Propagation Characteristics of Rotational Ground Motions in Layered Earth Media

Rotational ground motions have recently emerged as an important and independent observable in seismology, driven by advances in rotational seismometers and the growing availability of high-quality rotational datasets. These observations provide new insights towards understanding near-source and near-surface wave propagation beyond traditional translational measurement. To model rotational components, several analytical approaches have been proposed in the recent past. However, these formulations are typically restricted to idealized source representations and simplified Earth models, limiting their applicability to realistic geological settings accounting for three-dimensional complexities.

Finite-element modeling techniques provide a powerful alternative by enabling the simulation of seismic wavefields in complex media by incorporating heterogeneous velocity structures, layered stratigraphy, surface topography, and finite-fault earthquake sources. Despite this capability, commonly used ground motion simulation codes have not yet been adapted to compute rotational ground motions. In this study, we extend the spectral finite-element code SPECFEM3D to internally compute and output rotational ground motions alongside conventional translational components. The numerical implementation is validated against analytical solutions for two benchmark cases: (i) a homogeneous half-space and (ii) a three-layered velocity model, demonstrating excellent agreement in both amplitude and waveform characteristics. Following validation, the modified code is used to simulate rotational ground motions for a range of realistic scenarios, including layered representations of the subsurface and finite-fault source models. These simulations are used to investigate the generation and propagation characteristics of rotational motions and to examine their spatiotemporal relationship with translational ground motions. Differences in amplitude and propagation behavior between rotational and translational components are particularly analyzed in the present work.

Finally, we assess the potential implications of rotational ground motions for earthquake engineering by evaluating their relative amplitudes and propagation patterns under different source and structural conditions. The results provide a framework for identifying the source characteristics and conditions under which rotational components of ground motion may become significant and potentially influence structural response. These findings contribute to an improved understanding of whether, and under what circumstances, rotational ground motions should be considered in seismic analysis and earthquake-resistant design practice.

Keywords: Rotational ground motions, Seismic wave propagation, Numerical modeling, Earthquake engineering