Constraining Near-Surface Seismic Wave Speed Based on Body-Wave Polarization Analysis

Understanding the seismic responses of cities around the world is essential for the risk assessment of earthquake hazards. One of the important parameters is the elastic structure of the sites, in particular, near-surface seismic wave speed, that influences the level of ground shaking. Many methods have been developed to constrain the elastic structure of the populated sites or urban basins, and here, we introduce a new technique based on analyzing the polarization content or the three-dimensional particle motion of seismic phases arriving at the sites.

Polarization analysis of three-component seismic data was widely used up to about two decades ago, to detect signals and identify different types of seismic arrivals. Today, we have good understanding of the expected polarization direction and ray parameter for seismic wave arrivals that are calculated based on a reference seismic model. The polarization of a given phase is also strongly sensitive to the elastic wave speed immediately beneath the station. This allows us to compare the observed and predicted polarization directions of incoming body waves and infer the near-surface wave speed.

Figure 1: Geometry of the incident, reflected, and observed particle motions for incident (a) P and (b) S waves at a station (triangle). The particle motion or polarization directions are shown by arrows for P (blue), S (red), and apparent direction (purple). The angles θ and θ̄ correspond to the incident and the apparent polarisation directions of the P wave, respectively, measured from the vertical (dashed line). Similarly, the angles ϕ and ϕ̄ correspond to the wavevector directions perpendicular to the particle motions of the incident and the apparent polarisation of S wave, respectively, measured from the vertical.

The relationship between the body-wave polarization and the near-surface wave speeds is derived and it is demonstrated that P-wave polarization direction has no sensitivity to subsurface compressional wave speed but only to shear wave speed. The counter-intuitive reslationship arises from consideration of the reflected waves at the free surface (Figure 1). S-wave polarization direction, on the other hand, is sensitive to both compressional and shear wave speeds. Combining the P- and S- polarization directions measured by principal component analysis, therefore, provides estimates of both P- and S-wave speeds at shallow depths, for example, the top hundred metres. The polarization measurement and the wave speed estimation are computationally efficient, providing tremendous opportunities to study near-surface seismic structures of different parts of the world, some of which may be difficult to obtain using other computationally-intensive approaches such as noise correlation or invasive and expensive approaches such as well logging.

Figure 2: Near-surface Shear Wave Speed estimated using polarization analysis (Left) and measured from well logging (Right). The velocities are in km/s.

This approach is applied to High-Sensitivity Seismograph Network in Japan, where we benchmark the results against the well-log data that are available at most stations. There is a good agreement between our estimates of seismic wave speeds and those from well logs, confirming the efficacy of the new method (Figure 2). In most urban environments, where well logging is not a practical option for measuring the seismic wave speeds, this method can provide a reliable, non-invasive, and computationally inexpensive estimate of near-surface elastic properties.

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