Advances in the research of seismic-wave leaky modes

When seismic waves propagate in layered structures, dispersion phenomena occur. Based on the characteristics of dispersion curves, underground velocity structures can be estimated. Using the surface-wave dispersion curves extracted from seismic records and ambient noise for inversion is an important method to constrain the structures of the near surface and lithosphere. In addition to surface waves, significant progress has been made in the research and application of leaky modes and their dispersion in recent years. Leaky modes can provide constraint information for velocity structure inversion, including P-wave velocity, and can compensate for the shortcomings of surface-wave dispersion inversion, which results in more accurate and comprehensive velocity modeling. However, in comparison to surface waves, the amplitude of leaky waves in seismic records and ambient noise is typically much weaker, which leads to significant challenges for the extraction of leaky modes. Furthermore, the study of leaky modes requires a more intricate theoretical framework and numerical solution techniques, which have historically limited their attention in the scientific community. Over the past decades, the theories of leaky modes have been increasingly improved with the relevant research in seismology, optics, and acoustics, which give rise to effective numerical computation tools. This has laid a solid foundation for the practical application of leaky modes. With the increase of high-quality, high-density observational data and advancements in data processing techniques, geoscientists have successfully extracted leaky mode information from various types of data, including natural and artificial earthquakes, as well as ambient noise. This has led to the development of velocity structure imaging methods based on leaky modes. Currently, this imaging approach has been successfully applied in velocity modeling for earthquakes, ambient noise, and exploration seismology, which indicates promising potential for further utilization. In this review, we begin by introducing the theories and numerical methods of leaky modes. We further elaborate on the significance of leaky modes in velocity modeling from a sensitivity perspective. Subsequently, we review several representative studies to highlight the significant advancements in observation and analyze several proposed inversion techniques. Finally, we delve into the critical issues surrounding the use of leaky modes in seismic imaging.