Adjoint-state surface wave traveltime tomography: theoretical development and applications

• Main Author: Hao, Shijie
• Other Authors: Tong Ping
• Format: Thesis-Doctor of Philosophy
• Language: English
• Published: Nanyang Technological University 2025
• Subjects: Mathematical Sciences; Surface wave; Tomography; Seismic anisotropy
• Online Access: https://hdl.handle.net/10356/182247
• Institution: Nanyang Technological University

Surface wave traveltime tomography is a routine technique for investigating crustal and upper mantle structure. The key step in inversion is the forward modeling of traveltime using a shear wave velocity and azimuthal anisotropy model. An efficient method to conduct forward modeling is to separate it into two steps: first, model a phase velocity map from the body wave velocity model; second, model the phase traveltime between sources and receivers. In previous studies, the second step is usually conducted based on assumptions about surface wave propagation, such as assuming surface waves propagate along the great circle path between the source and receiver or using the propagation path in an isotropic velocity model for the inversion of an anisotropic model. In addition, the effects of topographic variation are also often ignored. These simplifications are not always reasonable, especially in complex media, and can lead to unreliable features in the tomographic model. In this thesis, I aim to develop a surface wave traveltime tomography method that models traveltimes more accurately while maintaining high computational efficiency. This method employs an elliptically anisotropic eikonal equation to model Rayleigh wave phase traveltimes, taking into account the heterogeneity of velocity and anisotropy, as well as topographic variation. We define an objective function based on traveltime residuals across all frequencies, and derive the sensitivity kernel of this objective function with respect to body wave velocity and anisotropy using the adjoint-state method. This approach enables the direct inversion of a 3D anisotropic shear wave velocity model. This technique is applied to the island of Hawaii to invert for a shear wave velocity model of the upper crust. Our model reveals seismic anomalies that are consistent with major geological units. Specifically, a high-velocity anomaly to the South of Hualalai's summit is detected, which may be associated with a buried rift zone. Furthermore, it is demonstrated that on the island of Hawaii, the incorporation of topographic variation can result in corrections in shear wave velocity model, with amplitude up to 0.8 %. Another case study is conducted in the western United States to invert Rayleigh wave phase traveltime for a shear wave velocity and azimuthal anisotropy model of the crust and upper mantle. The results are consistent with known geological features and major previous anisotropy models. Additionally, in the shallow crust near California, fast velocity directions parallel to SHmax are observed, which may indicate that the stress is the primary cause of the azimuthal anisotropy in this region.