Fractional-Order Viscoelastic Modeling of Seismic P-, S-, and Rayleigh-Wave Attenuation: Marmara Seismotectonic Context, Fault Geometry, and a Reproducible Strong-Motion Framework
Abstract
Abstract The authors’ earlier two-page note proposed the use of fractional differential operators for seismic waves and suggested an application to Istanbul earthquake intensity. That preliminary formulation did not specify a constitutive law, a fault-based geological setting, or a data-calibrated validation protocol. The present manuscript develops the idea into a mathematically explicit and geophysically grounded framework. The seismotectonic background of the Marmara region is first summarized using the segmented North Anatolian Fault geometry discussed in the Marmara literature, including the work of Naci Görür and collaborators. A dimensionally consistent fractional Kelvin–Voigt constitutive law is then introduced for P and S waves, from which complex wavenumbers, attenuation coefficients, phase velocities, and an effective Rayleigh-wave branch are obtained. Positive attenuation on the principal propagation branch is proved. To make the inverse problem reproducible, a synthetic joint P/S identification experiment is retained, but the manuscript now also embeds real data context through Marmara event metadata, the 26 September 2019 Silivri–High Kumburgaz Basin earthquake, and the national/international strong-motion databases used for a future full calibration. All figures are resized to fit the text width and all graphics are produced directly in TikZ/PGFPlots, including a schematic Marmara map, principal fault segments, and event-based wave-propagation illustrations.…
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