Full 3D Waveform Tomography: A Comparison Between the Scattering-Integral and Adjoint- Wavefield Methods

We analyze the computational issues of full 3D tomography, in which the starting model as well as the model perturbation is three-dimensional and the sensitivity (Fréchet) kernels are calculated using the full physics of three-dimensional wave propagation. We compare two formulations of the structural inverse problem: the adjoint-wavefield (AW) method, which time-reverses the data from the receivers to image the structure, and the scattering-integral (SI) method, which sets up the inverse problem by calculating and storing the Fréchet kernels for each data functional. The two inversion methods are closely related, but which one is more efficient depends on the overall problem geometry, particularly on the ratio of sources to receivers, as well as trade-offs in computational resources, such as the relative costs of compute cycles to data storage. We find that the SI method has significant computational advantages over the AW method in regional waveform tomography using large sets of natural sources recorded by the Southern California Seismic Network.