Topography-Incorporated Adjoint-State Surface Wave Traveltime Tomography: Method and a Case Study in Hawaii

In this study we recast surface wave traveltime tomography as an inverse problem constrained by an eikonal equation and solve it using the efficient adjoint-state method. Specifically, recognizing that large topographic variations and high surface wave frequencies can make the topographic effect too significant to ignore, we employ an elliptically anisotropic eikonal equation to describe the traveltime fields of surface waves on undulated topography. The sensitivity kernel of the traveltime objective function with respect to shear wave velocity is derived using the adjoint-state method. As a result, the newly developed method is inherently applicable to any study regions, whether with or without significant topographic variations. Hawaii is one of the most seismically and magmatically active regions. However, its significant topographic variations have made it less accurate to investigate using conventional surface wave traveltime tomography methods. To tackle this problem, we applied our new method to invert ambient noise Rayleigh wave phase traveltimes and construct a 3D shear wave velocity model. Our results reveal features that are consistent with geological structures and previous tomography results, including high velocities below Mauna Loa Volcano and Kilauea Volcano, and low velocities beneath the Hilina Fault Zone. Additionally, our model reveals a high-velocity anomaly to the South of Hualalai's summit, which may be related to a buried rift zone. Our findings further demonstrate that including topography can lead to a correction of up to 0.8% in the shear wave velocity model of Hawaii, an island spanning approximately 100 km with volcanoes reaching elevations exceeding 4 km. Surface wave traveltime tomography is a commonly used technique for constructing subsurface shear wave velocity models based on surface wave traveltime measurements, which has been widely used to investigate the structures of the crust and upper mantle. The accuracy of tomography relies on effective forward modeling, that is, computing traveltime fields in a given velocity model. In this study, we employ an elliptically anisotropic eikonal equation to model the traveltime fields of surface waves on undulated topography, ensuring precise forward modeling in regions with significant topographic variations. The inversion of surface wave traveltimes is formulated as an optimization problem constrained by this elliptically anisotropic eikonal equation, which is solved using the efficient adjoint-state method. We have applied the new tomography method to the Island of Hawaii. High shear wave velocities are revealed beneath the summits and rift zones of Mauna Loa Volcano and Kilauea Volcano, outlining the subsurface structures associated with magma storage and transportation. An elliptically anisotropic eikonal equation is used to model the traveltime fields of surface waves on an undulated topographyAn adjoint-state surface wave tomography method based on the anisotropic eikonal equation is developed to determine shear wave velocityThe case study in Hawaii suggests limited topography influence on velocity anomaly amplitudes in regions comparable or larger than Hawaii