A unified framework for extracting multimode surface-wave dispersion from seismic records accounting for source radiation patterns

Multimode surface-wave dispersion provides critical constraints on crustal and lithospheric velocity structures, with higher modes offering complementary sensitivity to different depth ranges compared to the fundamental mode. However, extracting reliable multimode information from seismic event records remains challenging under realistic observation conditions. Unlike ambient noise wavefields, seismic-event wavefields are strongly influenced by source radiation patterns, wavefront curvature, and complex angular structures, particularly when events occur within or near dense seismic arrays. Consequently, most existing multimode surface-wave methods rely on far-field plane-wave assumptions or azimuthal selection strategies, which limit their applicability for complex source–receiver geometries.

In this study, we propose a unified framework for extracting multimode surface-wave dispersion from seismic records by explicitly accounting for source radiation effects in the wavefield representation. Starting from a polar-coordinate description of the surface-wave displacement field, the wavefield is decomposed into angular components associated with different azimuthal orders, allowing isotropic and anisotropic contributions introduced by double-couple sources to be separated. This angular decomposition enables different Bessel-function components (e.g., zeroth- and higher-order terms) to be treated independently, thereby mitigating modal interference that commonly affects conventional frequency–Bessel approaches.

Furthermore, by exploiting the theoretical equivalence between the polar-coordinate formulation and a two-dimensional spatial Fourier transform, the proposed framework reformulates the conventional Bessel-integral representation into a unified and computationally efficient 2D Fourier-domain implementation. This transformation substantially simplifies the dispersion-spectrum calculation while preserving physical consistency, enabling robust multimode dispersion extraction under arbitrary array geometries without imposing far-field assumptions or azimuthal filtering.

Synthetic experiments and applications to dense-array seismic data demonstrate that the proposed method reliably retrieves both fundamental and higher-mode dispersion over a broad frequency range. The resulting multimode constraints provide improved resolution for seismic imaging of crustal and lithospheric structures, highlighting the potential of the framework for high-resolution studies using modern dense-array deployments.