We present a seismic model of the African Plate, made with the technique of full-waveform inversion. The purpose of our model is to become a foundation for future use and research, such as quantitative geodynamic interpretations, earthquake-induced ground motion predictions, and earthquake source inversion. Starting from the first-generation Collaborative Seismic Earth Model (CSEM), we invert seismograms filtered to a minimum period of 35 s and compute gradients of the misfit function with respect to the model parameters using the adjoint state method. In contrast to the conventional FWI approach, we use dynamically changing data subsets (mini-batches) of the complete dataset to compute approximate gradients at each iteration. This approach has three significant advantages: (1) it reduces computational costs for model updates and the inversion, (2) it enables the use of larger datasets without increasing iteration costs, and (3) it makes it trivial to assimilate new data since we can add it to the complete dataset without changing the misfit function, thereby enabling “evolutionary FWI". We perform 130 mini-batch iterations and invert data from 397 unique earthquakes and 184,356 unique source-receiver pairs at the cost of approximately 10 full-data iterations. We clearly image tectonic features such as the Afar triple junction. Particularly interesting are the low-velocity zones below the Hoggar, Aïr, and Tibesti Mountains, pronounced more than in earlier works. Finally, we introduce a new strategy to assess model uncertainty. We deliberately perturb the final model, perform additional mini-batch iterations, and compare the result with the original final model. This test uses actual seismic data instead of artificially generated synthetic data and requires no assumptions about the linearity of the inverse problem.

Ultrasound Computer Tomography (USCT) is an emerging technique for breast cancer screening. Ultrasonic waves are propagated through the tissue and recorded by a set of transducers that are surrounding the breast. The experiment collects transmission and reflection data, which are used to obtain quantitative images of acoustic properties of the tissue (see Figure). This information is useful to characterize the breast tissue, and improves the specificity of standard imaging modalities. However, providing a diagnostic tool with high accuracy and clinically affordable time-to-solution (goal: ~15 min/patient) still remains a challenge. The goal of this work is to show that, despite the vast scale differences, experiments in seismology and USCT share many similarities. In both fields, the relative wave speed variations are comparable and the number of propagated wavelengths in the domain has the same order of magnitude. Because the wave equation is scale invariant, the cross-fertilization between both fields will benefit imaging methods on all scales. In this study, we present methods from seismic tomography that we have recently introduced to USCT: 1) We employ a linearized finite-frequency traveltime tomography approach for speed-of-sound reconstruction. Using the cross-correlation traveltime misfit functional, we compute analytically the sensitivity kernels using adjoint techniques. Our method can operate almost in real time while still including finite-frequency effects. It also can retrieve useful 3D information from 2D acquisition systems. 2) Similar to exploration geophysics, both speed-of-sound and reflectivity images are important for the interpretation. Here, we suggest a framework that combines full-waveform inversion for speed-of-sound and reverse time migration for reflectivity. 3) We apply the Sequential Optimal Experimental Design (SOED) method to optimize the position and number of transducers, in terms of accuracy and cost, to image both reflection and transmission information. Using the Bayesian approach, we define the quality of a design as the average of the posterior variances of the parameters. SOED provides cost-benefit curves that quantifies the information gain versus the computational cost. These are useful to control the trade-off between accuracy and practicality.