Eikonal equation-based adjoint-state surface wave traveltime tomography: methodology and application

Abstract

With the deployment of numerous dense seismic arrays, there is a wealth of surface-wave dispersion data available that offers valuable support to investigate near-surface structures. Efficient and accurate imaging using these massive dispersion data is a critical topic in seismology. Aside the conventional two-step procedures, the recent one-step approaches need to store the sensitivity matrices which is typically memory-intensive and dependent on the number of station pairs and measurement periods. To address this difficulty, we propose to apply the adjoint state method to calculate the gradient of the objective function for ambient noise surface wave data. This innovative technique avoids cumbersome ray path generation and the heavy memory requirements of the sensitivity matrices. The proposed 3-D gradient consists of two parts: first part is the gradient of the objective function associated with the phase speed in the horizontal plane, and it is calculated by back-propagating the phase traveltime residuals between the observed and synthetic data, in which the synthetic phase traveltime is generated by solving 2-D eikonal equation with fast sweeping method through the phase speed map, and point-wise phase speed is calculated with the corresponding local 1-D model beneath each geographical location. Second part is 3-D phase speed sensitivity kernel with respect to the model parameters at each period, which is arranged by point-wise sensitivity kernel of local 1-D model. Finally a comprehensive 3-D gradient is assembled by summing up over all virtual sources and all periods. We validate the effectiveness and accuracy of the proposed method through theoretical model inversion and field data study conducted in the Grane area of the North Sea. The introduced approach represents an advancement in ambient noise tomography from dense seismic arrays, which offers a promising tool for further exploration in surface wave inversion.