Cyclicity and Persistence of Earth's Evolution Over Time: Wavelet and Fractal Analysis

Abstract

Accessing the cyclicity and persistence of geological records with time series analysis deepens our understanding of Earth's long‐term evolution. In this study, time series from recent global zircon U‐Pb age and δ18O databases are analyzed using wavelet transform from a fractal perspective. Continuous wavelet transform of the local fractal sequences of both zircon records indicates a strong, persistent ~760 million year cycle over the 4.4 billion years of Earth's history. Wavelet coherence analysis shows that the U‐Pb age and δ18O systems are coupled in significant in‐phase coherence for a cycle of ~760 million year, implying synchronization between the two underlying processes. This study also demonstrates that the variation in the time series records manifests as 1/f β scaling behavior that persists β ~ 1.8 over the entire interval. This 1/f fractal scaling nature furnishes evidence for the conjecture that rather than being an equilibrium system, Earth's long‐term evolution follows a self‐organized pattern.

Singularity Analysis of Volcanic Ages and Implications for Tectonic Setting in the Mesozoic, Great Xing’an Range, Northeast China

“…A persistent ca. 760 Ma cycle was identified in global zircon records from 4.4 Ga to present by a statistical method [17]. These results mentioned in the two examples above are very difficult to demonstrate by the conventional probability-age method or the histogram-age method.…”

“…In early studies, the singularity model was applied to the identification of the distributive patterns of ore deposits and the separation of geochemical anomalies from the background [14][15][16]. Recently, this model was used to understand the formation and growth of continental crust [17,18], and to predict the lifetime of global plate movement [19], and to characterize the flare up of magmatic activities in Himalayas [20]. However, singularity analysis has not yet been applied to volcanic zircon ages to understand the tectonic setting of the GXR.…”

Структурно-Текстурные И Вещественные Свойства Сульфидных Медно-Никелевых Руд.

“…С развитием вычислительной техники фрактальный анализ стал применяться в поисковых работах, фрактальная размерность различных отражений геологической природы стала использоваться как поисковый признак. Шире всего фрактальный анализ и его варианты (мультифрактальный, сингулярный) с целью поисков полезных ископаемых нашли применение при анализе геохимических полей (Afzal et al 2017;Chen and Cheng 2018a;Cheng et al 1994Cheng et al , 2000Pourgholam et al 2021;Wang et al 2013;Xiao et al 2016;Zuo and Wang 2015) и геофизических данных (Chandrasekhar et al 2014;Chen and Cheng 2018b;Goryainov et al 1997;Lyubchich 2017;Mandelbrot 1989;Turcotte 1992;Горяинов и др. 2012).…”

Unveiling Temporal Cyclicities in Seismic b-Values and Major Earthquake Events in Japan by Local Singularity Analysis and Wavelet Methods

“…The uniqueness of such techniques lies in their ability to effectively remove trend changes caused by nonlinear factors from intricate signals, thereby allowing periodic fluctuations or other key features hidden behind these trends to be clearly revealed. Local singularity analysis is often used in the preprocessing of data for time series spectrum analysis, such as Fourier transforms or wavelet transforms, with results showing significant improvements in the analysis of preprocessed time series data [19].…”