A Review on the Wave Gradiometry Method and Applications to Image the 3D Shear Wave Velocity, Anisotropy and Attenuation of the Lithosphere and Asthenosphere

The Wave Gradiometry Method(WGM) has emerged as a powerful multipurpose tool to  extract strain and rotation tensor, identify phases, and most importantly to image the near surface or deep structure. The WGM measures the spatial gradients of the wavefield within a subarray to extract 4 major attributes: phase velocity, wave directionality, geometrical spreading and radiation pattern. These attributes can be further used to extract strain and rotation tensor (Langston and Liang CT, 2008; Sollberger et al. 2016) and structural information. An azimuth-dependent dispersion curve inversion (ADDCI, Liang et al. 2020) is applied together with the WGM method to extract both 3D shear wave velocity and 3D azimuthal anisotropy. Additionally, the geometrical spreading extracted by the WGM is used to find the attenuation of the materials. In this study, we review the theoretical foundation, technical development, major applications of the WGM and compare the WGM with other major array-based imaging method.

 Similar with the Ambient Noise tomography, the WGM is also boiled down to dispersion curve inversion. Even though it can be applied to arrays with a wide range of scales, here we concentrate on the applications to large scale arrays such as the USARRAY (average spacing of 70km), CHINARRAY (average spacing of 40km). It may also be applied to any other dense regional array, such as the ALPARRAY and others. The imaging depth is only limited by the corner frequency of the seismometer. We will compare our results with that from other techniques to highlight its advantage and disadvantages.

References：

Cao F H, Liang C T. 2022, 3D velocity and anisotropy of the southeastern Tibetan plateau extracted by joint inversion of wave gradiometry, ambient noise, and receiver function, Tectonophysics, https://doi.org/10.1016/j.tecto.2022.229690

Cao, F., Liang, C., Zhou, L., & Zhu, J. (2020). Seismic azimuthal anisotropy for the southeastern Tibetan Plateau extracted by Wave Gradiometry analysis. Journal of Geophysical Research: Solid Earth, 124, e2019JB018395.  https://doi.org/10.1029/2019JB018395

Liang, C., Liu, Z., Hua, Q., Wang, L., Jiang, N., & Wu, J. (2020). The 3D seismic azimuthal anisotropies and velocities in the eastern Tibetan Plateau extracted by an azimuth‐dependent dispersion curve inversion method. Tectonics, 39, e2019TC005747. https://doi.org/10.1029/2019TC005747 

Langston, C. A. (2007). Wave gradiometry in two dimensions. Bulletin of the Seismological Society of America, 97(2), 401–416. https://doi.org/10.1785/0120060138 

Porter R, Liu YY, and Holt WE (2016). Lithospheric Records of Orogeny within the Continental U.S.. Geophysical Research Letters, 43(1), 144–153. https://doi.org/10.1002/2015GL066950

Sollberger D Schmelzbach C, Manukyan E, Greenhalgh SA, Van Renterghem C and Robertsson JOA (2019). Accounting for receiver perturbations in seismic wavefield gradiometry. Geophysical Journal International, 218(3), 1748–1760. https://doi.org/10.1093/gji/ggz258.