Adjoint-State Traveltime Tomography: Eikonal Equation-Based Methods and Application to the Anza Area in Southern California

Publication type

Journal Article

Research Area



Ray tracing is avoidable in seismic traveltime tomography. In this study, seismic traveltime tomography is reformulated as an eikonal equation-constrained optimization problem solved by the ray-free adjoint-state method. The resultant approach is called adjoint-state traveltime tomography. For completeness, an eikonal equation-based earthquake location method is developed to locate the hypocenters of earthquakes when necessary. The multiple-grid model parameterization is adopted to discretize the relative slowness perturbation urn:x-wiley:21699313:media:jgrb54900:jgrb54900-math-0001. The step-size-controlled gradient descent method, which has an effect of damping regularization, is used to find optimal earthquake hypocenters and velocity models. The performances of the earthquake location and adjoint-state traveltime tomography methods are tested in the source area of the 2020 Mw 4.9 Anza earthquake, a seismologically active place in southern California. The obtained high-resolution P-wave velocity model demonstrates that the 2020 Mw 4.9 Anza earthquake and other historic moderate-sized Anza earthquakes occurred near or at the boundaries of low VP rocks, a typical seismogenic environment for moderate to large crustal earthquakes. Meanwhile, the source zone of the Anza earthquakes is characterized by high VP/VS, indicating the possible existence of crustal fluids as well as the critical role of fluids in the occurrence of those moderated-sized Anza earthquakes. On the whole, the well-performed eikonal equation-based earthquake location method and adjoint-state traveltime tomography method provide competent and attractive tools for hypocenter and tomographic inversions.



Ping Tong

Publication Details


Journal of Geophysical Research: Solid Earth



Date Published



Article Number

Article number: e2021JB021818

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