Adjoint-state traveltime tomography: A new modality of seismic imaging

We have witnessed a transit of seismic tomography from ray-based traveltime inversion to wave equation-based waveform inversion during the past two decades. As is widely known, full waveform inversion outperforms traveltime tomography in resolving velocity variations with dimensions comparable and smaller than the dominant wavelength. However, this may not be always true in real practice, mainly due to the presence of unknown data noise, the lack of accurate initial models for the iterative inversion process (including material properties and source mechanisms), and the high demand for computational resources. Further efforts are required to develop techniques for using full waveform contents in seismic imaging studies, especially for the use of high-frequency waveform data (>1 Hz on regional scales). We have attempted to use common-source double-difference traveltime data in wave equation-based adjoint tomography studies of subsurface structures beneath Northeast Japan and Alaska. Because of the high level of waveform similarity, reliable common-source double-difference traveltime data at neighboring seismic stations are measured via cross-correlation approach. Insightful results are obtained. However, it is still computationally prohibitive to model high-frequency data by solving 3-D wave equations, limiting the resolution of seismic images. We admit that there is still a long way to go for the possible wide application of high-frequency full waveform inversion.

Traveltime is the most reliable information that can be extracted from raw seismological recordings.  We have developed a new modality of seismic imaging, called adjoint-state traveltime tomography, to unleash the full potential of traveltime in imaging subsurface structures. To avoid potential failure of ray tracing in 3D complex media, isotropic eikonal equation and anisotropic eikonal equations are used to model seismic traveltime field in heterogenous and anisotropic media, and the associated inverse problems are solved by the efficient adjoint state method. No ray tracing is required for the novel adjoint-state traveltime tomography method. Importantly, the sensitivities of traveltime-related objective functions to material parameters can be accurately measured even in complex media. We view adjoint-state traveltime tomography as a new framework for seismic tomography, as it naturally implements various body wave and surface wave tomographic inversions in a very similar way. Good performances of the adjoint-state traveltime tomography method will be reported via various case studies in regions with typically different tectonic settings. It is worth noting that an accompanying software package, TomoATT, is under development.