Tsunamis and rapid coastal remodeling: Linking energy and fractal dimension

Abstract

Tsunamis are one of several processes that contribute to coastal remodeling. This research interpreted geomorphic features over time to better understand if a relationship exists between the flash remodeling of coasts, expressed by bidimensional-fractal dimensions, and known tsunami energy. Fractal geometry analysis, through the box-counting and correlation integral methods, was applied to the physiography of four oceanic coastlands: three in Sumatra, Indonesia, and one in Japan, hit by tsunamis in the last 14 years. Their shoreline fractal dimensions before and after the events and the present-day ones were calculated and compared. Results highlighted any difference or convergence of calculated fractal dimensions. Significant numerical variations of fractal dimensions of the shores before and after each tsunami were registered, and those values gradually decreased post-tsunami. These shorelines, considered stable before tsunamis, increased in physiographic irregularity up to 5–11% immediately after the phenomena; this slowly diminished to 2–5% about 8 to 15 years later; and finally to 3–6% present-day, compared to the pre-event shorelines. Considering these changes of the fractal dimension and the hydrodynamic energy of the tsunami, responsible for the abrupt coastal remodeling, a simple empirical expression and evaluation of the residual resilience is proposed. As a first step, a real physical meaning, in terms of energy, is attributed to the (dimensionless) fractal dimension.

A novel approach to the classification of terrestrial drainage networks based on deep learning and preliminary results on solar system bodies

“…The former is rarely present in these natural systems, while the latter is proven mostly for limited portions (sub-basins), rather than for the entire river network. This depends on the difficulty of the geomorphology physics interpretation 12 . Therefore, we tend to identify a series of main and recurrent dimensionless patterns and their derivations (Fig.…”

Fractal and Multifractal Characteristics of Lineaments in the Qianhe Graben and Its Tectonic Significance Using Remote Sensing Images

“…Even though the faults can be extracted using automatic or semiautomatic methods, e.g., point clouds, images, and geophysical data [20][21][22][23], the qualitative description also restricts the scale and significance of tectonics. Recently, as one of the nonlinear sciences, fractal theory [24][25][26] offered geologists new insights to explore complexity and regularity by using the fractal dimension [4,[27][28][29][30][31][32][33]. The fractal geometry of lineaments helps geologists to understand very complex systems, which feature very organized patterns in seemingly chaotic phenomena [4,5].…”

Structural Fractal Analysis of the Active Site of Acetylcholinesterase in Complexes with Huperzine A, Galantamine, and Donepezil

“…The methods of fractal geometry are now widely used in scientific research. The key quantitative characteristic of fractal objects is fractal dimension D. Therefore, a significant number of modern works are devoted to the calculation and analysis of this quantity in various fields of knowledge, including physics, [22,23] geophysics, [24,25] chemistry, [26,27] biology, [28] medicine, [29,30] economics, [31,32] materials science, [33] and computer science. [34,35] Another important characteristic of fractals is Hurst exponent H, which is used as the measure of a long-range dependence in time and spatial series and changes from 0 to 1.…”