Accessed 2024-09-27. Morton, M. C. 2020. The delicacy of arches. Eos 101. DOI: 10.1029/2020EO146523.