Constraints on Crustal P Wave Structure With Leaking Mode Dispersion Curves

Abstract

Rayleigh and Love wave dispersion curves are known as normal modes and are utilized for inversion. These two waves arrive after the S wave and account for the main energy in all waveforms. However, weaker signals arriving between the P and S waves also have dispersive properties, which are controlled by so-called leaking modes.Studies of leaking mode can be traced back to Somville (1930), who identified and named the PL phase. The PL phase is a train of long-period (>10 s) dispersed waveforms that arrive shortly after the P wave. Oliver and Major (1960) measured PL phase dispersion curves and linked the PL phase with the leaking mode of the crust-mantle waveguide. In addition to the PL phase, some other phases are also considered to have the same wave behavior as the PL phase, which can be explained by the leaking mode (e.g., Pg phase, Shaw & Orcutt, 1984; W phase, Furumura & Kennett, 2018). The leaking mode describes waveguides (leaking waves) whose radiation energy leaks into half-space and phase velocities are higher than the maximum shear velocity (Phinney, 1961). Subsequently, studies have mainly focused on how to calculate leaking modes and simulate leaking waves through leaking modes (e.g., Gilbert, 1964;Haddon, 1984Haddon, , 1986Watson, 1972). However, due to the complexity of leaking modes, limited research has been conducted on imaging underground structures by using the dispersion of leaking waves, and most of the extracted dispersion is below 0.1 Hz for lithospheric research (e.g.,

Multiple Leaking Mode Dispersion Observations and Applications From Ambient Noise Cross‐Correlation in Oklahoma

“…In the Z‐Z theoretical dispersion spectra calculated from the average inverted model, the energies of the Π modes and 1 st Σ mode that correspond to the dispersion of the PL phase are much stronger than those of the other Σ modes, which indicates that only the PL phase dispersion and guided modes can be extracted. Since, the controlling equation of the layered Vp structure dispersion is basically consistent with the controlling function of SH wave dispersion (Li, Shi et al., 2021), in this study, we believe that G1 can be reliably identified.…”

“…Figure 3f exhibits the summation of the absolute values of the sensitivity kernels of normal and leaking modes used in inversion (detailed sensitivity kernels are shown in Figure S5 in Supporting Information S1). Leaking modes exhibits a very complex sensitivity to Vs (which is similar to the sensitivity kernel of PL mode in Li, Shi et al, 2021), while its sensitivity kernels to Vp are similar to those of normal modes. Compared with the normal modes, the leaking modes penetrate to a deeper detection depth, as is also reflected in the convergence of the Vp models obtained from the inversions (Figure 3).…”

“…To better illustrate the relationship of different modes, Figure 4a shows different modes with different colors and the Z-Z (Z-Z indicates a Z-component single force source and a Z-component receiver) theoretical dispersion spectrum for the average inverted model. The calculation method of the theoretical dispersion spectrum can be found in Li, Shi et al (2021). The maximum Vs separates normal modes and leaking modes.…”

“…Recently, by adopting an array-based dispersion extraction method, which is the frequency-Bessel transform (F-J) method, we successfully extracted multimodal leaking mode dispersion curves from earthquake-triggering seismic waves which are recorded between the arrivals of P and S waves (Li, Shi et al, 2021). This method uses a form of integrating product of the 0 th first kind Bessel function 𝐴𝐴 𝐴𝐴0(⋅) and the Green's function G(ω,r) along the epicenter distance (r) to recover the dispersion spectrum 𝐴𝐴 𝐴𝐴(𝜔𝜔𝜔 𝜔𝜔) in the records:…”

Improved High‐Resolution 3D Vs Model of Long Beach, CA: Inversion of Multimodal Dispersion Curves From Ambient Noise of a Dense Array

“…Subsequently, Li, Shi et al. (2021, 2022) verified the application of extracting normal mode and leaking mode dispersion curves by this method on earthquake records and ambient noise cross‐correlations. Currently, short‐period dense seismic arrays have been widely deployed for shallow structure imaging (Ma et al., 2020; Xie et al., 2021).…”