Membrane Wave Equation-Based Ambient Noise Adjoint Tomography: Verification and Application

Traditional ambient noise tomography contains two steps: (1) inverting the 2D phase and/or group velocity maps at different periods based on the dispersion curves of each station pair and (2) point-wise inversion to obtain 1D shear wave velocity model at each grid node and then gather together to obtain a 3D velocity model. In the first step, most studies use the travel-time tomography method based on ray theory or 2D finite-frequency sensitivity kernel that assumes the surface wave travels along the great circle path. This could introduce travel-time biases when surface wave propagates away from the great circle in complex media and further affect the imaging results.

To consider the ray bending effect and the finite-frequency effect simultaneously and to balance the computational efficiency and accuracy, we consider modeling the propagation of surface wave by solving the 2-D membrane wave equation. Sensitivity kernels with respect to phase velocity are constructed using the adjoint method, which could capture significant deviation of the ray path from the great circle path when the velocity perturbation is larger than 20%. Checkerboard tests have been applied to demonstrate the effectiveness of the new tomography method, compared with the finite-frequency tomography method based on analytical solutions. We test our method with ambient noise data in Southern California.